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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.

##### MSC:
 92D30 Epidemiology 34K20 Stability theory of functional-differential equations 34D23 Global stability of ODE 05C90 Applications of graph theory 34K60 Qualitative investigation and simulation of models 34D05 Asymptotic stability of ODE
##### Keywords:
multi-group model; global stability; Lyapunov functional
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##### References:
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