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Stochastic Analysis of an Eco-Epidemic Model with Biological Control

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  • Debasis Mukherjee

    (Vivekananda College)

Abstract

This paper analyses a stochastic eco-epidemic model with biological control. The deterministic model is already investigated thoroughly and we mention here some important results. Here we demonstrate the nature of the limit cycle emerging through Hopf bifurcation which is not addressed before. Furthermore, we develop the stochastic model by introducing white noise in the deterministic system. The existence of a unique global positive solution and ultimate boundedness are examined for the stochastic model. Asymptotic mean square stability of the positive equilibrium point is discussed. Finally, numerical simulations are carried out to validate the results obtained.

Suggested Citation

  • Debasis Mukherjee, 2022. "Stochastic Analysis of an Eco-Epidemic Model with Biological Control," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2539-2555, December.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09947-0
    DOI: 10.1007/s11009-022-09947-0
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    References listed on IDEAS

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    1. Feng Rao, 2014. "Dynamics Analysis of a Stochastic SIR Epidemic Model," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, March.
    2. Greg Dwyer & Jonathan Dushoff & Susan Harrell Yee, 2004. "The combined effects of pathogens and predators on insect outbreaks," Nature, Nature, vol. 430(6997), pages 341-345, July.
    3. Mandal, Partha Sarathi & Banerjee, Malay, 2012. "Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1216-1233.
    4. 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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