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Ergodic stationary distribution and extinction of a stochastic eco-epidemiological model with disease in prey

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  • Mishra, Shivam Kumar
  • Abbas, Syed
  • Debbouche, Amar

Abstract

We investigate a stochastic eco-epidemiological framework where disease transmission occurs within the prey population and interacts with the predators under environmental noise. By employing stochastic Lyapunov methods and Khasminskii’s theory, we establish persistence-extinction conditions and confirm the existence of an ergodic stationary distribution. Furthermore, we determine the threshold parameters that govern the long-term dynamics of the system. Theoretical results are supported through numerical simulations which illustrate how variations in key biological and noise parameters affect the coexistence and extinction of species. The study highlights the significant influence of stochastic perturbations on disease dynamics and provides useful insights into the stability of eco-epidemiological systems under random environmental effects.

Suggested Citation

  • Mishra, Shivam Kumar & Abbas, Syed & Debbouche, Amar, 2026. "Ergodic stationary distribution and extinction of a stochastic eco-epidemiological model with disease in prey," Chaos, Solitons & Fractals, Elsevier, vol. 203(C).
    • Handle: RePEc:eee:chsofr:v:203:y:2026:i:c:s0960077925016741
    DOI: 10.1016/j.chaos.2025.117661
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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. Sourav Roy & Sayantan Nag Chowdhury & Prakash Chandra Mali & Matjaž Perc & Dibakar Ghosh, 2022. "Eco-evolutionary dynamics of multigames with mutations," PLOS ONE, Public Library of Science, vol. 17(8), pages 1-26, August.
    3. 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).
    4. Belyaev, Alexander & Baiardi, Lorenzo Cerboni & Jungeilges, Jochen & Perevalova, Tatyana, 2025. "Noise-induced ecological shifts in a prey–predator model," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    5. Tyagi, Swati & Martha, Subash C. & Abbas, Syed & Debbouche, Amar, 2021. "Mathematical modeling and analysis for controlling the spread of infectious diseases," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    6. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "A stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
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