| Volume 6, Number 1, 2016, Pages 47-64 DOI：10.11948/2016005 |
| Global dynamics in a multi-group epidemic model for disease with latency spreading and nonlinear transmission rate |
| Haitao Song,Jinliang Wang,Weihua Jiang |
| Keywords:Multi-group epidemic model Exposed distribution Global stability Lyapunov functional Graph-theoretic approach. |
| 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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