Global dynamics in a multi-group epidemic model for disease with latency spreading and nonlinear transmission rate |
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Authors: | Haitao Song Jinliang Wang and Weihua Jiang |
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Institution: | Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, China,School of Mathematical Science, Heilongjiang University, Harbin, Heilongjiang 150080,China and Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, China |
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Abstract: | In this paper, we investigate a class of multi-group epidemic models with general exposed distribution and nonlinear incidence rate. Under biologically motivated assumptions, we show that the global dynamics are completely determined by the basic production number $R_0$. The disease-free equilibrium is globally asymptotically stable if $R_0\leq1$, and there exists a unique endemic equilibrium which is globally asymptotically stable if $R_0>1$. The proofs of the main results exploit the persistence theory in dynamical system and a graph-theoretical approach to the method of Lyapunov functionals. A simpler case that assumes an identical natural death rate for all groups and a gamma distribution for exposed distribution is also considered. In addition, two numerical examples are showed to illustrate the results. |
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Keywords: | Multi-group epidemic model Exposed distribution Global stability Lyapunov functional Graph-theoretic approach |
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