The asymptotic stability for an SIQS epidemic model with diffusion

Abstract

In this paper, an SIQS epidemic model with constant recruitment and standard incidence is investigated. Quarantine is taken into consideration on the basis of SIS model. The asymptotic stability of the equilibrium to a reaction–diffusion system with homogeneous Neumann boundary conditions is considered. Sufficient conditions for the local and global asymptotic stability are given by linearization and the method of upper and lower solutions and its associated monotone iterations. The result shows that the disease-free equilibrium is globally asymptotically stable if the contact rate is small.