期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 59, 期 9, 页码 3211-3221出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2010.03.009
关键词
SIRS epidemic model; Time delay; Saturation incidence; Temporary immunity; Stability; Bifurcation
资金
- National Natural Science Foundation of China [10671209, 10531030]
- Scientific Research Foundation for Returned Overseas Chinese Scholars, State Education Ministry
In this paper, a delayed SIRS epidemic model with saturation incidence and temporary immunity is investigated. The immunity gained by experiencing a disease is temporary, whenever infected the diseased individuals will return to the susceptible class after a fixed period. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is discussed. By comparison arguments, it is proved that if the basic reproduction number is less than unity, the disease-free equilibrium is globally asymptotically stable. If the basic reproduction number is greater than unity, by means of an iteration technique, sufficient conditions are obtained for the global asymptotic stability of the endemic equilibrium. Numerical simulations are carried out to illustrate the main theoretical results. (C) 2010 Elsevier Ltd. All rights reserved.
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