期刊
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
卷 19, 期 10, 页码 3753-3765出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2014.03.028
关键词
Waterborne diseases; Multiple infected compartments; M-matrices; Lyapunov function; Global stability
类别
资金
- National Natural Science Foundation of China [61272530, 11072059]
- Specialized Research Fund for the Doctoral Program of Higher Education [20110092110017, 20130092110017]
- Natural Science Foundation of Jiangsu Province of China [BK2012741]
- Scientific Research Foundation of Graduate School of Southeast University [YBJJ1330]
In this paper, mathematical analysis is carried out for a multiple infected compartments model for waterborne diseases, such as cholera, giardia, and rotavirus. The model accounts for both person-to-person and water-to-person transmission routes. Global stability of the equilibria is studied. In terms of the basic reproduction number R-0, we prove that, if R-0 <= 1, then the disease-free equilibrium is globally asymptotically stable and the infection always disappears; whereas if R-0 >= 1, there exists a unique endemic equilibrium which is globally asymptotically stable for the corresponding fast-slow system. Numerical simulations verify our theoretical results and present that the decay rate of waterborne pathogens has a significant impact on the epidemic growth rate. Also, we observe numerically that the unique endemic equilibrium is globally asymptotically stable for the whole system. This statement indicates that the present method need to be improved by other techniques. (C) 2014 Elsevier B. V. All rights reserved.
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