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Asymptotic behavior of stochastic multi-group epidemic models with distributed delays

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Listed:
  • Liu, Qun
  • Jiang, Daqing
  • Shi, Ningzhong
  • Hayat, Tasawar
  • Alsaedi, Ahmed

Abstract

In this paper, we introduce stochasticity into multi-group epidemic models with distributed delays and general kernel functions. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by using the method of stochastic Lyapunov functions, we carry out a detailed analysis on the asymptotic behavior of the stochastic model regarding of the basic reproduction number R0. If R0≤1, the solution of the stochastic system oscillates around the disease-free equilibrium E0, while if R0>1, the solution of the stochastic model fluctuates around the endemic equilibrium E∗. Moreover, we also establish sufficient conditions of these results.

Suggested Citation

  • Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2017. "Asymptotic behavior of stochastic multi-group epidemic models with distributed delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 527-541.
    • Handle: RePEc:eee:phsmap:v:467:y:2017:i:c:p:527-541
    DOI: 10.1016/j.physa.2016.10.034
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    References listed on IDEAS

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    1. Witbooi, Peter J., 2013. "Stability of an SEIR epidemic model with independent stochastic perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4928-4936.
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    4. 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:

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    4. Chinnadurai, M. & Fatini, Mohamed El & Rathinasamy, A., 2023. "Stochastic perturbation to 2-LTR dynamical model in HIV infected patients," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 473-497.
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    7. Zhou, Baoquan & Jiang, Daqing & Dai, Yucong & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary distribution and probability density function of a stochastic SVIS epidemic model with standard incidence and vaccination strategies," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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