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Global stability of multi-group epidemic models with distributed delays. (English) Zbl 1175.92046

Summary: We investigate a class of multi-group epidemic models with distributed delays. We establish that the global dynamics are completely determined by the basic reproduction number \(\mathcal R_0\). More specifically, we prove that, if \(\mathcal R_0\leqslant 1\), then the disease-free equilibrium is globally asymptotically stable; if \(\mathcal R_0>1\), then there exists a unique endemic equilibrium and it is globally asymptotically stable. Our proof of global stability of the endemic equilibrium utilizes a graph-theoretical approach to the method of Lyapunov functionals.

MSC:

92D30 Epidemiology
34K20 Stability theory of functional-differential equations
34D23 Global stability of solutions to ordinary differential equations
05C90 Applications of graph theory
34K60 Qualitative investigation and simulation of models involving functional-differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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