Determination of best fit model for the distribution and crop loss associated with Bacterial 
wilt of tomatoes 

 

 

 

Ogeya Fredrick Odoyo 

 

Master of Science 

(Research Methods) 

 

 

 

 

 

 

A dissertation submitted to the Department of Horticulture in the Faculty of Agriculture in 
partial fulfillment of the requirements for the award of the degree of Masters of Science in 
Research Methods of the Jomo Kenyatta University of Agriculture and Technology 

 

 

 

 

 

 

 

 

 

 

 

2016 


DECLARATION 

This dissertation is my original work and has not been submitted to any other University for 
examination. 

 

Signature ……………………………………. Date …………………………. 
Ogeya Fredrick Odoyo Registration Number: AG332-1930/2014 

 

DECLARATION BY SUPERVISORS 

This dissertation has been submitted for examination with our approval as Supervisors: 

 

Signature ………………………………………………… Date ………………………… 

Prof. Losenge Turoop, Department of Horticulture, Jomo Kenyatta University of Agriculture 
and Technology 

 

Signature ………………………………………………… Date ………………………… 

Dr. Washingon Otieno, Plantwise Programme Executive, CAB International 

CABI, Kenya 

 

Signature ………………………………………………… Date ………………………… 

Dr. Joseph Kyalo Mung'atu, Department of Statistics and Actuarial Science, Jomo Kenyatta 
University of Agriculture and Technology 

 

 


DEDICATION 

To all who inspired me to treasure education. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


ACKNOWLEDGEMENTS 

I profoundly acknowledge all those who have been very influential in my studies especially my 
supervisors; Professor Turoop Losenge, Department of Horticulture, Jomo Kenyatta University 
of Agriculture and technology, Dr. Kyalo Mung'atu, Department of Statistics and Actuarial 
Science, Jomo Kenyatta University of Agriculture and technology, and Dr. Washington Otieno, 
Plantwise Programme Executive, CABI for their diligent guidance, support and encouragement. I 
register special thanks to Dr. Adimo Ochieng', of Jomo Kenyatta University of Agriculture and 
technology for his exceptional assistance in GIS. 

I express my sincere gratitude to Eastern Africa Agricultural Productivity Project (EAAPP), who 
financed my postgraduate education. I extend special appreciation to Mr. Morris Akiri; the 
Regional Director CABI Africa, for giving me the opportunity of being attached to CABI during 
my study period where I gained valuable experience of work and research. I would also like to 
thank all Plant wise programme staff members at CABI especially Dr. Mary_Lucy Oronje and 
Mr. Willis Ochilo who went out their way to mentor me. Appreciation to you all for your 
contribution and now look at research in a more pragmatic way. 

I am very grateful for CABI for allowing the use of Plantwise data and awhere API services for 
enabling me to assess their programmatic weather data through the their platform that is 
available for organizations and individual to access the rich data library. Finally, much gratitude 
to all my MSc. Colleagues for the many brainstorming sessions we had from the onset of 
research, you made my work easier. 

 

 

 

 

 


Table of Contents 
DECLARATION .............................................................................................................................................. ii 
DEDICATION................................................................................................................................................ iii 
ACKNOWLEDGEMENTS ............................................................................................................................... iv 
LIST OF TABLES ........................................................................................................................................... ix 
LIST OF FIGURES .......................................................................................................................................... x 
LIST OF ACRONYMS .................................................................................................................................... xi 
ABSTRACT .................................................................................................................................................. xii 
CHAPTER 1 ................................................................................................................................................... 1 
INTRODUCTION ........................................................................................................................................... 1 
1.1 Overview and purpose of the study ..................................................................................................... 1 
1.2 Background information of the study ................................................................................................. 1 
1.3 Statement of the problem .................................................................................................................... 4 
1.4 Objectives of the Study ....................................................................................................................... 5 
1.4.1 General Objective ........................................................................................................................ 5 
1.4.2 Specific Objectives ...................................................................................................................... 5 
1.5 Research question ............................................................................................................................... 5 
1.6 Justification of the study ..................................................................................................................... 6 
1.7 Scope of the study ............................................................................................................................... 6 
1.8 Assumptions made in the study .......................................................................................................... 7 
CHAPTER 2 ................................................................................................................................................... 8 
LITERATURE REVIEW ................................................................................................................................... 8 
2.1 Tomato production .............................................................................................................................. 8 
2.2 Constraints to tomato production ........................................................................................................ 8 
2.3 Control of bacterial wilt ...................................................................................................................... 9 
2.4 Overview of the Logistic models ........................................................................................................ 9 
2.5 Binary data and the use of linear regression ..................................................................................... 10 
2.5.1 Conceptual problem ................................................................................................................... 10 
2.5.2 Probabilistic problem ................................................................................................................. 12 
2.6 Some studies which applied logistic models ..................................................................................... 13 
2.7 Over dispersion and under dispersion of model parameters ........................................................... 14 
2.8 Over parameterization of the logistic model ..................................................................................... 14 
2.9 Orthogonal effect of data .................................................................................................................. 14 
2.10 Diagnostics of the fit of model ........................................................................................................ 15 
2.10.1 Residuals and Deviance ........................................................................................................... 15 
2.11 Logistic Regression Transformation ............................................................................................... 15 
2.11.1 Logarithmic transformation ..................................................................................................... 15 
2.11.2 The Logit (Logged Odds) ........................................................................................................ 15 
2.12 Interpretation of logistic regression parameters .............................................................................. 16 
2.12.1 Interpretation in terms of logged odds (logit) .......................................................................... 16 
2.12.2 Interpretation in terms of odds ................................................................................................. 17 
2.12.3 Interpretation in terms of Odds Ratio....................................................................................... 17 
CHAPTER 3 ................................................................................................................................................. 18 
MATERIALS AND METHODS ....................................................................................................................... 18 
3.1 Study Area ....................................................................................................................................... 18 
3.2 Study design and data collection ....................................................................................................... 18 
3.3 Distribution of bacterial wilt in the counties. .................................................................................... 19 
3.4 Modeling distribution of bacterial wilt ............................................................................................. 19 
3.4.1 Selection of logistic models for distribution of bacterial wilt of tomato.................................... 20 
3.5 Crop losses Assessment .................................................................................................................... 21 
3.6 Data and analysis .............................................................................................................................. 23 
CHAPTER FOUR .......................................................................................................................................... 24 
RESEARCH FINDINGS ................................................................................................................................. 24 
4.1 Distribution of Bacterial wilt in thirteen counties in Kenya ............................................................. 24 
4.1.1 Proportion of bacterial wilt incidents in clinic queries by county .............................................. 24 
4.2.1 Trend of cases of bacterial wilt reported to plant clinics ........................................................... 25 
4.2 Modeling the distribution of bacterial wilt using the logistic models ............................................... 26 
4.2.1 Normality assumption and exploratory analysis for weather data from January to December.. 26 
4.2.2 Results of model 1, 2 and 3 on z-statistic with appended likelihood ratio p-values .................. 29 
4.2.2.1 Model 1 .................................................................................................................................. 29 
4.2.2.2 Model 2 .................................................................................................................................. 30 
4.2.3.3 Model 3 .................................................................................................................................. 31 
4.2.3 Re-fitted model adjusted for over parameterization ................................................................... 33 
4.2.4.1 Refitting of models.................................................................................................................. 34 
4.3 Poisson Model for the assessment of reported crop loss due to bacterial wilt .................................. 35 
4.3.1 Model 4 ..................................................................................................................................... 35 
4.3.2 Model 5 ..................................................................................................................................... 37 
CHAPTER FIVE ............................................................................................................................................ 39 
DISCUSSION OF RESULTS ............................................................................................................................ 39 
5.1 Interpretation of the fitted binary logistic models ............................................................................. 39 
5.1.1 Model 1 ..................................................................................................................................... 39 
5.1.3 Model 2 ..................................................................................................................................... 40 
5.1.4 Model 3 ..................................................................................................................................... 41 
5.2 Interpretation of the fitted poisson models........................................................................................ 42 
CHAPTER SIX .............................................................................................................................................. 44 
CONCLUSIONS AND RECOMMENDATIONS ............................................................................................... 44 
6.1 Introduction ...................................................................................................................................... 44 
6.2 Conclusion ....................................................................................................................................... 44 
6.3 Recommendation .............................................................................................................................. 45 
REFERENCE ................................................................................................................................................. 46 
APPENDICES ............................................................................................................................................... 53 
Appendix 1: Data exploration using box plot for weather data .............................................................. 53 
Appendix 2: Modeling the incidence of bacterial wilt ............................................................................ 54 
Appendix 3: Selected R codes ................................................................................................................ 55 


 

 

 

 

 

 

 

 

 

 

 


LIST OF TABLES 

Table 1: Summarized data on reported cases of bacterial wilt presented relative to crop 
development stage ................................................................................................................. 25 
Table 2: Parameter estimates of the logistic regression model used to explain the incidence of 
bacterial wilt using weather parameters and development stage of infestation .................... 30 
Table 3: Parameter estimates of the logistic regression model used to explain the incidence of 
bacterial wilt by using weather parameters ........................................................................... 31 
Table 4: Parameter estimates of the logistic regression model used to explain the incidence of 
bacterial wilt in relation to agro-ecological zones and crop development stage ................... 32 
Table 5: Model 1a, 2a and 3a output are refitted models after readjusting for over 
parameterization to improve estimation of bacterial wilt incidence ...................................... 34 
Table 6: Parameter estimates of the Poisson regression model of disease prevalence as relates to 
weather and crop development stage ..................................................................................... 36 
Table 7: Parameter estimates of the Poisson regression model on disease prevalence in relation to 
agro-ecological zones and crop loss as reported by farmers ................................................. 37 


 

 

 

 

 


LIST OF FIGURES 

Figure 1: Reported cases of bacterial wilt of tomato at the plant clinics in thirteen counties in 
Kenya .................................................................................................................................... 24 
Figure 2: Bacterial wilt incident cases reported by farmers to the plant clinics over time ........... 26 
Figure 3:Paired box plot of monthly minimum and maximum temperatures (oC) from January to 
December ............................................................................................................................... 27 
Figure 4: Paired box plot of monthly minimum and maximum relative humidity (%) from 
January to December ............................................................................................................. 28 
Figure 5: Paired box plot of monthly and daily precipitation (mm) from January to December . 28 


 

 

 

 

 

 

 

 

 

 

 


LIST OF ACRONYMS 

AC Area of one plant of tomato 

AIC Akaike Information Criterion 

ANOVA Analysis of Variance 

BW Bacterial Wilt 

CL Crop loss 

Exp Exponential 

GLM Generalized Linear Model 

HL Hosmer and Lemshow 

IC Infected crops 

LA Available land in acres for crop 

LL Log-likelihood 

ML Maximum Likelihood 

OLS Ordinary Least Square 

PDF Probability Density Function 

POMS Plant wise Online Management System 

TC Total crops in the farm, 

 

 

 

 


ABSTRACT 

Tomato is the second leading crop in Kenya in terms of production and value after potato. It is 
widely used as vegetable across the world. However, tomato varieties are attacked by bacterial 
wilt which devastates farmers. The bacterium is soil borne and persists in contaminated soils. It 
can be vector transmitted and has wide host’s range of over 50 plant species making it difficult to 
control. Bacterial wilt attack on tomato farm results to losses of more than 90%. Its manifestation 
changes with varying conditions and farm management practices. Bacterial wilt infects roots and 
stems of many plants that are considered alternative hosts. This enables it to continue spreading 
across the tomato growing regions. The study used logistic model to determine the distribution, 
of bacterial wilt. 

