Persistence and extinction of disease in non-autonomous SIRS epidemic models with disease-induced mortality

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• 作者：Zhidong Teng ; Yanping Liu ; Long Zhang
• 关键词：Non-autonomous SIRS model ; Disease ; Threshold value ; Persistence ; Permanence ; Extinction
• 刊名：Nonlinear Analysis
• 出版年：2008
• 出版时间：15 October 2008
• 年：2008
• 卷：69
• 期：8
• 页码：2599-2614
• 全文大小：359 K

文摘

In this paper, non-autonomous SIRS epidemic models with bilinear incidence and disease-induced mortality are studied. Under the quite weak assumptions, the sufficient and necessary conditions on the permanence and strong persistence of the disease and the sufficient condition on the extinction of the disease are established. Some new threshold values of the integral form , and are obtained. We prove that the disease is permanent if and only if , and if or , then the disease is extinct. As applications of the main results, we discuss the periodic and almost periodic models. The corresponding basic reproductive numbers R₀ are obtained. We show that if R₀>1, then the disease is permanent and if R₀≤1, then the disease is extinct.