Stochastic stability and instability of an epidemic model with relapse

摘要

In this paper, we present a stochastic epidemic model with relapse. First, we prove global positivity of solutions. Then we discuss stability of the disease-free equilibrium state and we show extinction of epidemics using Lyapunov functions. Furthermore we show persistence of the disease under some conditions on parameters of the model. Our numerical simulations confirm the analytical results.