The study used secondary data obtained from the plant clinics on reported cases of bacterial wilt. 
In this study, disease incidents and distribution were inferred from cases presented by farmers to 
plant clinics. The response variables used were presence of bacterial wilt and estimated crop loss 
in the farm. The explanatory variables used in the model were weather data (minimum daily 
temperature, maximum daily temperature, minimum relative humidity, maximum relative 
humidity and precipitation), development stage of tomato and agro ecological zones (AEZ). Data 
from the year 2012 to 2013 obtained from Plantwise Online Management System (POMS) on 
tomato crop was used. R-Statistical Programming Package was used for the logistic analysis. 

The results showed that relative humidity and minimum temperature significantly influenced 
bacterial wilt incidence and distribution as inferred from cases presented by farmer to plant 
clinics. In the analysis, agro-ecological zones, LH2, LM3, LM4, LM7, UM2 and UM4 
significantly influence tomato losses in the farm due to attack by bacterial wilt. In the AEZ, the 
coefficient estimates are positive showing an increase in the bacterial wilt incidents. The disease 
incidents as presented cases brought to clinics by farmers varied in each county. Kirinyaga 
showed the highest incidents of the disease followed by Nakuru and Embu at 20.6%, 20.2% and 
19.1% respectively. Bacterial wilt was found to be present in all the counties irrespective of 
difference in AEZ. 

 


CHAPTER 1 

INTRODUCTION 

1.1 Overview and purpose of the study 

The study aimed at using binary logistic model tool for estimating the bacterial wilt incidence and 
distribution among the tomato farmers in Kenya. In this study the disease incidence and distribution as 
presented was inferred from cases of crop anomalies brought to plant clinics by farmers. The study 
borrowed binary logistic application in health sector, education, social science and mathematics to 
enrich this study of determining best fit model for the distribution and crop loss associated with 
Bacterial wilt of tomatoes. In this study, I reviewed the state of bacterial wilt incidence and 
distribution. The problem of analyzing binary data collected in surveys and the need of logistic model 
is also presented. In chapter two, previous studies that applied binary logistic models and techniques 
used in parameter estimation are reviewed. Limitations of ordinary least square approaches in data 
analysis in the context of binary response data are also discussed. Chapter 3 gives details on the source 
of data used in this study. Logistic model results and discussions are presented in chapter 4. In chapter 
5, conclusions on the application of binary logistic models and recommendations are discussed. 

1.2 Background information of the study 

Globally, the trends in food production has been on a decline due to the incidences of pest and diseases 
which are causing around 800 million people to lack enough food and at least 10% of food produced is 
lost to diseases (Strange & Scott, 2005). 

Incidence of pests and diseases have contributed significantly to the reduction in food production in 
most agricultural regions (Oerke, 2006) and diseases are major problems for small scale farmers in the 
production of tomatoes and other crops (Yadessa, Bruggen, & Ocho, 2010). Tomato is the second 
leading crop in Kenya in terms of production and value after potato (Geoffrey, Hillary, Antony, 
Mariam, & Mary, 2014). It is widely used as vegetable across the world (Wani, 2011). 

In Kenya, tomato is majorly grown in the open field, but use of greenhouses has been adopted in the 
recent past in most regions (Geoffrey et al., 2014). The protected production in greenhouses is 
essential for continuous production of tomato even during the adverse weather condition, though it can 


act as optimal condition for rapid multiplication of many pathogens (Buschermohle & Grandle, 2012). 
The incidences of pest and diseases in greenhouse production are a major problem in tomato growing 
counties in Kenya viz Kiambu, Kajiado, Laikipia and Kirinyaga, (KARI, 2005). 

In most cases poor practices in the farm such as hygiene, irrigation methods, continuous farming and 
cultural practices lead to increase in the incidence of pests and diseases in the farms (Abawi & 
Widmer, 2000). Among the diseases, bacteria wilt is a disease of economic importance in tomato 
production in the tropics (Lebeau et al., 2011) and a major constraint to tomato production ( Hayward, 
1991). 

Bacterial wilt caused by Ralstonia solanacearum formerly known as Pseudomonas solanacearum 
affects all varieties of tomato (Afroz et al., 2009). The bacterium is soil borne and persists in 
contaminated soils and can be vector transmitted (Wani, 2011). It has a wide host’s range of over 50 
plant species (Maji & Chakrabartty, 2014). The pathogen is difficult to control and devastates farmers 
as it can cause losses of more than 90% when it infests tomatoes (Ajanga, 1987). Though it is 
persistent and resistant to most available control measures, its manifestation changes with varying 
conditions and management practices (Prior, Bart, Leclercq, Darrasse, & Anais, 1996). The use of 
disease free seedling is reported to delay disease onset and subsequent severity (Miller & Crosier, 
2015). According to Chen et al. (2009), inducing resistance through gene silencing is reported to 
control bacterial wilt in tomato. Nutritional soil amendment with silicon is also known to control 
bacterial wilt in tomato (Ayana et al., 2011). However, continuous use of silicon in disease 
management will results into low soil pH which negatively affect crop production (Ogbodo, 2013). 
Despite the cultural management practices such as use of organic matter, control of bacterial wilt is 
still a challenge to farmers in the tropics. 

Ralstonia Solanacearum can infect roots and stems of many plants which are considered as alternative 
hosts (Wenneker et al., 1999). This enables it to continue spreading across the tomato growing regions. 
The interaction of various environmental factors such as weather (temperature and rainfall), soil type 
and tillage practices determine the infection, distribution and survival of the pathogen. In order to 
understand the contributions and interactions of these factors the use of models is important. 


Currently, the field of plant pathology embraces the use of statistical models to estimate the 
relationship between disease components to a number of environmental farm practices and host factors 
(Contreras-Medina, 2009). Various models are applied in understanding disease dynamics in crops. 
These models are useful for predicting diseases progression, development, distribution and epidemics 
(Calonnec, Cartolaro, & Chadoeuf, 2009). Linear regression models, multiple regression models and 
non-linear regression are commonly used in understanding disease epidemics. 

Linear models are used in continuous data in sectors such as agriculture and social sciences (Wagner, 
2013). They help in studying the relationship between the dependent variable and independent 
variable(s) (Wagner, 2013). In situations where the response variable is binary, it is extended to 
generalized linear model (GLM) which is efficient for nonlinear covariates (Hastie & Tibshirani, 
1990). Binary response variable does not give a direct interpretation of the parameters as in the case of 
linear model since in binary the response estimate lies between 0 and 1. When linear regression model 
is used in a dichotomous (binary) dependent variable, linearity assumptions: homoscedasticity, zero 
mean and independent error terms are violated (Poole & O’Farrell, 1970), therefore logistic model is 
useful for the binary response (Haberman & Sinharay, 2010). 

Logistic regression models were proposed for the first time in 1970s as the alternative technique used 
to model categorical response variable against other explanatory variables (Peng & Harry, 2002). The 
technique has been widely used in the fields of health sector in disease epidemiology, education and 
mathematics. Logistic model is efficient and gives various ways of coefficient interpretation and 
parameter estimation which are more intuitive (Babtain, 2015) and its efficiency in estimating 
probabilities, odds and odds ratios (Hosmer & Lemeshow, 1997). Since this study has a dichotomous 
response variable it suffices as the probability estimates lies between 0 and 1. 

In an experimental design study, most cases the treatments are unbalanced and this results into 
inaccurate findings. However, logistic models are widely applied in unbalanced data and accurate 
estimates are obtained (Cnaan, Laird, & Slasor, 1997). However, application of binary logistic model 
has not been used to study distribution of diseases in various regions presumably due to difficulties in 
obtaining adequate data (Mila, Carriquiry, & Yang, 2004). 


Understanding the distribution of bacterial wilt (BW) and crop loss associated with it helps in 
establishing appropriate measures and methods of managing the disease. Binary logistic model is the 
best model for estimating diseases occurrence and distribution while the crop loss is modeled using 
Poisson distribution. This type of model is useful in count data (Cameron & Trivedi, 2003). 

Persistence of bacterial wilt of tomato and losses incurred as reported by farmers at the plant clinics 
led to a necessity to study the bacterial wilt distribution and incidences from the inferred cases in 
selected counties where clinics are operating. The study used logistic model to identify the distribution 
of bacterial wilt from inferred cases as reported by farmers at clinics. The purpose of this study is 
therefore to (i) determine the distribution of bacterial wilt of tomato in thirteen counties in Kenya, (ii) 
model the distribution of bacterial wilt under different agro-ecological zones and (iii) assess the crop 
losses attributed to bacterial wilt. 

1.3 Statement of the problem 

Tomato is the second leading vegetable crop in Kenya in terms of production and value after potato 
(Geoffrey et al., 2014). It is widely used as vegetable across the world (Wani, 2011). Tomato is 
attacked by bacterial wilt that is a problem in most regions. The persistence of bacterial wilt in the 
farms is due to poor practices in the farm such as hygiene, irrigation methods, continuous farming and 
cultural practices (Abawi & Widmer, 2000). Bacterial wilt lowers yield and quality of tomatoes 
(Oerke, 2006). It is a disease of economic importance in tomato production in the tropics (Lebeau et 
al., 2011) and a major constraint to tomato production ( Hayward, 1991). 

In Kenya, tomato is majorly grown in the open field which exposes tomato to attack by bacterial wilt, 
but use of greenhouses has been adopted in the recent past in most regions (Geoffrey et al., 2014). 
However, incidence of bacterial wilt in greenhouse production is still a problem in tomato growing 
counties in Kenya viz Kiambu, Kajiado, Laikipia and Kirinyaga, (KARI, 2005). 

Bacterial wilt persistence in the soil and its wide range of alternative hosts facilitate its spread to 
regions which were not initially affected (Kelman, 1998). To determine the distribution, application of 
logistic model is effective. The study has a dummy response variable of presence of bacterial wilt as 
reported by farmers at the clinic 1= bacterial wilt present and 0 = No bacterial wilt. 


Policy makers need the information on factors influencing bacterial wilt distribution for quick combat 
of the disease to help farmers produce quality tomatoes. The results obtained are important to farmers 
for effective planning to increase tomato production and yield. They would also make informed 
decision on correct methods of hygienic farming to control bacterial wilt and for more tomato 
production. 

1.4 Objectives of the Study 

1.4.1 General Objective 

The overall objective of the study was to apply binary logistic model in determining the disease 
distribution and crop loss caused by bacterial wilt on tomatoes in selected counties in Kenya. 

1.4.2 Specific Objectives 

The specific objectives of the study were: 

1. To determine the distribution of bacterial wilt of tomato in thirteen Counties in Kenya using 
descriptive statistics. 
2. To model the distribution of bacterial wilt using binary logistic models under different 
ecological zones. 
3. To assess the crop losses attributed to bacterial wilt using the logistic models. 


1.5 Research question 

The research questions which the study answered were: 

1. Is the pattern of the distribution of bacterial wilt of tomato the same under different ecological 
zones? 
2. Is bacterial wilt a major contributor to tomato crop loss under different agro-ecological zones? 
3. Is the logistic model effective in explaining the distribution of bacterial wilt and mapping the 
crop losses associated with the disease? 



1.6 Justification of the study 

Bacterial wilt is a diseases of particular concern in tomato growing areas, as they reduce yield and 
quality of tomatoes (Oerke, 2006). Bacterial wilt is a disease of economic importance in tomato 
production in the tropics (Lebeau et al., 2011) and a major constrain to farmers ( Hayward, 1991). 

