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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 $\cal R_0$. More specifically, we prove that, if $\cal R_0\leqslant 1$, then the disease-free equilibrium is globally asymptotically stable; if $\cal R_0>1$, 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.

34K20Stability theory of functional-differential equations
34D23Global stability of ODE
05C90Applications of graph theory
34K60Qualitative investigation and simulation of models
34D05Asymptotic stability of ODE
Full Text: DOI
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