Analysis of epidemic models with demographics in metapopulation networks

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• 作者：Jianrong Wang ; Maoxing Liu ; ^{liumaoxing@126.com} ; Youwen Li
• 关键词：SIS epidemic model ; Demographics ; Metapopulation networks ; Stability
• 刊名：Physica A
• 出版年：2013
• 出版时间：1 April, 2013
• 年：2013
• 卷：392
• 期：7
• 页码：1621-1630
• 全文大小：601 K

文摘

In this paper, two susceptible-infected-susceptible (SIS) epidemic models are presented and analyzed by reaction-diffusion processes with demographics in metapopulation networks. Firstly, an SIS model with constant-inputting is discussed. The model has a disease-free equilibrium, which is locally asymptotically stable when the basic reproduction number is less than unity, otherwise it is unstable. It has an endemic equilibrium, which is globally asymptotically stable. Secondly, in another SIS model, the birth rate is the form of Logistic. Similarly, the stability of disease-free equilibrium and endemic equilibrium is also proved. Finally, numerical simulations are performed to illustrate the analytical results.