GLOBAL DYNAMICS IN A MULTI-GROUP EPIDEMIC MODEL FOR DISEASE WITH LATENCY SPREADING AND NONLINEAR TRANSMISSION RATE

Haitao Song; Jinliang Wang; Weihua Jiang

doi:10.11948/2016005

2016 Volume 6 Issue 1

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Haitao Song, Jinliang Wang, Weihua Jiang. GLOBAL DYNAMICS IN A MULTI-GROUP EPIDEMIC MODEL FOR DISEASE WITH LATENCY SPREADING AND NONLINEAR TRANSMISSION RATE[J]. Journal of Applied Analysis & Computation, 2016, 6(1): 47-64. doi: 10.11948/2016005

Citation:

Haitao Song, Jinliang Wang, Weihua Jiang. GLOBAL DYNAMICS IN A MULTI-GROUP EPIDEMIC MODEL FOR DISEASE WITH LATENCY SPREADING AND NONLINEAR TRANSMISSION RATE[J]. Journal of Applied Analysis & Computation, 2016, 6(1): 47-64. doi: 10.11948/2016005

GLOBAL DYNAMICS IN A MULTI-GROUP EPIDEMIC MODEL FOR DISEASE WITH LATENCY SPREADING AND NONLINEAR TRANSMISSION RATE

1 Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, P. R. China;
2 School of Mathematical Science, Heilongjiang University, Harbin, Heilongjiang 150080, P. R. China;
3 Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, P. R. China

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Abstract

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 R₀. The disease-free equilibrium is globally asymptotically stable if R₀ ≤ 1, and there exists a unique endemic equilibrium which is globally asymptotically stable if R₀>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.
- Multi-group epidemic model /
- Exposed distribution /
- Global stability /
- Lyapunov functional /
- Graph-theoretic approach
MSC: 34D23;90D30

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References

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