MATHEMATICAL MODEL FOR CO-INFECTION OF PNEUMONIA AND TYPHOID FEVER DISEASE WITH OPTIMAL CONTROL

Abstract

Pneumonia has claimed and continues to claim the lives of millions of people worldwide. Also, its effect on countrys and households cannot be ignored since most of the people that get infected and/or die from the diseases are usually future generation childrens. The impact of Pneumonia worsened in the presence of opportunistic infections like Typhoid fever. Thus, firms need to get involved in the fight against Pneumonia and its co-infection with these opportunistic infections. This thesis presents three detailed deterministic mathematical models that are aimed at describing the dynamics of Pneumonia and its co-infection with Typhoid fever. The first model is a general one that describes the dynamics of Pneumonia. The model is qualitatively analyzed to determine conditions for successful campaign against Pneumonia. Numerical simulations are also carried out and various combinations of interventions strategies are compared to determine the most cost-effective strategy that should be employed for the campaign against the disease. It is observed that the strategy that adopts prevention and treatment is most cost-effective in the fight against the spread of the disease. The second model considers dynamics of the Typhoid fever. This model is qualitatively analyzed to determine conditions for eradication of the disease. Numerical simulations and comparison of various intervention schemes revealed that the most cost-effective scheme that should be adopted for a successful campaign against the disease is one that implements prevention and treatment strategies. The third model considers the dynamics of co-infection of Pneumonia and Typhoid fever diseases The model is also qualitatively analyzed and numerically simulated. It is revealed that a successful campaign against the co-infection of the two diseases will have to include preventative measure for Typhoid fever and treatment for Pneumonia.