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Persistence and extinction for an age-structured stochastic SVIR epidemic model with generalized nonlinear incidence rate

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  • Lu, Ruoxin
  • Wei, Fengying

Abstract

We formulate an epidemic model with age of vaccination and generalized nonlinear incidence rate, where the total population consists of the susceptible, the vaccinated, the infected and the removed. We then reach a stochastic SVIR model when the fluctuation is introduced into the transmission rate. By using Itô’s formula and Lyapunov methods, we first show that the stochastic epidemic model admits a unique global positive solution with the positive initial value. We then obtain the sufficient conditions of the stochastic epidemic model. Moreover, the threshold tells the disease spreads or not is derived. If the intensity of the white noise is small enough and R˜0<1, then the disease eventually becomes extinct with negative exponential rate. If R˜0>1, then the disease is weakly permanent. The persistence in the mean of the infected is also obtained when the indicator Rˆ0>1, which means the disease will prevail in a long run. As a consequence, several illustrative examples are separately carried out with numerical simulations to support the main results of this paper.

Suggested Citation

  • Lu, Ruoxin & Wei, Fengying, 2019. "Persistence and extinction for an age-structured stochastic SVIR epidemic model with generalized nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 572-587.
    • Handle: RePEc:eee:phsmap:v:513:y:2019:i:c:p:572-587
    DOI: 10.1016/j.physa.2018.09.016
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    References listed on IDEAS

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    1. Zhang, Xinhong & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Dynamical behavior of a stochastic SVIR epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 94-108.
    2. Wang, Lianwen & Liu, Zhijun & Zhang, Xingan, 2016. "Global dynamics of an SVEIR epidemic model with distributed delay and nonlinear incidence," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 47-65.
    3. Teng, Zhidong & Wang, Lei, 2016. "Persistence and extinction for a class of stochastic SIS epidemic models with nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 507-518.
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    Cited by:

    1. Li, Yan & Ye, Ming & Zhang, Qimin, 2019. "Strong convergence of the partially truncated Euler–Maruyama scheme for a stochastic age-structured SIR epidemic model," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    2. Zhai, Xuanpei & Li, Wenshuang & Wei, Fengying & Mao, Xuerong, 2023. "Dynamics of an HIV/AIDS transmission model with protection awareness and fluctuations," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Bobryk, R.V., 2021. "Stability analysis of a SIR epidemic model with random parametric perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    4. Liu, Fangfang & Wei, Fengying, 2022. "An epidemic model with Beddington–DeAngelis functional response and environmental fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).

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