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Understanding the dynamics of hepatitis B transmission: A stochastic model with vaccination and Ornstein-Uhlenbeck process

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  • Wu, Shuying
  • Yuan, Sanling
  • Lan, Guijie
  • Zhang, Tonghua

Abstract

In this paper, we explore and analyze a stochastic epidemiological model with vaccination and two mean-reverting Ornstein-Uhlenbeck processes to describe the dynamics of HBV transmission. Our study begins by deriving a sufficient condition for the extinction of hepatitis B. Additionally, we determine the presence of a stationary distribution using the Markov process stability theory. Next, we utilize algebraic equation theory and the associated Fokker-Planck equation to derive an explicit expression for the unique probability density function. To validate our theoretical findings, we conduct several numerical simulations using hepatitis B data provided by the World Health Organization (WHO). The results of these simulations support and complement our analytical approach.

Suggested Citation

  • Wu, Shuying & Yuan, Sanling & Lan, Guijie & Zhang, Tonghua, 2024. "Understanding the dynamics of hepatitis B transmission: A stochastic model with vaccination and Ornstein-Uhlenbeck process," Applied Mathematics and Computation, Elsevier, vol. 476(C).
    • Handle: RePEc:eee:apmaco:v:476:y:2024:i:c:s0096300324002340
    DOI: 10.1016/j.amc.2024.128766
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