Dynamics of a Vector-Borne model with direct transmission and age of infection

Abstract

In this paper we the study of dynamics of time since infection structured vector born model with the direct transmission. We use standard incidence term to model the new infections. We analyze the corresponding system of partial differential equation and obtain an explicit formula for the basic reproduction number ℜ0. The diseases-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number is less than one, ℜ0 < 1. Endemic equilibrium exists and is locally asymptotically stable when ℜ0 > 1. The disease will persist at the endemic equilibrium whenever the basic reproduction number is greater than one.