Stability analysis of an SIR epidemic model with homestead-isolation on the susceptible and infectious, immunity, relapse and general incidence rate

In this paper, we propose the global dynamics of an SIR epidemic model with distributed latent period, immunity, relapse, homestead-isolation of the susceptible and infectious individuals and general incidence rate. The resulting model has a disease-free equilibrium and if R-0 > 1, then the SIR epidemic model admits a unique endemic equilibrium. By using suitable Lyapunov functionals and LaSalle's invariance principle, the global stability of the disease-free equilibrium and the endemic equilibrium is established, under suitable monotonicity conditions on the incidence function.