Abstract
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 ℜ 0 ≤ 1 and that the disease becomes endemic if ℜ 0 > 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].
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