Global dynamics of delay epidemic models with nonlinear incidence rate and relapse

A mathematical model for a disease with a general exposed distribution, the possibility of relapse and nonlinear incidence rate is proposed. By the method of Lyapunov functionals, it is shown that the disease dies out if ℜ0≤1ℜ0≤1 and that the disease becomes endemic if ℜ0>1ℜ0>1. Applications are also made to the special case with a discrete delay and the result confirms that the endemic equilibrium is globally asymptotically stable as suggested in van den Driessche et al. (2007) [4].