Global stability of general cholera models with nonlinear incidence and removal rates

被引:44
作者
Wang, Yi [1 ,2 ]
Cao, Jinde [1 ,3 ]
机构
[1] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China
[2] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
[3] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah 21589, Saudi Arabia
来源
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS | 2015年 / 352卷 / 06期
基金
中国国家自然科学基金;
关键词
EPIDEMIC; DYNAMICS; TRANSMISSION; INFECTION; PATHOGEN; DISEASES; NUMBERS; HOST;
D O I
10.1016/j.jfranklin.2015.03.030
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In the real world, cholera may be transmitted through both direct human-to-human and indirect water-to-human mechanisms, but most of the previous studies assume linear progression rates for multistage models or linear death rate of infected individuals, which limits well understanding of the transmission dynamics of cholera. In this paper, we formulate a general compartmental multistage cholera model that incorporates nonlinear host recruitment, nonlinear incidence, nonlinear removal and nonlinear progression rates. Under biologically motivated assumptions, the basic reproduction number R-0 is derived in detail, and presents a sharp threshold property. In particular, if R-0 < 1, the disease-free equilibrium is globally asymptotically stable, and cholera dies out from all stages of host and water independent of initial burden; whereas if R-0 > 1, by employing Lyapunov functions and graph-theoretic results the endemic equilibrium is globally asymptotically stable, which also guarantees its uniqueness. The results are of biological significance for devising control strategies and possible extensions of the model are also discussed. (C) 2015 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
引用
收藏
页码:2464 / 2485
页数:22
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