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Unraveling the transmission mechanism of animal disease: Insight from a stochastic eco-epidemiological model driven by Lévy jumps

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  • Zhao, Zhuoying
  • Zhang, Xinhong

Abstract

In order to study the transmission mechanism of animal disease, thereby better controlling it and protecting human health, this work deals with a stochastic eco-epidemiological model, in which the infectious force of animal disease is described by the half-saturated incidence rate. And we attempt to introduce white noises and Lévy jumps as environmental perturbances in our proposed model. Before analyzing the dynamical characteristics of the stochastic model, the article firstly proves that there is a unique global positive solution. Then, we explore the thresholds to make the animal disease extinct from the perspective of environmental perturbances, which provide valuable suggestions for controlling the outbreak of animal disease. Furthermore, we analyze the long-term dynamical behavior of the stochastic model by establishing sufficient condition for the existence of a stationary distribution, which is of great significance for maintaining the ecological balance. Finally, we verify the theoretical results by numerical simulations and explore the impacts of white noises and Lévy jumps on the eco-epidemiological model, contributing to a better understanding of the stochastic model’s dynamical behaviors and the development of effective animal disease control strategies.

Suggested Citation

  • Zhao, Zhuoying & Zhang, Xinhong, 2025. "Unraveling the transmission mechanism of animal disease: Insight from a stochastic eco-epidemiological model driven by Lévy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924014115
    DOI: 10.1016/j.chaos.2024.115859
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    References listed on IDEAS

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    1. Meng, Xinzhu & Li, Fei & Gao, Shujing, 2018. "Global analysis and numerical simulations of a novel stochastic eco-epidemiological model with time delay," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 701-726.
    2. Zhou, Yanli & Zhang, Weiguo, 2016. "Threshold of a stochastic SIR epidemic model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 204-216.
    3. Kumar, Ajay & Kumar, Sunil, 2022. "A study on eco-epidemiological model with fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    4. Zhang, Xinhong & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Dynamics of a stochastic SIS model with double epidemic diseases driven by Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 767-777.
    5. Bagheri, Safieh & Akrami, Mohammad Hossein & Loghmani, Ghasem Barid & Heydari, Mohammad, 2024. "Traveling wave in an eco-epidemiological model with diffusion and convex incidence rate: Dynamics and numerical simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 347-366.
    6. Selvan, T. Tamil & Kumar, M., 2024. "Stationary distribution of a double epidemic stochastic model driven by saturated incidence rates," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    7. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
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