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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.

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