Mathematical Theory and Applications ›› 2024, Vol. 44 ›› Issue (4): 70-87.doi: 10.3969/j.issn.1006-8074.2024.04.005

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Global Stability and Bifurcation Analysis of a Cholera Transmission Model

Liu Qiumei , Liu Lingling*, Xu Fang   

  1. Institute for Artificial Intelligence School of Science, Southwest Petroleum University, Chengdu 610500, China
  • Online:2024-12-28 Published:2025-01-21
  • Contact: Liu Lingling
  • Supported by:

    This work is supported by the National Natural Science

    Foundation of China (No. 12171337), the Central Government Guided Local Science and Technology Development Projects

    (No.2024ZYD0059), the Natural Science

    Foundation of Sichuan Province (No. 2022NSFSC0529) and the Open Research Fund Program of Data Recovery Key Laboratory of Sichuan Province (No. DRN2405)

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Abstract:

This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again. The threshold for determining disease prevalence is established, and the parameter conditions for

the existence of equilibria are discussed. The Routh-Hurwitz criterion is applied to demonstrate the local asymptotic stability of equilibria.

By utilizing composite matrices and geometric techniques, the global dynamic behavior of the endemic equilibrium is investigated, and the sufficient conditions for its global asymptotic stability are derived. Furthermore, the disease-free equilibrium is a saddle-node when the basic reproductive number is 1, and tthe transcritical bifurcation in this case is discussed.

Key words: Cholera model , Basic reproductive number, Global asymptotic stability, Saddle-node, Transcritical bifurcation

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