Bacterial wilt caused by Ralstonia solanacearum affects all varieties of tomato (Afroz et al., 2009). 
The bacterium is soil borne and persists in contaminated soils and can be vector transmitted (Wani, 
2011). It has a wide host’s range of over 50 plant species (Maji & Chakrabartty, 2014). The pathogen 
is difficult to control and it can cause losses of more than 90% when it infests tomatoes (Ajanga, 
1987). Though it is persistent and resistant to most available control measures, its manifestation also 
changes with varying conditions and management practices (Prior et al., 1996). The use of disease free 
seedling is reported to delay disease onset and subsequent severity (Miller & Crosier, 2015). 

Bacterial wilt can infect roots and stems of many plants which are considered as alternative hosts 
(Wenneker et al., 1999). This enables it to continue spreading across the tomato growing regions. The 
interaction of various environmental factors such as weather (temperature and rainfall), AEZ and 
development stage of tomato determine the infection, distribution and survival of bacterial wilt. To 
understand the contributions and interactions of these factors the use of logistic model becomes 
important. Logistic model was therefore used to study the distribution due to the dummy nature of 
response variable of 0 and 1 for presence of bacterial wilt and absent of bacterial wilt respectively 
(Mhamad, 2011). 

1.7 Scope of the study 

Bacterial wilt has been a devastating disease to farmers due to its persistence in the affected regions. In 
Kenya, most farmers grow tomatoes and bacterial wilt attacks them in the farm lowering the yield and 
quality. The study used secondary data on reported cases by farmers to the plant clinics to determine 
distribution and crop loss associated with bacterial wilt of tomatoes in Kenya. Plant clinics are set in 
thirteen counties in Kenya viz. Nakuru, Trans-Nzoia, Embu, Machakos, Nyeri, Kirinyaga, Kajiado, 
Kiambu, Bungoma, Marakwet, Narok, Tharakanithi and west Pokot. These counties are under 
different agro-ecological zones and different climatic conditions. The study used data set from 1980 
tomato farmers for the year 2012 and 2013. 


1.8 Assumptions made in the study 

It was assumed that all wilted tomatoes reported or brought to the plant clinics were as result of 
bacterial wilt. Irrigation, farm management practices, source of tomato seeds were held constant across 
the ecological zones under the area of study 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


CHAPTER 2 

LITERATURE REVIEW 

2.1 Tomato production 

Vegetables are one of the key income generating crops to the economy in developing countries, they 
are recognized for their nutritional values and income generation for small scale farmers (Lenne' & 
Spence, 2005). Tomato is a vegetable crop which is classified as one of the most important crop for 
generating income and building the economy (Domis et al., 2002). In Kenya vegetables farming have 
proved effective and shown huge potential in terms of growth rate and demand leading to growth of 
economy and creation of job opportunity to small scale farmers and the locals (Philip & Jaffee, 2004) 

In Kenya horticulture has become effective and is steadily improving and among the crop exports, 
horticulture has accounted for two-thirds of all the exports (Philip et al., 2004). Tomato is one of the 
major horticulture crop grown in the country in both open and closed fields, though use of protected 
fields was adopted in the recent past (Geoffrey et al., 2014). According to Geoffrey et al., (2014), 
tomato is the second leading crop in Kenya in terms of production and value after potato. Tomato is 
financially attractive vegetable crop to both the small scale farmers in rural and peri-urban dwellings 
(Singh, & Regmi, 2013). 

2.2 Constraints to tomato production 

Key challenges faced by farmers in tomato production is pest and diseases (Lange & Bronson, 1981) 
as well as marketing (KHCP, 2011). Incidence of pests and diseases have contributed significantly to 
the reduction in food production in most agricultural regions (Oerke, 2006) and diseases is a major 
problem for small scale farmers in the production of tomatoes and other crops (Yadessa, Bruggen, & 
Ocho, 2010). 

Diseases remain the biggest challenge to the tomato growing farmers globally and at least 10% of food 
produced is lost to diseases (Strange & Scott, 2005). Tomato is grown both outdoors and under glasses 
for both fresh market consumption and processing. It requires protection from a variety of pests 
including pathogens, weeds and diseases. Among the diseases, bacterial wilt has been a devastating 
disease to farmers and it affects various varieties of tomato (Afroz et al., 2009). The bacterium is soil 
borne and persists in contaminated soils for a long time and can be vector transmitted (Wani, 


2011).Tomatoes offer a good condition for the stay of the bacterium pathogen and whenever tomato is 
grown it acts as a host for bacterial wilt pathogen since it offers shelter, food and production site for 
multiplication (Lange & Bronson, 1981). 

2.3 Control of bacterial wilt 

Though it is persistent and resistant to most available control measures, its manifestation changes with 
varying conditions and management practices (Prior et al., 1996). Attempts have been done in 
controlling the disease. The use of disease free seedling is reported to delay disease onset and 
subsequent severity (Miller & Crosier, 2015). According to Chen et al. (2009), inducing resistance 
through gene silencing is reported to control bacterial wilt in tomato. Nutritional soil amendment with 
silicon is also known to control bacterial wilt in tomato (Ayana et al., 2011). However, continuous use 
of silicon in disease management results into low soil pH which negatively affect crop production 
(Ogbodo, 2013). 

Good intercropping of tomato with non host crops and a pre-planting soil amendment with urea was 
observed to reduce the disease incidents (Michel & Hartman, 1997). Despite the cultural management 
practices such as use of organic matter, control of bacterial wilt is still a challenge to farmers in the 
tropics. 

2.4 Overview of the Logistic models 

Binary logistic is an extension of linear regression due to its qualitative dummy covariate as response 
variable (Agresti, 2002). It measures the relationship between the outcome of one response variable 
and one or many explanatory variable. The response variable must be a dummy variable with a 
probability of success coded one and probability of failure coded zero. This will enable for 
investigation of the relationship between the response and explanatory variables. Logistic regression 
analysis is the technique of fitting a model to give the probability and odds ratio of an outcome on the 
binary response variable. It is more useful when using a binary response rather than just fitting a value 
of the response and the explanatory variables. 

Logistic models is widely used in various areas to analyze most non-normal distributions. It is efficient 
in modeling dichotomous response variable and it was proposed in the 1970s to be used instead of 
Ordinary Least Square (OLS) to overcome the limitation of OLS (Peng & Harry, 2002). The statistical 


problem of using the OLS to fit data that has non-normal distribution response variables violates the 
assumptions of linear regression models such as heteroscedasticity (Constant variance of error term), 
normality and linearity which always arise due to the nature of binary response which is either success 
or failure (Williams, 2014). The general linear regression model equation, which is the universal set 
containing simple regression and multiple regression as complementary subsets (Nau, 2014), is 
represented as; 

Y= ί0 + ei ~N(0,s2) (2.1) ikiiiX.....1

where Y is the response variable; Xi, are explanatory variables i=1, 2, 3,..., k; ί0 and ίi are the 
regression coefficients, representing the parameters of the model for a specific population; and ei is a 
stochastic term which is interpreted as resulting from the effect of unspecified explanatory variables or 
a totally random element in the relationship specified. Equation 2.1 expresses the form in which other 
distributions are based when link transformation is applied on the exponential families (Peng & Harry, 
2002). 

2.5 Binary data and the use of linear regression 

The binary response variable is one in which the response outcome is either success or failure, and 
always coded as a dummy variable (success=1 and failure =0). This shows that the response variable 
has a probability between zero and one (Berry et al., 2015). However, use of least square regression 
model to fit the data of binary response variable is confronted by two major problems; conceptual in 
nature and statistical in nature. 

2.5.1 Conceptual problem 

In the process of fitting binary data in OLS regression, probability estimate which is above the 
maximum limit (one) or below minimum limit (zero) will be obtained, though according to the 
definition of probability, it should not be below zero or above one (Dixon & Koehler, 2001). Fitting 
binary data in a scatter plot results in two parallel lines on the ceiling (maximum limit) and on the 
bottom (minimum limit). The ceiling has a value of one and at the bottom a zero value. Fitting a 
straight line in this data will give a predicted value of response variable which may go below zero and 


above one as shown in figure 1 (Koehler, 2001). The line fitted is either positive or negative depending 
on the coefficient of the covariates measured. 

 

Figure 1: Fitted line plot (Source:(Dixon & Koehler, 2001). 

However, to avoid the problem in linear line, non-linear curve is appropriate in binary response 
variable to ensure that the curve is not beyond one and zero resulting into a S-curve (Traditional & 
Methods, 2001; Mhamad, 2011) and the non-linear relationship will be the same as the S-curve as 
shown in Figure 2. This curve is positive if the coefficients are greater than zero and negative when 
they are less than zero. 


 

Figure 2: Representation of relationship between variables by logistic curve (Koehler K., Meeker, 
2001) 

The logistic regression above depends on the expression E.q 2.2, instead of the ordinary least square 
regression model that assumes for linearity. To develop the strict binary regression model, we begin by 
setting the notation used to describe the model. In the case of binary response and observe n 
independent pairs of (xi, yi), i= 1, 2,…, n, Xi'= (x0i, x1i, …, xki), x0i =1, denotes a vector K+1 for the 
assumed fixed covariates for the ith subject and yi =0,1 denotes an observation of the outcome for the 
response random variable Yi. When using the logistic model we assume that p( Yi = 1| Xi ) = p(Xi), 
where, p(Xi) = exp(g(Xi) / (1+ exp(g(Xi)) and g(Xi) = Xi'ί. Therefore, the parameter estimates are 
obtained by maximum likelihood (ML) and are denoted by '= (0, 1, , k). 
^
.
^
.

 Pr (Yi=1 | Xi ) = 2.2 
g(Xi) 
g(Xi)
1ee
.

2.5.2 Probabilistic problem 

The statistical problem of using the least squares regression analysis on a binary response variable 
value, is violation of assumptions of linear regression models such as; heteroscedasticity (Constant 
variance of error term), normality and linearity. These problems always arise due to the nature of 
binary response which only take value one or zero (Williams, 2014). In the case of bacterial wilt 
attack, it is either presence of bacterial wilt in a sample or no bacterial wilt 


In a binary variable, only two Y values and only two residuals exist for any single X value. For any 
value Xi the predicted probability equals to bo+b1X1 and ei is the residual term which is obtained when 
Y=1 or Y=0. Therefore, the residuals take the value of: 

ei = 1- (bo-b1X1) 2.3a When Yi is equal to one 

ei = 0- (bo-b1X1) 2.3b When Yi is equal to zero 

These two equations 2.3a and 2.3b suggest the distribution has two values and the error term will 
never be normal at each level of the explanatory variable. According to Razali & Wah (2011), 
Kolmogorov-Smirnov (KS) statistic is used to test for normality of data of some ordered n and data 
points, x1<x2...<xn and shows significant difference when the statistic value is bigger. 

Shapiro- Wilk (S-W) is also used to test for normality of data. It is not based on a graphical test but it 
is still most preferred to test for normality of data, assuming that the data is independent and 
identically distributed observations and is arranged in ascending order (Razali & Wah, 2011). 

2.6 Some studies which applied logistic models 

A study by Mila et al.(2004), used logistic models in agricultural sectors to investigate prevalence of 
soybean sclerotinia stem rot in the North-central region of United States. The factors used in the 
model were weather condition, tillage practices, region and soil type. The study used logistic 
regression model to investigate factors associated with the disease prevalence. The study also used 
Poisson model to estimate the incidence of disease on plants using the same explanatory variables. 

