Existence of traveling waves by means of fixed point theory for an epidemic model with Hattaf-Yousfi incidence rate and temporary immunity acquired by vaccination

Abstract

The main aim of this work is to investigate the existence of traveling waves of an epidemic model with temporary immunity acquired by vaccination. The incidence rate of the disease used in the epidemic model is of the form Hattaf-Yousfi that includes many types existing in the literature. By means of Schauder fixed point theorem and construction of a pair of upper and lower solutions, the existence of traveling wave solution that connects the disease-free equilibrium and the endemic equilibrium is obtained and characterized by two parameters that are the basic reproduction number and the minimal wave speed.