SEIR Childhood Disease Model With Constant Vaccination Strategy

Abstract

Childhood diseases are increasingly becoming the most common form of infectious diseases. These diseases include measles, mumps, Influenza, smallpox, chicken pox, Rubella, Polio etc., which take special interest to children under-five years who are born highly susceptible. Childhood vaccination programs and campaigns have yielded in high levels of permanent immunity against childhood diseases. Childhood diseases have several characteristics which make them well fit for mathematical modeling such as a relatively short incubation and infectious periods and confer permanent immunity when vaccinated. In this study, a SEIR model that monitors the temporal transmission dynamics of a childhood disease in the presence of preventive vaccine was formulated and analyzed. We normalized the governing model. Maple was used in carrying out the simulations. Semi-numerical Adomain Decomposition method was used to compute an approximate solution of the non-linear system of differential equations governing the model. The results obtained by Adomain Decomposition method are compared with the pure numerical classical fourth order Runge-Kutta integration method to gauge it’s effectiveness in describing the transmission dynamics of the model. Graphical results were presented and discussed to illustrate the solution of the problem. The achieved results reveals that the disease will die out within the community if the vaccination coverage is above the critical vaccination proportion, Pc.