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Stochastic SEIR epidemic models with virus mutation and logistic growth of susceptible populations

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  • Wang, Qi
  • Xiang, Kainan
  • Zhu, Chunhui
  • Zou, Lang

Abstract

This article introduces a kind of stochastic SEIR models containing virus mutation and logistic growth of susceptible populations, whose deterministic versions have a positively invariant set and globally asymptotically stable equilibrium points. For these stochastic SEIR epidemic models, we prove they have a unique global positive solution, and also obtain sufficient conditions respectively for survival and extinction of the infectious disease. Eventually, we validate our theoretical findings using numerical simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:212:y:2023:i:c:p:289-309
    DOI: 10.1016/j.matcom.2023.04.035
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    References listed on IDEAS

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    1. Xu, Rui & Wang, Zhili & Zhang, Fengqin, 2015. "Global stability and Hopf bifurcations of an SEIR epidemiological model with logistic growth and time delay," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 332-342.
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    3. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Ahmad, Bashir, 2017. "Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 476(C), pages 58-69.
    4. 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).
    5. 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.
    6. 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).
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