Global asymptotic stability of a diffusive SVIR epidemic model with immigration of individuals

Abstract

In this article, we consider a spatially SVIR model of infectious disease epidemics which allows for continuous immigration of all classes of individuals. We show that the proposed model has a unique steady state that is asymptotically stable. Using an appropriately constructed Lyapunov functional, we establish its global asymptotic stability. Numerical results obtained through Matlab simulations are presented to confirm the results.

Keywords

• Reaction diffusion systems
• SVIR
• immigration
• Lyapunov functional
• large time behavior