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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 \(\operatorname{Re}_{0}\leq 1\) and that the disease becomes endemic if \(\operatorname{Re}_{0}>1\). Applications are also made to the special case with a discrete delay and the result confirms that the endemic equilibrium is globally asymptotically stable.

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K20 Stability theory of functional-differential equations
92D30 Epidemiology
Full Text: DOI
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