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Global analysis on a class of multi-group SEIR model with latency and relapse. (English) Zbl 1326.92071

Summary: In this paper, we investigate the global dynamics of a multi-group SEIR epidemic model, allowing heterogeneity of the host population, delay in latency and delay due to relapse distribution for the human population. Our results indicate that when certain restrictions on nonlinear growth rate and incidence are fulfilled, the basic reproduction number \(\mathfrak{R}_0\) plays the key role of a global threshold parameter in the sense that the long-time behaviors of the model depend only on \(\mathfrak{R}_0\). The proofs of the main results utilize the persistence theory in dynamical systems, Lyapunov functionals guided by graph-theoretical approach.

MSC:

92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
05C90 Applications of graph theory
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