Stability Analysis of a Diffusive SVIR Epidemic Model with Distributed Delay, Imperfect Vaccine and General Incidence Rate

TL;DR

This paper analyzes a reaction-diffusion SVIR epidemic model incorporating distributed delay, imperfect vaccination, and general incidence rate, establishing conditions for disease stability and supporting findings with numerical simulations.

Contribution

It introduces a comprehensive SVIR model with distributed delay and nonlinear incidence, proving stability results and providing numerical validation.

Findings

Disease-free equilibrium is globally stable when R0 ≤ 1.

Endemic equilibrium is globally stable when R0 > 1.

Numerical simulations confirm theoretical stability results.

Abstract

In this chapter, we consider a reaction-diffusion SVIR infection model with dis-tributed delay and nonlinear incidence rate. The wellposedness of the proposed model is proved. By means of Lyapunov functionals, we show that the disease-free equilibrium state is globally asymptotically stable when the basic reproduction number is less or equal than one, and that the disease endemic equilibrium is globally asymptotically stable when the basic reproduction number is greater than one. Numerical simulations are provided to illustrate the obtained theoretical results.