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Global dynamics of multi‐group dengue disease model with latency distributions
Author(s) -
Huang Gang,
Wang Jinliang,
Zu Jian
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3252
Subject(s) - lyapunov function , dengue fever , mathematical proof , basic reproduction number , mathematics , latency (audio) , stability (learning theory) , epidemic model , graph , infectious disease (medical specialty) , exponential stability , disease , computer science , biology , virology , discrete mathematics , medicine , nonlinear system , population , telecommunications , physics , geometry , environmental health , quantum mechanics , machine learning , pathology
In this paper, by incorporating latencies for both human beings and female mosquitoes to the mosquito‐borne diseases model, we investigate a class of multi‐group dengue disease model and study the impacts of heterogeneity and latencies on the spread of infectious disease. Dynamical properties of the multi‐group model with distributed delays are established. The results showthat the global asymptotic stability of the disease‐free equilibrium and the endemic equilibrium depends only on the basic reproduction number. Our proofs for global stability of equilibria use the classical method of Lyapunov functions and the graph‐theoretic approach for large‐scale delay systems. Copyright © 2014 John Wiley & Sons, Ltd.