According to Williams (2014), a comparison study on ordinary least square model and logistic model 
on qualitative response variable suggested that ordinary least square model is not appropriate. The 
main purpose of the study was to obtain the model suitable for the binary response outcome. He used 
both OLS and logistic model and concluded that logistic regression model is the best for the 
categorical response. 

In one instance, (Calonnec et al., 2009), conducted a study on development of powdery mildew 
epidemics on vines. Their main aim was to identify features of spatiotemporal spread of powdery 
mildew in the fields. Logistic regression technique was used to highlight the features of the disease. 
The model developed managed to predict changes in powdery mildew over time. 


2.7 Over dispersion and under dispersion of model parameters 

Over dispersion and under dispersion is essential in model fitting as it ensures that the parameters 
fitted are of importance and do not show correlation. Over dispersion in logistic models majorly works 
in the principle of depending on the mean and variance of the observed variables (Rodriguez, 2013). 
Wrong measurement or omission of important covariates in the model gives a positive correlation and 
results into a wrong description of probability of success (Follmann & Lambert, 1989), but can be 
corrected by introducing the random effect in the model. The variation maybe introduced through 
geographical regions or individuals in a continuous response variable, though this may not be easy 
(Browne, et. al., 2003). According to Rodriguez (2013) under dispersion occurs when the variation is 
less than the expected variables. Various ways of testing over dispersion such as Pearson statistic is 
essential in modeling to avoid fitting a wrong model (Dean, 1992). 

2.8 Over parameterization of the logistic model 

Parameterization is a process of deciding or setting the parameters necessary for a complete or relevant 
specification on model of interest. According to Whittaker et al., (2010), hydrological models always 
uses more parameters causing over parameterization and poor prediction of the model through use of 
Soil and Water Assessment Tool (SWAT). However, when few covariates were fitted, the model 
prediction was accurate. Use of conditional distribution in an unbalanced data and small sample size 
may give unreliable results due to inclusion of many parameters in the model (Forster et al., 1995). 
Over parameterization is a problem in most studies and it results into unrealistic results on the model 
predictions. Therefore, only parameters of interest should be incorporated in the model to obtain a best 
fit model (Whittaker et al., 2010). 

2.9 Orthogonal effect of data 

In most cases, data is analyzed without confirming its orthogonal state. Before fitting any model or 
carrying out any analysis on non-orthogonal data, we have to appreciate the difference on the two set 
of data and kind of output we may get. Non-orthogonal data is complex to interpret, though under 
sampling or over sampling is carried out to ensure that the data is orthogonal (Kotsiantis, 
Kanellopoulos, & Pintelas, 2006). Though, there are controversial issues on handling unbalanced data 
(Kotsiantis et al., 2006), general linear mixed models is still efficient to analyze the unbalanced data 
and longitudinal data (Cnaan et al., 1997). 


2.10 Diagnostics of the fit of model 

In model development, diagnostic tests are important. This helps in choosing the best model and use 
appropriate model for a given study. The diagnostic test helps in detecting various aspect of the data 
variables to be investigated such as outlier response, extreme points and quantifying their effect on the 
model (Pregibon, 1981). Model diagnostics is used in various aspects including the residuals and 
deviance. 

2.10.1 Residuals and Deviance 

Effect of residuals in the model is important in discriminating models and selecting a suitable model 
with least deviance value (Landwehr, Pregibon, & Shoemaker, 1984). Residuals is measured by either 
using deviance or partial residuals. Deviance calculation is important in obtaining the best model by 
considering the model with least deviance value (Landwehr et al., 1984). The model building was 
obtained by running the iteration to select the best model. The model with the least Deviance and AIC 
is then refitted. This is done through backward processing to eliminate variables that add no impact in 
the model. 

2.11 Logistic Regression Transformation 

2.11.1 Logarithmic transformation 

Logarithmic function are important in improving the fit of the logistic regression model for binary data 
by transforming the explanatory variables and the methods are based on consideration of the 
distributions of these variables and the outcome group (Kay, 1987). The transformations required are 
the functions of the explanatory variables which appear as the log distributions. The transformation of 
the data helps in solving the problem of heteroscedasticity, skewness; enable simplifying the model 
and converting multiplicative model to additive model for efficient interpretation of the output. 

2.11.2 The Logit (Logged Odds) 

Odds ratio is the probability value of an event occurring (pi) and event not occurring (1- pi). When the 
odd is less than one, then the event is less likely to occur than it is not to occur. When the odds is 
greater than one then there is high likely that the event occur than it is not to occur. According to 
Rodriguez (2013) the odds ratio is: 


Odds = 2.4 
ii
.
.
.1

Since : 0 = p = 1 

Then: 0= Odds = 8 

where pi is the probability of success and 1-pi is the probability of failure. 

Therefore transformation of odds using log-odds remove the restriction on the probability and model 
is transformed as a linear function of the covariates of the explanatory variables (Rodriguez, 2013). 
Thus; 

logit(p) = ln () 
ii
.
.
.1

Based on this, the relationship between logit (log odds) and explanatory variable is a linear 
relationship. 

log odds= ln (p) = bo+ 2.5 ..
niiixb1

2.12 Interpretation of logistic regression parameters 

The impact of explanatory variables on the response presence of bacterial wilt has several 
interpretations. It can be interpreted in terms of logged odds (logit), odds and Odds ratio. 

2.12.1 Interpretation in terms of logged odds (logit) 

Logit uses parameters obtained from logistic regression model. It shows the change in the predicted 
logged odds for a unit change in the explanatory variables used in the model. The method is similar to 
the interpretation linear regression parameters, though in logistic regression, units change in 
explanatory variable is explained by the logged odds of the explanatory variable to obtain the resulting 
impact on the response variable. 


2.12.2 Interpretation in terms of odds 

This interpretation is useful by transforming logistic regression parameter so that the explanatory 
affects the odds and not the logged odds. It is achieved by taking exponential on the logit to enable 
explanatory variables have an effect on the odds as follows: 

ln() = 
ii
.
.
.1..
kiiix1
.

 exp (ln ())= exp() ...
kiiix1
.

Odds= () = exp() 2.6 ..
kiiix1
.

In the case of linear regression, when ίi's are negative then it shows a decrease in the response 
variables and a positive explains an increase. However, in the binary logistic models, exponential 
values for the parameter which exceeds one indicate an increase in Odds but values which are less than 
one or equal to zero explains that odds is decreasing. 

2.12.3 Interpretation in terms of Odds Ratio 

This is obtained through determination of the ratio of odds. It is not equivalent to the Odds since this is 
the ratio of probabilities (Glas, Lijmer, Prins, Bonsel, & Bossuyt, 2003). Odds ratio is obtained by 
comparing the relationship between a specific level of explanatory variable (Xi) and after adding one 
to the previous explanatory variable (Xi +1), this implies that Xi' = Xi +1, it is from this where odds 
ratio will be computed. Odds ratio is obtained by the formula (2.6), It may also be obtained by 
obtaining exp(ί). This helps in explaining the estimate of factors that affect the distribution of 
bacterial wilt and crop loss associated with bacterial wilt. 

 

 

 

 

 


CHAPTER 3 

MATERIALS AND METHODS 

3.1 Study Area 

The study was conducted using data from 57 plant clinics in 13 counties in Kenya viz. Nakuru, Trans-
Nzoia, Embu, Machakos, Nyeri, Kirinyaga, Kajiado, Kiambu, Bungoma, Marakwet, Narok, 
Tharakanithi and west Pokot County. These counties are not delimited according to weather patterns. 
Agro-ecological zones (AEZ) were therefore used in considering weather aspects. Some AEZ overlap 
across counties and variations in the AEZs led to heterogeneity of environmental factors and farming 
activities. 

3.2 Study design and data collection 

The regions where the clinics are located were purposively selected according to the general plant 
health problems that farmers experience. Within the counties, sites for clinic location were randomly 
selected from a pool of several other possible alternatives. Different counties formed one level of 
interest and individual clinics were considered as another level. 

The data collected at the clinics were both qualitative and quantitative viz. county, demographic 
information of farmers, type of crop, development stage of disease, parts of crop affected, area under 
crop, crop loss, distribution of disease in the farm, type of pest and disease, classification of diseases 
and methods of controlling diseases. The study used secondary data obtained from the plant clinics 
queries. The response variables used were presence of bacterial wilt and estimated crop loss. The 
explanatory variables used in the model were weather data, (minimum daily temperature, maximum 
daily temperature, minimum relative humidity, maximum relative humidity and precipitation), 
development stage of crops and agro ecological zones. 

Data on the presence of bacterial wilt and crop loss were obtained from plant clinic records captured as 
farmers visit with diseased plant samples. The data from 2012 to 2013 used in the study was organized 
into various variables and filtered. The filtering entailed identification of entries that were not coded 
well and outlier in the data. The outliers were checked using the box plots and excluded in the 
analysis. 


3.3 Distribution of bacterial wilt in the counties. 

Disease distribution was determined in the thirteen counties according to plant clinic locations. 
Comparative analysis using cross-tabulation was employed using data from each county, taking into 
consideration that the counties have varied ecological zones. The disease incidents as inferred from 
clinic queries were compared across the counties and the statistical difference in the parameter tested 
was performed using Chi-square tests. 

3.4 Modeling distribution of bacterial wilt 

The study used binary logistic regression model with a dummy variable response outcome for either 
disease presence =1 or disease absence = 0 to investigate the distribution of bacterial wilt and other 
factors which influence disease distribution such as farming practices, AEZ, type of crop and weather. 
The Binary logistic model for the disease presence in the ith field was presented using generalized 
linear models (Koehler K., Meeker, 2001). 

Y= . + . = .' + e, 3.1 

Eq. 3.1 has the following components: 

i. a random component, denoted . 
ii. a linear relationship between the dependent variable and its predictors. The estimate or 
predicted values of the prediction is denoted . 
iii. a link function captures the form of relationship between the dependent variable and predictors 
expected value. Log link (΅)= exp (.) or .= log (΅) 


The impacts of predictor variables are multiplicative for k parameters. That is I = 1,2,3,…,k: 

Y= exp(b0) exp(b1X1) exp(b2X2)… exp(bkXk) 

where Y denotes the dependent variable, the presence of bacterial wilt in tomato sample taken to the 
plant clinic between the year 2012 to 2013. In the binary regression, the logit link function was used. 


p(Yij=1|Xij)= pij = 3.2 
)(1)(
1010ijjjijjjXExpXExp
..
..
..
.

where i=1,2,...,N represent the sample size while j=1,2,...,k, represent the Independent variables while 
ί's represent the parameters. 

The exponent parameters (.) in equation (3.2) can be expressed in a matrix format as; 

3.4.1 Selection of logistic models for distribution of bacterial wilt of tomato 

 The logistic models fitted for the bacterial wilt incidence using a log link function of exponential 
family, binomial (Appendix 2A, 2B and 2C). The binary logistic was fitted using the "glm" function in 
model 1, 2 and 3 respectively. They were developed using main effect parameters and the interactions 
of the main effects for model 1 and 2. Agro-ecological zones and weather parameters were correlated, 
possibly leading to multi-co-llinearity effect. Model 3 was developed using only the AEZ parameter 
and development stage of crops to investigate the dominance stage in the bacterial wilt incidence. 

