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

Haitao Song | Zendy; Jinliang Wang | Zendy; Weihua Jiang | Zendy

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

Author(s) -

Haitao Song,

Jinliang Wang,

Weihua Jiang

Publication year - 2016

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2016005

Subject(s) - lyapunov function , mathematics , transmission rate , stability theory , epidemic model , nonlinear system , mathematical proof , distribution (mathematics) , statistical physics , transmission (telecommunications) , mathematical analysis , computer science , population , physics , demography , quantum mechanics , telecommunications , geometry , sociology

In this paper, we investigate a class of multi-group epidemic models with general exposed distribution and nonlinear incidence rate. Under biologi- cally 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 endem- ic 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 gam- ma distribution for exposed distribution is also considered. In addition, two numerical examples are showed to illustrate the results.

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