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Threshold dynamics of a nonlinear multi-group epidemic model with two infinite distributed delays. (English) Zbl 1366.34110
Summary: The global stability of equilibria is investigated for a nonlinear multi-group epidemic model with latency and relapses described by two distributed delays. The results show that the global dynamics are completely determined by the basic reproduction number $$\mathcal{R}_0$$ under certain reasonable conditions on the nonlinear incidence rate. Moreover, compared with the results in [M. Y. Li and Z. Shuai, J. Differ. Equations 248, No. 1, 1–20 (2010; Zbl 1190.34063)], it is found that the two distributed delays have no impact on the global behaviour of the model. Our study improves and extends some known results in recent literature.

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