Dynamics and density function for a stochastic anthrax epidemic model

Bing Zhao; Shuting Lyu; Qimin Zhang; Bing Zhao; Shuting Lyu; Qimin Zhang

doi:10.3934/era.2024072

Electronic Research Archive

2024, Volume 32, Issue 3: 1574-1617. doi: 10.3934/era.2024072

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Research article

Dynamics and density function for a stochastic anthrax epidemic model

Bing Zhao ¹,
Shuting Lyu ^{1
,
,},
Qimin Zhang ^{1,2
,
,}

1.
School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China
2.
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China

Received: 20 November 2023 Revised: 29 January 2024 Accepted: 02 February 2024 Published: 19 February 2024

In response to the pressing need to understand anthrax biology, this paper focused on the dynamical behavior of the anthrax model under environmental influence. We defined the threshold parameter $ R^s $, when $ R^s > 1 $; the disease was almost certainly present and the model exists a unique ergodic stationary distribution. Subsequently, statistical features were employed to analyze the dynamic behavior of the disease. The exact representation of the probability density function in the vicinity of the quasi-equilibrium point was determined by the Fokker-Planck equation. Finally, some numerical simulations validated our theoretical results.
- stochastic anthrax model,
- ergodic stationary distribution,
- Fokker-Planck equation,
- probability density function
Citation: Bing Zhao, Shuting Lyu, Qimin Zhang. Dynamics and density function for a stochastic anthrax epidemic model[J]. Electronic Research Archive, 2024, 32(3): 1574-1617. doi: 10.3934/era.2024072

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Abstract

In response to the pressing need to understand anthrax biology, this paper focused on the dynamical behavior of the anthrax model under environmental influence. We defined the threshold parameter $ R^s $, when $ R^s > 1 $; the disease was almost certainly present and the model exists a unique ergodic stationary distribution. Subsequently, statistical features were employed to analyze the dynamic behavior of the disease. The exact representation of the probability density function in the vicinity of the quasi-equilibrium point was determined by the Fokker-Planck equation. Finally, some numerical simulations validated our theoretical results.

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