 

 

 

 

 

 

 

 

 

 


Figure 1: Selected three models using the "glm" function for binary logistic model on bacterial wilt 

model1<-glm(PresenceBW ~ Minimum Temperature+ Maximum Temperature+ Precipitation 
+Minimum Relative Humidity + Maximum Relative Humidity+ Dev. Stage Seedling +Dev. Stage 
Intermediate+Dev. Stage Flowering+ Dev. Stage Fruiting +Dev. Stage Mature +Dev.Stage Post 
Harvest+ Minimum Temperature:Precipitation+ Maximum Temperature:Precipitation+ Minimum 
Relative Humidity: Precipitation+ Maximum Relative Humidity: Precipitation, data=BWdata, 
family="binomial") 

summary(model1) 

model2<glm(PresenceBW~MinTemp+MaxTemp+Precipitation+MinRelHumidity+MaxRelHumidity+
Precipitation:MinRelHumidity+Precipitation:MaxRelHumidity+Precipitation:MinTemp+Precipitation:
MaxTemp,data=BWdata, family="binomial") 

summary(model2) 

model3<-glm(Presence BW~AEZ+ Dev.Stage Seedling + Dev.Stage Intermediate + Dev.Stage 
Flowering + DevStageFruiting + Dev.Stage Mature + Dev.Stage Post Harvest, data= BWdata, 
family="binomial") 

summary(model3) 

3.5 Crop losses Assessment 

Poisson regression analysis was used to estimate the tomato crop loss. These were number of tomato 
plant in the farm that were reported by farmers to have been affected by bacterial wilt. Farmers 
assessed their farms and estimated tomato crop loss. 

In fitting the poisson model for the estimated crop losses incurred. farmers estimated the crop loss due 
to bacterial wilt in the farm. Data was filtered for only tomato cases reported to have been attacked by 
the bacterial wilt. This reduced whole data set of tomato farmers from 1980 to a sample size of 267 as 
these were the reported cases of tomato crops prescribed by clinic doctors to be infested by bacterial 
wilt. 


Crop loss was estimated using the standard unit of meter squared since farmers have different land 
sizes for growing tomato. In obtaining best model the variation in land size was extrapolated to one 
unit (M2) for an accurate model estimate. Extrapolation of land size was effective in removing 
discrepancy due to variability of land size. The number of tomato plants infected as reported by 
farmers was recorded then a total number of tomato crops in the farm estimated. Total crop in square 
meters farm was calculated as in (Eq. 3.3). The proportion of crop loss was then calculated by 
obtaining the ratio of crops infected in the crop population and then extrapolating to a standard unit of 
one meter square. The tomato losses was estimated using AEZ and weather variables for each county 
to estimate the regions that were most affected. 

CL = () 3.3 
LATCIC%)100*)((

where 

CL= crop loss 

IC= Infected crops 

TC= Total crops in the farm, but TC= 
ACFarmM2

AC= Area of one plant of tomato in meters square 

LA = Available land in meters square for tomato crop 

The study used poisson regression model to estimate crop loss in tomato. The response variable was 
crop loss and the independent variables were similar to the parameters used in determination of 
bacterial wilt disease distribution. Following Mila et al. (2004), Poisson model is written as: 

p(Y=y | ΅) = 3.4 
)!(yey...

p(Y=y | ΅) = , 
y!
X)] exp[-exp( *X)] [exp(y....


where, .= exp( SίX ) this ensured that . is non-negative integer because Poisson distribution is 
defined for only positive values (Mila et al., 2004). Hence, the estimated Poisson model is specified 
as: 

Estimated tomato loss (y) = f(weather data, (minimum daily temperature, maximum daily temperature, 
minimum relative humidity, maximum relative humidity and precipitation), development stage of crops 
and agro ecological zones.) 

3.6 Data and analysis 

Data was first filtered to remove any outliers and wrong entry in each variable of data set. Box plot 
was used in checking skewness and outliers in the data. From the box plot, any data point outside the 
range of upper and lower whiskers was categorized as outliers. Skewness of variables was confirmed 
by establishing the middle value of box plot to divide the first quarter and upper quarter of box plot 
into two equal parts. The filtered data was analyzed using R Statistical Programming Package and 
Statistical Package for Social Scientist (SPSS, version 19). In the analysis both descriptive and 
inferential statistics were used. Descriptive statistics was used to estimate the percentages of farms 
attacked by bacterial wilt in each county while logistic models (inferential statistics) was used to 
estimate the bacterial wilt distribution and crop loss associated with bacterial wilt. 


CHAPTER FOUR 

RESEARCH FINDINGS 

4.1 Distribution of Bacterial wilt in thirteen counties in Kenya 

4.1.1 Proportion of bacterial wilt incidents in clinic queries by county 

The results in this study showed that bacterial wilt is present in twelve counties. Among the thirteen 
counties where clinics are set, in Elgeyo Marakwet, farmers did not report any case of bacterial wilt of 
tomato in any clinic most probably due to other factors such as good farming practices or limited 
access to plant clinics. Bacterial wilt distribution a cross counties were significant (.2 = 202.079, p-
value<0.001). Kirinyaga county had the highest bacterial wilt attack of reported cases of the disease 
followed by Nakuru and Embu at 20.6%, 20.2% and 19.1% respectively. In Narok, West Pokot, 
Tharaka-Nithi, Kajiado and Kiambu Counties, the cases of disease attack reported was 0.4%, 2.2%, 
2.2%, 2.2% and 2.6% respectively as shown in (Fig. 1). 

 

Figure 1: Reported cases of bacterial wilt of tomato at the plant clinics in thirteen counties in Kenya 

Bacterial wilt cases on tomato were presented by farmers to plant clinics at various development 
stages. In the twelve counties, sample cases reported were showing signs of wilting presumably due to 
bacterial wilt infestation at fruiting and flowering stages. No reported cases of bacterial wilt at post 
harvest stage as shown in Table 1. During flowering and fruiting stage farmers pay much attention to 
tomatoes this is because at this stages of growth most wilting cases were reported to the clinic. No 


samples were presented to the clinics at seedlings stage having bacterial wilt but reports on infestation 
at the intermediate stage indicate a high level of incidence. This is partly due to possible transplanting 
healthy seedlings from clean nurseries in already infested fields. 

Table 1: Summarized data on reported cases of bacterial wilt presented relative to crop development 
stage 

Development stage 

No (%) 

Yes (%) 

Seedling 

92.5% 

7.5% 

Intermediate 

65.9% 

34.1% 

Flowering 

64.0% 

36.0% 

Fruiting 

59.6% 

40.4% 

Mature 

83.1% 

16.9% 

Post Harvest 

100.0% 

- 



4.2.1 Trend of cases of bacterial wilt reported to plant clinics 

The trend in the incidence of cases reported by farmers showed that weather parameters used in the 
model influences the disease incidences. It was found that between January and March, temperature, 
precipitation and humidity was low but on a increasing trend (Fig.2). This showed that trend in the 
disease incidence was also observed to be higher in those months. However, between April and June 
the number of disease incidence reported was declining and increasing from June to November. 
December showed a decline and this may be attributed by the fact that during this month, farmers 
don’t harvest tomato and rain is also reducing. Weather parameters have similar pattern with disease 
incidence. However, this could be enhanced if other farm practices that were not within the scope of 
this study would have been considered. 


 

Figure 2: Bacterial wilt incident cases reported by farmers to the plant clinics over time 

4.2 Modeling the distribution of bacterial wilt using the logistic models 

4.2.1 Normality assumption and exploratory analysis for weather data from January to 
December 

A range of temperature 27 0C to 32 0C is essential for optimum tomato production but this also 
influences the spread of R. Solanacearum (Mew, 1977). In the month of January to December the 
minimum temperatures (14 to 16 oC) was recorded which was slightly skewed (Fig. 3). However, the 
upper quartile range of temperature fluctuated over the months with narrow whiskers in May 
indicating low temperature variation. 

The average monthly maximum temperature ranged from 24 0C to 28 0C, the maximum temperature 
increasing from January to March then falling until June, over the period of rainy season and then 
temperatures rose steadily from July to December. 

 

 

 


 12345678910128101214161820Monthly minimum 
temperatureMonthMin temperature123456789101220222426283032Monthly maximum 
temperatureMonthMax temperature

Figure 3:Paired box plot of monthly minimum and maximum temperatures (oC) from January to 
December 

Relative humidity was also a component of weather data used. The minimum monthly relative 
humidity ranges between 30% to 52%. For the month of January to March, minimum relative humidity 
was almost constant at 35% while during the month of April to June humidity increases steadily. 
However, between July to December it was falling. Monthly minimum relative humidity was 
normality distributed. 

The monthly maximum relative humidity ranged between 90% and 98%, which showed less 
fluctuation as compared to the minimum monthly relative humidity. In the month of January to March, 
relative humidity was almost constant and this period rainfall is low. Then between April to May the 
humidity was increasing and falling between June to September and a slight increase for October to 
December. The distribution for the maximum relative humidity for the month of March, April and 
May was negatively skewed (Fig, 4). 

 

 

 

 

 


 

 

 
1234567891012203040506070Monthly minimum 
Relative humidity %
MonthMin reative humidity1234567891012708090100Monthly maximum 
Relative humidity %
MonthMax relative humidity

Figure 4: Paired box plot of monthly minimum and maximum relative humidity (%) from January to 
December 

Monthly and daily precipitation was observed across the year. The average monthly precipitation was 
below 5mm and this would be attributed by diverse agro-ecological zones. In areas like Kirinyagathe 
annual rainfall is about 60mm. However, the daily precipitation showed a great fluctuation on the 
rainfall received in each day indicating that there were some days that there was no rainfall recorded. 
Majority of the days recorded rainfall below 20 mm (Fig. 5) Rainfall pattern in the selected regions 
was not normally distributed, this might have been caused by the change in the weather pattern in 
Kenya. 

 
123456789101201020304050Monthly precipitation in mmMonthPrecipitation050010001500200001020304050Daily precipitation in mmDaily temperaturePrecipitation

Figure 5: Paired box plot of monthly and daily precipitation (mm) from January to December 


4.2.2 Results of model 1, 2 and 3 on z-statistic with appended likelihood ratio p-values 

4.2.2.1 Model 1 

In Table 2 below, the fitted logistic model 1 based on the selected parameters using "glm" function 
(Appendix 2A). The interaction terms of minimum temperature and precipitation; maximum 
temperature, minimum relative humidity and maximum relative humidity had no significant impact on 
the incidence of BW on tomato. The main effect on climatic factors also did not show any significant 
difference on bacterial wilt incidence as reported by farmers. However, variation in development stage 
showed an significant impact on bacterial wilt attack in tomato at various stages of development. The 
study also found out that some variables contributed negatively to the bacterial attack on tomato. For 
instance, minimum temperature had an estimate of -1.94E-02. This implies that as temperature 
decreases the attack of bacterial wilt in tomato will decline. 

