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Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment

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  • Rajasekar, S.P.
  • Pitchaimani, M.
  • Zhu, Quanxin

Abstract

In this paper, a stochastic epidemic model with logistic growth and saturated treatment is formulated to probe the effect of white noise on population. We show that the proposed autonomous stochastic model possess a unique and non-negative solution. We obtain the sufficient conditions for extinction of the infectious disease and persistent in the mean of the stochastic autonomous epidemic model with probability one. That is, if ℛ0˜<1, under some parametric conditions then the infection goes to extinction with probability one and if ℛ0˜>1, under some parametric conditions then the infection persist with probability one. By using Has’minskii’s theory of periodic solutions, we show that the stochastic non-autonomous epidemic model has at least one nontrivial positive θ-periodic solution. Finally, the theoretical results are illustrated by numerical simulations which obtains some additional interesting phenomena.

Suggested Citation

  • Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2020. "Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    • Handle: RePEc:eee:phsmap:v:538:y:2020:i:c:s0378437119315122
    DOI: 10.1016/j.physa.2019.122649
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    References listed on IDEAS

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    Cited by:

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    3. Rajasekar, S.P. & Pitchaimani, M., 2020. "Ergodic stationary distribution and extinction of a stochastic SIRS epidemic model with logistic growth and nonlinear incidence," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    4. Wang, Qi & Xiang, Kainan & Zhu, Chunhui & Zou, Lang, 2023. "Stochastic SEIR epidemic models with virus mutation and logistic growth of susceptible populations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 289-309.
    5. M., Pitchaimani & M., Brasanna Devi, 2020. "Random effects in HIV infection model at Eclipse stage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    6. Saha, Sangeeta & Dutta, Protyusha & Samanta, Guruprasad, 2022. "Dynamical behavior of SIRS model incorporating government action and public response in presence of deterministic and fluctuating environments," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    7. Antonio Barrera & Patricia Román-Román & Francisco Torres-Ruiz, 2021. "Hyperbolastic Models from a Stochastic Differential Equation Point of View," Mathematics, MDPI, vol. 9(16), pages 1-18, August.
    8. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Dynamical behavior of a higher order stochastically perturbed SIRI epidemic model with relapse and media coverage," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

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