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Dynamic threshold probe of stochastic SIR model with saturated incidence rate and saturated treatment function

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

Abstract

In this discourse, we establish and investigate the pervasive of environmental variability in a deterministic epidemic model with saturated incidence rate and saturated treatment function. We exemplify that the proposed stochastic model reveals an exclusive and universal positive solution. We deal with equilibrium solution of stochastic model which contribute few biological intrinsic manifestation for the model. We attain the sufficient conditions for extinction of the infectious disease and persistent in the mean of the stochastic epidemic model with probability one, if ℛ0˜<1 and if ℛ0˜>1 respectively. Eventually, numerical probing is furnished to elucidate the analytical outcomes.

Suggested Citation

  • Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2019. "Dynamic threshold probe of stochastic SIR model with saturated incidence rate and saturated treatment function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    • Handle: RePEc:eee:phsmap:v:535:y:2019:i:c:s0378437119313329
    DOI: 10.1016/j.physa.2019.122300
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    References listed on IDEAS

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    1. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2017. "Stationary distribution and extinction of a stochastic SIRS epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 510-517.
    2. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Asymptotic behavior of a stochastic delayed HIV-1 infection model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 867-882.
    3. M. Pitchaimani & R. Rajaji, 2016. "Stochastic Asymptotic Stability of Nowak-May Model with Variable Diffusion Rates," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 901-910, September.
    4. Rajasekar, S.P. & Pitchaimani, M., 2019. "Qualitative analysis of stochastically perturbed SIRS epidemic model with two viruses," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 207-221.
    5. Liu, Qun & Chen, Qingmei, 2015. "Analysis of the deterministic and stochastic SIRS epidemic models with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 140-153.
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    Cited by:

    1. Jiang, Jiehui & Ma, Jie, 2023. "Dynamic analysis of pandemic cross-regional transmission considering quarantine strategies in the context of limited medical resources," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    2. 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).
    3. 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).
    4. 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).
    5. Sabbar, Yassine & Kiouach, Driss & Rajasekar, S.P. & El-idrissi, Salim El Azami, 2022. "The influence of quadratic Lévy noise on the dynamic of an SIC contagious illness model: New framework, critical comparison and an application to COVID-19 (SARS-CoV-2) case," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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