 

 

 

 

 

 

 

 

 

 

 

 


Table 2: Parameter estimates of the logistic regression model used to explain the incidence of bacterial 
wilt using weather parameters and development stage of infestation 

 

Estimate 

Std. Error 

z-value 

pr(>|z|) 

Intercept 

-4.77E+00 

2.19E+00 

-2.175 

0.02962 

Minimum Temperature 

-1.94E-02 

5.80E-02 

-0.334 

0.73842 

Maximum Temperature 

5.98E-02 

6.22E-02 

0.962 

0.33607 

Precipitation 

-4.73E-01 

4.38E-01 

-1.081 

0.27962 

Minimum Relative Humidity 

2.17E-02 

1.18E-02 

1.835 

0.06653 

Maximum Relative Humidity 

6.16E-03 

1.66E-02 

0.37 

0.71111 

Dev. Seedling 

-4.00E-02 

2.64E-01 

-0.152 

0.87948 

Dev. Intermediate 

4.41E-01 

1.53E-01 

2.871 

0.00409 

Dev. Flowering 

3.41E-01 

1.46E-01 

2.343 

0.01911 

Dev. Fruiting 

-8.07E-02 

1.44E-01 

-0.56 

0.57555 

Dev. Mature 

-3.89E-01 

1.83E-01 

-2.132 

0.033 

Dev. Post Harvest 

-1.25E+01 

3.12E+02 

-0.04 

0.96799 

Minimum Temp*Precipitation 

1.57E-02 

1.23E-02 

1.275 

0.20216 

Maximum Temp*Precipitation 

1.86E-04 

1.08E-02 

0.017 

0.9863 

Min Relative Humidity*Precipitation 

-2.60E-04 

1.77E-03 

-0.147 

0.88331 

Max Relative Humidity*Precipitation 

2.41E-03 

4.20E-03 

0.572 

0.56698 



a Significant codes: 0'***', 0.001'**', 0.01'*', 0.05'.', 0.1' ', 1 

b Null deviance: 1566.2 on 1979 degrees of freedom; Residual deviance: 1520.9 on 1964 degrees of 
freedom; AIC: 1552.9; Number of Fisher Scoring iterations: 13 

c Min Relative Humidity= Minimum Relative Humidity, Max Temperature= Maximum Temperature, 
Dev= Development stages of plant when disease incidents recorded (no, 0; yes, 1), Std. Error= 
Standard Error. 

4.2.2.2 Model 2 

In Table 3 the study found that minimum relative humidity was significant and had a positive 
coefficient estimate on bacterial wilt incidence (p= 0.0295). The intercept represent the base line value 


of the response variable assuming no contribution of any explanatory variables. From the analysis it 
was found that the intercept was negative an indication of a decline on the bacterial wilt cases reported 

Table 3: Parameter estimates of the logistic regression model used to explain the incidence of bacterial 
wilt by using weather parameters 

 

Estimate 

Std. Error 

z value 

Pr(>|z|) 

Intercept 

-5.844243 

2.053974 

-2.845 

0.00444** 

Min Temperature 

0.009965 

0.054479 

0.183 

0.85486 

Max Temperature 

0.080334 

0.058211 

1.38 

0.16757 

Precipitation 

-0.001271 

0.009585 

-0.133 

0.89454 

Minimum Relative Humidity 

0.024293 

0.011166 

2.176 

0.02958* 

Maximum Relative Humidity 

0.007095 

0.015756 

0.45 

0.65251 



a Significant codes: 0'***', 0.001'**', 0.01'*', 0.05'.', 0.1' ', 1 

b Null deviance: 1566.2 on 1979 degrees of freedom; Residual deviance: 1554.0 on 1974 degrees of 
freedom; AIC: 1566 

4.2.3.3 Model 3 

The findings in Table 4 presents the fitted model based on the selected binary logistic model on the z-
statistics using "glm" function. The study showed that agro-ecological zones (AEZ) have no 
significant impact on bacterial wilt attack in tomato. This could be attributed by poor farming practices 
that most farmers adopt to reduce cost of production. Farmers always recycle seeds and continuously 
plant tomato in the same farm for many years. AEZ though not significant, a reduction in the disease 
cases reported by farmers. However, LM4, UM1 and UM3 had positive coefficient estimate indicating 
an increase in the BW attack on tomatoes with respect to LH1 

 

 

 

 


Table 4: Parameter estimates of the logistic regression model used to explain the incidence of bacterial 
wilt in relation to agro-ecological zones and crop development stage 

 

Estimate 

Std. Error 

z value 

Pr(>|z|) 

Intercept 

-1.86369 

0.63634 

-2.929 

0.0034** 

AEZ LH2 

-0.63965 

0.74033 

-0.864 

0.38758 

AEZ LH3 

-0.76433 

0.77983 

-0.98 

0.32702 

AEZ LH4 

-0.24353 

1.23843 

-0.197 

0.84411 

AEZ LM3 

-0.16672 

0.82976 

-0.201 

0.84075 

AEZ LM4 

0.28389 

0.64871 

0.438 

0.66166 

AEZ LM5 

-0.51012 

0.7186 

-0.71 

0.47778 

AEZ LM6 

-1.09581 

0.77797 

-1.409 

0.15897 

AEZ LM7 

-0.65875 

1.21909 

-0.54 

0.58895 

AEZ UH1 

-13.97764 

0.91752 

-0.019 

0.98451 

AEZ UH2 

-1.38677 

1.20158 

-1.154 

0.24845 

AEZ UM1 

0.3291 

0.69903 

0.471 

0.63779 

AEZ UM2 

-0.13272 

0.65456 

-0.203 

0.83932 

AEZ UM3 

0.04208 

0.63655 

0.066 

0.94729 

AEZ UM4 

-0.28786 

0.65021 

-0.443 

0.65797 

AEZ UM5 

-14.06598 

0.95072 

-0.024 

0.98101 

Dev. Seedling 

0.02005 

0.26245 

0.076 

0.93911 

Dev. Intermediate 

0.41146 

0.15474 

2.659 

0.00783** 

Dev. Flowering 

0.33014 

0.14509 

2.275 

0.02288* 

Dev. Fruiting 

-0.05577 

0.14382 

-0.388 

0.69821 

Dev. Mature 

-0.35736 

0.18223 

-1.961 

0.04988* 

Dev. PostHarvest 

-13.43874 

1.43525 

-0.026 

0.97904 



aSignificant codes: 0'***', 0.001'**', 0.01'*', 0.05'.', 0.1' ', 1 

bAEZ= Agro-ecological zone, LH= Lower upper land, LM= Lower middle land, UH= Upper highland, 
UM= Upper middle land, Dev= Development stages of plant when disease incidents recorded (no, 0; 
yes, 1). 


4.2.3 Re-fitted model adjusted for over parameterization 

Models in Tables 2, 3 and 4 above were over parameterized based on the z-values. The parameters 
were re-fitted considering the high AIC values and low value of residual deviance. The best-fit model 
was selected through the backward iteration process obtaining the model with the low residual 
deviance. Resulting model gives the model with parameters that have significant influence on the 
disease incidence. In the refitted model for model 1a, showed that the intercept, fruiting and maturity 
stage of tomato had a negative estimate. This is an implication of decline in the bacterial wilt attack on 
tomato (Table 5) 

 

 

 

 

 

 

 

 

 

 

 

 

 


4.2.4.1 Refitting of models 

Table 5: Model 1a, 2a and 3a output are refitted models after readjusting for over parameterization to 
improve estimation of bacterial wilt incidence 

Model 1a 

 

Estimate 

Std. Error 

z value 

Pr(>|z|) 

Intercept 

-2.820777 

0.338807 

-8.326 

< 2e-16*** 

Min Relative Humidity 

0.017943 

0.006915 

2.595 

0.00946** 

Dev. Flowering 

0.362961 

0.141947 

2.557 

0.01056* 

Dev. Fruiting 

-0.043275 

0.140261 

-0.309 

0.75768 

Dev. Intermediate 

0.474264 

0.150113 

3.159 

0.00158** 

Dev. Mature 

-0.345616 

0.178042 

-1.941 

0.05223. 

Dev. Post Harvest 

-12.568472 

311.375236 

-0.04 

0.9678 

Model 2a 

Intercept 

-5.261978 

1.263135 

-4.166 

3.1e-05 *** 

Min Relative Humidity 

0.026624 

0.007814 

3.407 

0.000656 *** 

MaxTempeature 

0.08502 

0.040427 

2.103 

0.035460 * 

Model 3a 

Intercept 

-2.035 

0.1074 

-
18.944 

< 2e-16 *** 

Dev. Intermediate 

0.5039 

0.1454 

3.464 

0.000531 *** 

Dev. Flowering 

0.3426 

0.1406 

2.436 

0.014847 * 

Dev. Mature 

-0.3531 

0.1776 

-1.988 

0.046790 * 

Dev. Post Harvest 

-12.5594 

310.6138 

-0.04 

0.967747 



a Significant codes: 0'***', 0.001'**', 0.01'*', 0.05'.', 0.1' ', 1 

b Min Relative Humidity= Minimum Relative Humidity, Max Temperature= Maximum Temperature, 
Dev= Development stages of plant when disease incidents recorded 

c Model 1a, 2a, and 3a has different residuals deviance and AIC. They were developed from model 1, 2 
and 3 through backward iteration process to take care of over parameterization. Model 1a has residuals 
deviance (1532.0) and AIC (1546), model 2a has residuals deviance (1554.2) and AIC (1560.2) and 
model 3a has a residuals deviance (1538.8) and AIC (1548.8). 


4.3 Poisson Model for the assessment of reported crop loss due to bacterial wilt 

4.3.1 Model 4 

The parameters used in assessing tomato losses due to bacterial wilt were weather data (minimum 
temperature, maximum temperature, precipitation, minimum relative humidity and maximum relative 
humidity) and development stages of the disease on the tomato crop. From the analysis, minimum 
temperature, minimum relative humidity, maximum relative humidity, development stages; seedling, 
intermediate, flowering and fruiting had impact on tomato loss due to bacterial wilt prevalence (Table 
6). From the study minimum relative humidity had a negative coefficient and showed that a unit 
increase in the minimum relative humidity would lead to a decrease of BW attack. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Table 6: Parameter estimates of the Poisson regression model of disease prevalence as relates to 
weather and crop development stage 

Full model 4 

 

Estimate 

Std. Error 

z value 

Pr(>|z|) 

Intercept 

2.3271553 

0.3360046 

6.926 

4.33e-12*** 

Min Temperature 

0.0279995 

0.0090071 

3.109 

0.00188** 

Max Temperature 

0.0001011 

0.0098366 

0.01 

0.991803 

Precipitation 

0.0023042 

0.0016014 

1.439 

0.150193 

Min Relative Humidity 

-0.0051192 

0.0018794 

-2.724 

0.006454** 

Max Relative Humidity 

0.0087269 

0.0025266 

3.454 

0.000552*** 

Dev. Seedling 

0.3707622 

0.0371957 

9.968 

< 2e-16*** 

Dev. Intermediate 

0.0611297 

0.0244035 

2.505 

0.012247* 

Dev. Flowering 

0.1085326 

0.0241847 

4.488 

0.0000072** 

Dev. Fruiting 

0.0446686 

0.0232861 

1.918 

0.055079 

Dev. Mature 

-0.0352253 

0.0330898 

-1.065 

0.287086. 

Refitted model 4 to adjust for over parameterization 

Intercept 

2.30406 

0.231598 

9.949 

< 2e-16 *** 

Min Temperature 

0.028855 

0.005981 

4.824 

1.40e-06 *** 

Min Relative Humidity 

-0.00465 

0.001344 

-3.46 

0.000540 *** 

Max Relative Humidity 

0.008567 

0.002502 

3.424 

0.000616 *** 

Dev. Seedling 

0.378026 

0.036761 

10.283 

< 2e-16 *** 

Dev. Intermediate 

0.070608 

0.023482 

3.007 

0.002640 ** 

Dev. Fruiting 

0.048927 

0.022948 

2.132 

0.032999 * 

Dev. Flowering 

0.112032 

0.023107 

4.848 

1.24e-06 *** 



a Significant codes: 0'***', 0.001'**', 0.01'*', 0.05'.', 0.1' ', 1 

b Min Relative Humidity= Minimum Relative Humidity, Max Temperature= Maximum Temperature, 
Dev= Development stages of plant when disease incidents recorded 

c Full model and refitted model based on the AIC process of selecting significant variables. Residual 
deviance of full model is 1459.7 and AIC of 2873.3 while the refitted model has a residual deviance 
(1462.4) and AIC (2870.1). 


