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《Chinese Journal of Engineering Mathematics》 2009-03
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Analysis of an SIS Epidemic Model with Temporary Immunity and Nonlinear Incidence Rate

HU Zhi-xing, CHENG Xiao-wei, MA Wan-biao (Department of Applied Mathematics and Mechanics, Beijing University of Science and Technology, Beijing 100083)  
Studied in this paper is an SIS epidemic model with a time delay, a general contact rate, constant recruitment and disease-caused death. It is assumed that the time delay represents the temporary immunity period, i.e., the time from recovered to becoming the susceptible again, which incorporates the infected recovery and the recovery of the susceptible due to vaccinating. The basic reproduction number is found. The existence of disease-free and endemic equilibria is analyzed. By the Hurwitz criterion, the local asymptotic stability of disease-free and endemic equilibria is investigated. By means of the Liapunov functional and Lasalle’s invariant principle, we prove the global stability of the disease-free equilibrium and the endemic equilibrium in a special case that the incidence rate is bilinear. It is shown that the reproduction number is related with the rate of effcient vaccination for the susceptible, and the disease may be eradicated by increasing the effcient vaccination rate. Numerical simulations support our analytical conclusions.
【Fund】: The National Natural Science Foundation of China (10671011)
【CateGory Index】: O175.14
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