Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission

Ming-Tao Li, Gui-Quan Sun, Juan Zhang and Zhen Jin

Discrete Dynamics in Nature and Society, 2013, vol. 2013, 1-11

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:703826

DOI: 10.1155/2013/703826

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