4.3.2 Model 5 

The analysis showed that in upper midlands, the disease incidents as inferred from data queries 
brought to plant clinics was low compared to low midlands. This would be attributed by the low 
temperatures in the upper midlands (Table 7). Agro-ecological zones were found from the analysis to 
have significant influence on bacterial wilt incidents thereby resulting into losses of tomato due to 
infestation of BW. Various AEZ, LH2, LM3, LM4, LM7, UM2 and UM4 had a positive significant 
impact on average tomato loss with reference to LH1. It was an indication that bacterial wilt could be 
found across various AEZ 

Table 7: Parameter estimates of the Poisson regression model on disease prevalence in relation to 
agro-ecological zones and crop loss as reported by farmers 

 

Estimate 

Std. Error 

z value 

Pr(>|z|) 

Intercept 

3.20545 

0.11625 

27.574 

< 2e-16*** 

AEZ LH2 

0.35803 

0.13252 

2.702 

0.006899** 

AEZ LH3 

-0.01087 

0.14734 

-0.074 

0.941193 

AEZ LH4 

-0.0274 

0.2349 

-0.117 

0.907146 

AEZ LM3 

0.4122 

0.14221 

2.898 

0.00375** 

AEZ LM4 

0.45297 

0.11844 

3.824 

0.000131**
* 

AEZ LM5 

0.20312 

0.13111 

1.549 

0.121319 

AEZ LM6 

-0.01087 

0.14734 

-0.074 

0.941193 

AEZ LM7 

0.70657 

0.18307 

3.86 

0.000114**
* 

AEZ UH2 

-0.0274 

0.2349 

-0.117 

0.907146 

AEZ UM1 

-0.01466 

0.12914 

-0.114 

0.909621 

AEZ UM2 

0.3632 

0.11998 

3.027 

0.002468** 

AEZ UM3 

0.10799 

0.11783 

0.916 

0.359423 

AEZ UM4 

0.27902 

0.11967 

2.332 

0.019721* 



aSignificant codes: 0'***', 0.001'**', 0.01'*', 0.05'.', 0.1' ', 1 


bAEZ= Agro-ecological zone, LH= Lower upper land, LM= Lower middle land, UH= Upper highland, 
UM= Upper middle land. 

c Model 5 has residuals deviance (1414.6) and AIC (2834.3) at 253 degree of freedom and null 
deviance (1628.7). 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


CHAPTER FIVE 

DISCUSSION OF RESULTS 

This chapter discusses the results obtained from modeling bacterial wilt in tomato. 

5.1 Interpretation of the fitted binary logistic models 

5.1.1 Model 1 

In Model 1, weather data and development stage was used as independent variables. From the results it 
was observed bacterial wilt cases were reported to the plant clinics at intermediate, seedling 
development stage, flowering stage and maturity stage. Minimum relative humidity had significant 
impact on bacterial wilt incidence. However, minimum and maximum temperature, rainfall and 
maximum relative humidity did not show significant influence on BW incidence according to the 
reported cases of disease. 

The intercept value of Model 1 was -4.773 indicated a reduction in incidence of bacterial wilt 
incidence (Table 2). Minimum temperature and rainfall showed a reduction in the presence of bacterial 
wilt though they were not significant. However, maximum temperature, minimum relative humidity, 
and maximum relative humidity had a positive impact in the presence BW as inferred cases from 
clinic queries. It was found that maximum relative humidity followed by maximum temperature had a 
greater impact (Table 2). From model 1a, it was observed that the intercept increased from -4.773 to -
2.821 an indication of more attack of bacterial wilt. The null deviance explained more incidents of BW 
with the residual deviance of 1532 and AIC 1546. From the study, it was found that flowering, 
intermediate, and maturity stage, farmers reported more cases of bacterial wilt attack on tomatoes 
(Table 5). Temperature and precipitation did not significantly influence the bacterial wilt incidents as 
reported by farmers to the clinics. This would have been attributed by the fact that small scale farmers 
only plant during rainy season and solely depends on rainfall. Therefore, during dry season tomatoes 
are not in the field. However, minimum relative humidity was significant (z=2.595, p=0.00946). Daily 
temperature and precipitation influenced the distribution of bacterial wilt as it leads to its spread due to 
the runoff from the infested farms. According to Mila et al. (2004), temperature and precipitation 
increased the risk in bacterial wilt incidence as the it can tolerate up to a temperature of 32 0C. A study 


by Mew et al. (1977) also observed that bacterial wilt can survive under varied range 26 0C to 32 0C 
temperature that tomato may scorch out while BW still survive. 

In Table 5, there were some variable with negative coefficient on presence of bacterial wilt. The 
negative estimates indicated that on the reported cases by farmers these variables led to a decline in 
bacterial wilt incidents. The results indicated that at fruiting and maturity stage the bacterial wilt 
incidents were observed to be decreasing. However, at flowering and intermediate stage, the bacterial 
wilt incidents were observed to have increased. The Minimum relative humidity showed that with a 
unit increase in the temperature, bacterial wilt incidents increased by 0.0179 (z=2.595, p=0.00946). 

5.1.3 Model 2 

In Model 2 only weather variable was used. In the analysis, though maximum and minimum 
temperature had a positive coefficient of estimate, they were not significantly influencing BW 
incidences in tomato according to the reported cases. This may be attributed to other factors such as 
good farming practices and type of irrigation method used by farmers. A study carried out by Mila et 
al. (2004), determined temperature and precipitation as important factors to consider when 
investigating bacterial wilt incidence as it requires optimal condition to survive. In Table 2, it was 
found that minimum relative humidity increased the level of bacterial wilt incidents by 0.0242 and was 
significant (z= 2.176, p=0.02958) as from the clinic data queries. Maximum temperature, minimum 
temperature, maximum relative humidity and precipitation were not significant. The results showed 
that daily precipitation was fluctuating with some days recording no rain. Maximum relative humidity 
and minimum temperature had low coefficient estimates. 

Considering the weather variables, the intercept showed that when no other factor was considered, the 
disease incidence reported reduced by 5.844 (Table 3). The refitted Model 2a was selected by 
comparing the AIC in the iterated models and the model with the least AIC. The variables used were 
maximum temperature and minimum relative humidity. The refitted Model 2a had an intercept of -
5.262, an indication that bacterial wilt incidents was reduced by the magnitude that is slightly lower 
than the value when all variables are used (Table 5). 

The results on Model 2a showed that from the clinic queries on bacterial wilt of tomato, maximum 
temperature was significant on the presence of bacterial wilt (z= 2.103, p= 0.035) and minimum 


relative humidity was also significant (z= 3.407, p=0.00066) as shown in Table5. It was observed that 
the two variables increased the estimate of BW incidents that is an indication that most farmers 
reported more cases of the disease to plant clinics. 

From the study, the mean maximum monthly temperature was observed to be in the range of 24 0C to 
28 0C from January to December (Figure 4.1a). The temperature achieved throughout the year was 
advantageous for the survival of Ralstonia solanacearum as it can survive for long and in varied 
temperature over 210C. A study by Persley (1986), showed that R. solanacearum can survive in the 
soil for long time and within the range of 28 0C to 32 0C. 

5.1.4 Model 3 

In this model, agro-ecological zones were used to estimate the reported cases of bacterial wilt in 
tomato. Various counties were sub-grouped into various AEZ. However, the AEZ may be similar to 
other regions which are spatially different. The AEZ is based on the weather pattern of regions and 
since they are demarcated based on the weather data, there is correlation between the weather 
variables and AEZ. It therefore prompts for the separation of these two variables to avoid 
multicollinearity effect that results into biased standard error of the estimates. 

The AEZ did not show any significant to the bacterial wilt incidents as per the reported cases (Table 
4). This may be due to farm practices farmers adopted. A study by Michel et al. (1997), showed that 
various farm practices such as intercropping and soil amendment significantly reduces the population 
of BW of tomato. Although AEZ did not affect bacterial wilt incidents significantly in this study, the 
coefficient of estimates were negative. The intercept of the model was -1.897, an indicator of bacterial 
wilt incidents reduced by 1.897. The effect of AEZ on bacterial wilt showed a reduction and an 
increase in disease incidents. This showed that under AEZ with positive coefficient estimate, cases of 
disease incidents increased while the AEZ with negative coefficient estimates showed that cases of the 
bacterial wilt incidents reported by farmers reduced (Table 4). These estimates majorly depend on the 
farmers who visited the clinic and a practical study conducted may conform to what other researchers 
found. A study in Nigeria on agro-ecological effect of bacterial wilt on cassava showed significant 
difference of the disease attack under different environmental conditions (Ngeve & Nukenine, 2002). 


Model 3a was refitted using both the development stage and AEZ. It showed that development stages 
significantly attribute to the bacterial wilt incidents as reported by farmers to the plant clinics.. 
Intermediate, flowering and mature stage was significant. However, at mature stage BW reported 
incidents decreased by 0.353 while flowering and intermediate stage showed an increase in the 
incidents of bacterial wilt with 0.343 and 0.504 respectively (Table 5). 

5.2 Interpretation of the fitted poisson models 

It was found that minimum temperature, minimum relative humidity and maximum relative humidity 
had impact on tomato loss due to attack by bacterial wilt. High and low relative humidity areas was 
found to influence the disease incidents resulting into tomato losses in the farm (Geoffrey et al., 2014). 
These losses were majorly observed at different stages of tomato development as reported by farmers. 
Farmers majorly recorded losses at seedling stage, intermediate stage, flowering and fruiting stage 
(Table 6). The intercept revealed a mean loss of tomato of 2.304. The coefficient of Model 4 and 
refitted Model 4a were slightly different. The optimal model obtained by refitting the parameters 
showed the best estimates since it had the least AIC of 2870.1 compared to 2873.3 AIC of the model 
fitted with all the parameters. Minimum relative humidity reduced the rate of crop loss by 0.0046 and 
(z= 3.460, p= 0.00054). This maybe attributed by canopy and poor farming practices most farmers do 
and overcrowded tomato plant in the farms. The overcrowding of tomato and its vegetative stems may 
form a canopy creating humid environment leading to rise bacterial incidence (Geoffrey et al., 2014). 

Bacterial wilt was reported to be present in the lower elevated regions due to the warm temperature 
(Ajanga, 1987) and it leads to production of high quality tomato seeds in the high altitude regions 
where the BW is not widespread. However, since most farmers are small scale and cannot afford good 
seeds, they use the low quality seeds that are used over period leading to consistency in BW persistent 
in the farms. 

Agro-ecological zones were used in Model 5. The AEZ which were significant in estimating crop 
losses due to attack by bacterial wilt were LH2, LM3, LM4, LM7, UM2 and UM4 (Table 8) and from 
the study, it was found that the risk of tomato crop infected by bacterial wilt increased. These AEZ are 
warm and due to their warm states they encourage the spread of bacterial wilt and its reoccurrence in 
the farm as it can survive at high temperatures of 27 0C to 32 0C (Deberdt et al., 1999). 


Farmers in these regions recycle their tomato seeds making it difficult to eradicate the disease. 
According to Ajanga (1987), most of the own produced seeds in the lower elevated regions get into the 
market and farmers purchase them due to their low income status resulting into the spread of the BW. 
Bacterial wilt was observed to be spreading in all the regions and this would have been led by 
recycling own produced seeds. Hayward (1991), reported that BW is widely distributed in tropical, 
sub-tropical and some warm temperate regions leading to crop loss. The model coefficient estimates of 
different AEZ had a positive and negative marginal effect, the negative coefficient estimates indicated 
a diminishing marginal return of crop loss as a result of bacterial wilt while the positive coefficient 
estimates indicated an increase in tomato crop loss. When good farm practices are followed these 
losses would probably reduce due to reduction in bacterial wilt infestation on tomatoes. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


CHAPTER SIX 

CONCLUSIONS AND RECOMMENDATIONS 

6.1 Introduction 

In this chapter, the presentation of conclusions and recommendations for further research arising from 
the study. 

