Dynamics of a Stochastic BrucellosisModel with Vaccination and Environmental Pollution Transmission

• Xiaodong Wang ^[1] ; Kai Wang ^[1] ; Lei Wang ^[1] ; Zhidong Teng ^[1]
  1. [1] Xinjiang Medical University

     Xinjiang Medical University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-01158-x
• Enlaces
  • Texto completo
• Resumen

  • In this paper, the dynamical behavior of a stochastic brucellosis model that incorporates vaccination and environmental pollution transmission is investigated. Some preliminary results are first proposed, which include the existence of global positive solutions and the stability of the corresponding deterministic model. Secondly, two distinct threshold values Rs0 and m are derived for the stochastic extinction of the disease by utilizing two different calculation methods. That is, when Rs0 < 1 or m < 0, then the disease will be extinct with probability one, irrespective of whether the basic reproduction number R0 of the deterministic model is greater than 1 or less than 1. Additionally, a new threshold RS 0 is established for the persistence in the mean of disease and the existence of a stationary distribution for the model. Namely, if RS 0 > 1, the disease will persist in the mean with probability one, and any positive solution is ergodic, and possessing a unique stationary distribution. Finally, the numerical simulations are presented to validate the theoretical findings, and the impacts of key parameters and stochastic terms on the spread of brucellosis are further explored.

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