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Analysis of epidemic models with demographics in metapopulation networks

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  • Wang, Jianrong
  • Liu, Maoxing
  • Li, Youwen

Abstract

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.

Suggested Citation

  • Wang, Jianrong & Liu, Maoxing & Li, Youwen, 2013. "Analysis of epidemic models with demographics in metapopulation networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1621-1630.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:7:p:1621-1630
    DOI: 10.1016/j.physa.2012.12.007
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    References listed on IDEAS

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    1. Julien Arino & P. van den Driessche, 2003. "A multi-city epidemic model," Mathematical Population Studies, Taylor & Francis Journals, vol. 10(3), pages 175-193.
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