Global Stability of a Diffusive SEIR Epidemic Model with Distributed Delay

TL;DR

This paper analyzes a reaction-diffusion SEIR epidemic model with distributed delay, establishing conditions for global stability of disease-free and endemic states, supported by Lyapunov functionals and numerical simulations.

Contribution

It introduces a globally well-posed reaction-diffusion SEIR model with distributed delay and nonlinear incidence, proving stability results using Lyapunov functionals.

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

We study the global dynamics of a reaction-diffusion SEIR infection model with distributed delay and nonlinear incidence rate. The well-posedness 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.