Modelling childhood disease outbreak in a community with inflow of susceptible and vaccinated new-born

Abstract

This paper investigates the transmission dynamics of a Childhood disease outbreak in a community with direct inflow of susceptible and vaccinated new-born. Qualitative analysis of the SEIR nonlinear model is performed for disease free and endemic equilibria using the stability theory of differential equations. The disease free state is found to be both locally and globally asymptotically stable when the vaccination reproductive number v R is less than unity. In addition, the model exhibits transcritical forward bifurcation phenomenon and the sensitivity indices of the vaccination reproductive number with respect to various model parameters is determined. Using the Adomian decomposition method (ADM) and the fourth order Runge-Kutta integration scheme (RK4), the semi-analytical and numerical solutions of the nonlinear model are obtained. Pertinent results are displayed graphically and in tabular form. A vaccination coverage threshold is obtained above which the disease will be effectively eliminated from the community.