On non-pertubative approach to transmission dynamics of infectious diseases with waning immunity

Abstract

On this paper, a mathematical model that describes the dynamics of re-infection under the assumption that the vaccine induced immune protection may wane over time is presented. The qualitative analysis reveals that the disease eradication depends on vaccination coverage as well as on vaccine efficacy. Using an appropriate Lyapunov function, we establish that the disease free equilibrium is globally asymptotically stable if the vaccination coverage level exceeds a certain threshold value. Numerical algorithm based on Adomian decomposition method (ADM) coupled with Padé approximation technique and He's variational iteration method (VIM) are developed and implemented in MAPLE to approximate the solution of the governing non-linear systems. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.