Stability analysis of a deterministic vaccination model with non-monotonic incidence rate

Abstract

In this study, a deterministic epidemic model with vaccination and non-monotonic incidence rate is considered. This model also included the effect of temporary immunity. The model shows a disease free and an endemic equilibrium. Threshold R0 (also known as basic reproduction number) is obtained, which gives the complete dynamics of the disease. If this threshold is less than unity, the disease-free equilibrium exists and infection disappears. If it is greater than unity, the endemic equilibrium exists and infection persists. The local and global stability of disease-free and endemic equilibrium are established. Global stability of positive equilibrium is proved by using a geometric approach given by Li and Muldowney. Numerical simulations are also given to support theoretical findings.