Further stability analysis for a multi-group SIRS epidemic model with varying total population size

In this paper, we focus on a multi-group SIRS epidemic model with varying total population size and cross patch infection between different groups. By applying a monotone iterative approach to the model, we establish a new sufficient condition for large recovery rates δk,k=1,2,…,n on the global asymptotic stability of endemic equilibrium of the model. By combining the sufficient condition for small δk,k=1,2,…,n obtained by Lyapunov functional approach, we obtain new sufficient conditions which extend the known results in recent literature.