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Global dynamics of delay epidemic models with nonlinear incidence rate and relapse. (English) Zbl 1208.34125
Summary: 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 0 1 and that the disease becomes endemic if 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.
MSC:
34K60Qualitative investigation and simulation of models
34K20Stability theory of functional-differential equations
92D30Epidemiology
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