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Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission

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  • Ming-Tao Li
  • Gui-Quan Sun
  • Juan Zhang
  • Zhen Jin

Abstract

For a multigroup cholera model with indirect transmission, the infection for a susceptible person is almost invariably transmitted by drinking contaminated water in which pathogens, V. cholerae , are present. The basic reproduction number is identified and global dynamics are completely determined by . It shows that is a globally threshold parameter in the sense that if it is less than one, the disease-free equilibrium is globally asymptotically stable; whereas if it is larger than one, there is a unique endemic equilibrium which is global asymptotically stable. For the proof of global stability with the disease-free equilibrium, we use the comparison principle; and for the endemic equilibrium we use the classical method of Lyapunov function and the graph-theoretic approach.

Suggested Citation

  • Ming-Tao Li & Gui-Quan Sun & Juan Zhang & Zhen Jin, 2013. "Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-11, December.
    • Handle: RePEc:hin:jnddns:703826
    DOI: 10.1155/2013/703826
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