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Stationary distribution and probability density function of a stochastic SVIS epidemic model with standard incidence and vaccination strategies

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  • Zhou, Baoquan
  • Jiang, Daqing
  • Dai, Yucong
  • Hayat, Tasawar
  • Alsaedi, Ahmed

Abstract

Considering the great effect of vaccination and the unpredictability of environmental variations in nature, a stochastic Susceptible-Vaccinated-Infected-Susceptible (SVIS) epidemic model with standard incidence and vaccination strategies is the focus of the present study. By constructing a series of appropriate Lyapunov functions, the sufficient criterion R0s>1 is obtained for the existence and uniqueness of the ergodic stationary distribution of the model. In epidemiology, the existence of a stationary distribution indicates that the disease will be persistent in a long term. By taking the stochasticity into account, a quasi-endemic equilibrium related to the endemic equilibrium of the deterministic system is defined. By means of the method developed in solving the general three-dimensional Fokker-Planck equation, the exact expression of the probability density function of the stochastic model around the quasi-endemic equilibrium is derived, which is the key aim of the present paper. In statistical significance, the explicit density function can reflect all dynamical properties of an epidemic system. Next, a simple result of disease extinction is obtained. In addition, several numerical simulations and parameter analyses are performed to illustrate the theoretical results. Finally, the corresponding results and conclusions are discussed at the end of the paper.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309929
    DOI: 10.1016/j.chaos.2020.110601
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    2. Rajchakit, G. & Sriraman, R. & Vignesh, P. & Lim, C.P., 2021. "Impulsive effects on Clifford-valued neural networks with time-varying delays: An asymptotic stability analysis," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    3. Saha, Pritam & Mondal, Bapin & Ghosh, Uttam, 2023. "Dynamical behaviors of an epidemic model with partial immunity having nonlinear incidence and saturated treatment in deterministic and stochastic environments," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
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    6. Rao, Feng & Luo, Junling, 2021. "Stochastic effects on an HIV/AIDS infection model with incomplete diagnosis," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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