6.2 Conclusion 

The study applied binary logistic to model the distribution and crop loss associated with bacterial wilt 
of tomatoes within the scope of logistic models. Binary logistic model was used because the response 
variable was a dummy. The study found out that bacterial wilt attack to tomato was reported in all the 
thirteen counties where clinics are located in Kenya. Among those counties, The highest attack was 
reported in Kirinyaga followed by Nakuru and Embu. The least percentage of farms attacked were 
reported in Narok, West Pokot, Tharaka-Nithi, Kajiado and Kiambu. 

Inferring from the binary logistic model, it was found that, distribution of bacterial wilt is not 
necessarily influenced by agro-ecological zones. The agro-ecological zones of a region is dependant 
on weather pattern of the region. Therefore, bacterial wilt distribution was determined independently 
based on weather data and agro-ecological zones. The study found out that, agro-ecological zones had 
no impact on the bacterial wilt distribution. This is due to poor farming practices within the tomato 
growing regions. 

However, using the weather data, it was found that relative humidity and temperature had an impact 
on the bacterial wilt attack. Bacterial wilt can persist in the soil for a long time leading to frustration of 
farmers in managing. In cold regions, bacterial wilt does not express itself and remains in dormant 
state till a favorable temperature is attained. This may also results into bacterial wilt not identified at 
some stage in crop development. In tomato development stage, farmers reported more cases of 
bacterial wilt attack during intermediate, flowering and maturity stage. Farmers are always attentive to 
any anomalies in their crops especially incidents of any wilting in tomato as it is widely used for food 
and for commercial purpose. However, at some stages in tomato growth such as seedling, fruiting, and 
post harvest stage, the bacterial wilt cases reported had no impact in presence of bacterial wilt 


Estimated tomato loss was determined using poisson model using the weather, agro-ecological zones 
and development stage. This helped to estimate the impact of these variables on the tomato losses 
associated with bacterial wilt. The study found out that, minimum temperature and maximum relative 
humidity increased the tomato loss associated by bacterial wilt. However, minimum relative humidity 
showed a decrease of tomato loss due to attack by bacterial wilt. The study also found that the 
development stages which farmers mostly reported attack on tomato were at seedling, intermediate, 
fruiting and flowering. They showed an increase in the impact of bacterial wilt attack on tomato. This 
study assumed that wilting was caused by bacterial wilt and irrigation, management practices and 
source of tomato seeds were held constants. 

6.3 Recommendation 

The study findings indicated that bacterial wilt is distributed in 12 out of 13 the counties under study. 
The distribution of bacterial wilt could have been attributed by factors that were assumed to be 
constant in all the counties. However, in some regions, the bacterial wilt attacks reported were low. 
The disease distribution presumably would be due to poor farming practices of farmers 

Tomato farmers should be advised using the findings from the study by the policy makers to reduce 
bacterial distribution and crop loss associated by bacterial wilt. This would help farmers to improve 
the tomato yield and encounter the attack by bacterial wilt that has been reported in the 12 out of 13 
counties in Kenya. Good training of farmers using the findings on the external factors that influence 
distribution of bacterial wilt in the tomato growing regions would lead to reduction of bacterial wilt 
and more production of tomatoes in the farm. The other external factors such as farming practices, 
irrigation and soil type can be further explored for more studies. 

 

 

 

 

 


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APPENDICES 

Appendix 1: Data exploration using box plot for weather data 

===================================================================== 

==Exploratory analysis using box plot for the parameter which influence BW incidence ====== 

===================================================================== 

par(mfrow=c(1,2)) 

boxplot(BWdata$MinTemperature~BWdata$Month,col="blue", xlab="Month", ylab="Min 
temperature", main="Daily minimum\n temperature") 

boxplot(BWdata$MaxTemperature~BWdata$Month, col="blue", xlab="Month", ylab="Max 
temperature", main="Daily maximum\n temperature") 

par(mfrow=c(1,2)) 

boxplot(BWdata$PercentMinRelativeHumidity~BWdata$Month, col="blue", xlab="Month", 
ylab="Min reative humidity", main="Daily minimum\n Relative humidity %") 

boxplot(BWdata$PercentMaxRelativeHumidity~BWdata$Month, col="blue", xlab="Month", 
ylab="Max relative humidity", main="Daily maximum\n Relative humidity %") 

par(mfrow=c(1,2)) 

plot(BWdata$Precipitation_mm, type="l") 

boxplot(BWdata$Precipitation_mm~BWdata$Month,col="blue",xlab="Month", 
ylab="Precipitation", main="Daily precipitation in mm") 

abline(plot(BWdata$Precipitation_mm, type="l",ylab="Precipitation",xlab="Daily temperature", 
main="Daily precipitation in mm"), h=2.374, col="red", lwd=3) 



 

 

 

 

 

 


Appendix 2: Modeling the incidence of bacterial wilt 

2A. Model 1 

============================================================================ 

==== model for BW incidence using Climatic data and development stage====== 

============================================================================ 

 

model1<-glm(PresenceBW~MinTemp+MaxTemp+Precipitation+MinRelHumidity+ 
MaxRelHumidity+DevStageSeedling+DevStageIntermediate+DevStageFlowering+DevStageFruiting+DevStageMature+DevStagePostHarvest+MinTemp:Precipitation+MaxTemp:Precipitation+MinRelHumidity:Precipitation+MaxRelHumidity:Precipitation,data=BWdata, 
family="binomial") 

 

summary(model1) 



2B. Model 2 

model2<-
glm(PresenceBW~MinTemp+MaxTemp+Precipitation+MinRelHumidity+MaxRelHumidity+Precipitation:MinRelHumidity+Precipitation:MaxRelHumidity+Precipitation:MinTemp+Precipitation:MaxTemp,data=BWdata, family="binomial") 

summary(model2) 

 



2C. Model 3 

model3<-glm(PresenceBW~AEZ+ DevStageSeedling + DevStageIntermediate + 
DevStageFlowering + DevStageFruiting + DevStageMature + DevStagePostHarvest, 
data= BWdata, family="binomial") 

summary(model3) 



 

 


Appendix 3: Selected R codes 

Data management 

 

library(foreign, pos=4) 

BWdata<-read.csv(file.choose(), header=T) 

BWdata 

summary(BWdata) 

MinTemp<-(BWdata$MinTemperature) 

MaxTemp<-(BWdata$MaxTemperature) 

Precipitation<-(BWdata$Precipitation_mm) 

MinRelHumidity<-(BWdata$PercentMinRelativeHumidity) 

MaxRelHumidity<-(BWdata$PercentMaxRelativeHumidity) 

CropAffected<-(BWdata$CropAffected) 

AEZ<-(BWdata$Agro.ecological.zones) 

County<-factor(BWdata$FarmerCounty, levels=c(1,2,3,4,5,6,7,8,9,10,11,12,13),labels=c("Embu", 
"Kirinyaga", "Machakos", "Nakuru", "Bungoma","Elgeyo Marakwet","Kajiado", "Kiambu", "Narok", 
"Nyeri","Tharaka Nithi", "Trans Nzoia", "West Pokot")) 

AEZ<-factor(BWdata$Agro.ecological.zones, 
lables=c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16),levels=c("LH1","LH2","LH3","LH4","LM3","LM4",
"LM5","LM6","LM7","UH1","UH2","UM1","UM2","UM3","UM4","UM5")) 

PresenceBW<-factor(BWdata$PresenceBacterialWilt, levels=c(0,1), labels=c("No","Yes")) 

DevStageSeedling=factor(BWdata$DevStageSeedling, levels=c(0,1), labels=c("No","Yes")) 

DevStageIntermediate=factor(BWdata$DevStageIntermediate, levels=c(0,1), labels=c("No","Yes")) 

DevStageFlowering=factor(BWdata$DevStageFlowering, levels=c(0,1), labels=c("No","Yes")) 

DevStageFruiting=factor(BWdata$DevStageFruiting, levels=c(0,1), labels=c("No","Yes")) 

DevStageMature=factor(BWdata$DevStageMature, levels=c(0,1), labels=c("No","Yes")) 

DevStagePostHarvest=factor(BWdata$DevStagePostHarvest, levels=c(0,1), labels=c("No","Yes")) 



 


Model Selection codes 

Model 1 

Initial model specification 

model1<-glm(PresenceBW~MinTemp+MaxTemp+Precipitation+MinRelHumidity+ 
MaxRelHumidity+DevStageSeedling+DevStageIntermediate+DevStageFlowering+DevStageFruiting+DevStageMature+DevStagePostHarvest+MinTemp:Precipitation+MaxTemp:Precipitation+MinRelHumidity:Precipitation+MaxRelHumidity:Precipitation,data=BWdata, 
family="binomial"(link="logit")) 

summary(model1) 

model1.b<-step((model1), direction="backward") 

 

Model selection using backward method 

modelrefit<-
glm(PresenceBW~MinRelHumidity+DevStageFlowering+DevStageFruiting+DevStageIntermediate+DevStageMature+DevStagePostHarvest,data=BWdata, 
family="binomial"(link="logit")) 

summary(modelrefit) 

 

Model 2 

Initial model specification 

model2<-
glm(PresenceBW~MinTemp+MaxTemp+Precipitation+MinRelHumidity+MaxRelHumidity+Precipitation,data=BWdata, family="binomial"(link="logit")) 

summary(model2) 

model2.b<-step((model2), direction="backward") 

 

Model selection using backward method 

modelrefit2<-glm(PresenceBW~MinRelHumidity+ MaxTemp 

, data=BWdata, family="binomial"(link="logit")) 

summary(modelrefit2) 

 

 


Model 3 

Initial model specification 

model3<-
glm(PresenceBW~AEZ+DevStageSeedling+DevStageIntermediate+DevStageFlowering+DevStageFruiting+DevStageMature+DevStagePostHarvest, data=BWdata, 
family="binomial"(link="logit")) 

summary(model3) 

model3.b<-step((model3), direction="backward") 

 

Model selection using backward method 

modelrefit3<-
glm(PresenceBW~DevStagePostHarvest+DevStageFlowering+DevStageMature+DevStageIntermediate,data=BWdata, family="binomial"(link="logit")) 

summary(modelrefit3) 

Poisson Model for the bacterial wilt prevalence 

Mode 4 

model4<-
glm(Cropattacked~MinTemp+MaxTemp+Precipitation+MinRelHumidity+MaxRelHumidity+ 

DevStageSeedling+DevStageIntermediate+DevStageFlowering+DevStageFruiting+ 

DevStageMature+DevStagePostHarvest, data=CropAffected, family="poisson" 

(link = "log")) 

summary(model4) 

model4.b<-step((model4), direction="backward") 

 

Model selection using backward method 

modelrefit4<-
glm(Cropattacked~MinTemp+MinRelHumidity+MaxRelHumidity+DevStageSeedling+ 

DevStageIntermediate+DevStageFruiting+DevStageFlowering, data=CropAffected, 
family="poisson"(link="log")) 

summary(modelrefit4) 

Mode 5 

model5<-glm(Cropattacked~AEZ,data=CropAffected, family="poisson"(link="log")) 

summary(model5)