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Global stability of multi-group SEIR epidemic models with distributed delays and nonlinear transmission. (English) Zbl 1254.92085
Summary: The dynamics of multi-group SEIR epidemic models with distributed and infinite delay and nonlinear transmission are investigated. We derive the basic reproduction number R 0 and establish that the global dynamics are completely determined by the values of R 0 : if R 0 1, then the disease-free equilibrium is globally asymptotically stable; if R 0 >1, then there exists a unique endemic equilibrium which is globally asymptotically stable. Our results contain those for single-group SEIR models with distributed and infinite delays. In the proof of global stability of the endemic equilibrium, we exploit a graph-theoretical approach to the method of Lyapunov functionals. The biological significance of the results is also discussed.
MSC:
92D30Epidemiology
37N25Dynamical systems in biology
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