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.
