An epidemic model with different distributed latencies and nonlinear incidence rate

An SEIR epidemic model with different distributed latencies and general nonlinear incidence is presented and studied. By constructing suitable Lyapunov functionals, the biologically realistic sufficient conditions for threshold dynamics are established. It is shown that the infection-free equilibrium is globally attractive when the basic reproduction number is equal to or less than one, and that the disease becomes globally attractively endemic when the basic reproduction number is larger than one. The criteria in this paper generalize and improve some previous results in the literatures.