Mathematical Biosciences and Engineering, 2016, 13(1): 209-225. doi: 10.3934/mbe.2016.13.209

Primary: 92B05, 34D23; Secondary: 34D20.

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Global analysis on a class of multi-group SEIR model with latency and relapse

1. School of Mathematical Science, Heilongjiang University, Harbin 150080
2. Department of Mathematics, Tongji University, Shanghai 200092

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 torelapse 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 indynamical systems, Lyapunov functionals guided by graph-theoretical approach.
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