Stationary distribution, extinction and probability density function of a stochastic SEIV epidemic model with general incidence and Ornstein–Uhlenbeck process

Tan Su, Qing Yang, Xinhong Zhang and Daqing Jiang

Physica A: Statistical Mechanics and its Applications, 2023, vol. 615, issue C

Abstract: Considering the great benefit of vaccination and the variability of environmental influence, a stochastic SEIV epidemic model with mean-reversion Ornstein–Uhlenbeck process and general incidence rate is investigated in this paper. First, it is theoretically proved that stochastic model has a unique global solution. Next, by constructing a series of suitable Lyapunov functions, we obtain a sufficient criterion R0s>1 for the existence of stationary distribution which means the disease will last for a long time. Then, the sufficient condition for the extinction of the infectious disease is also derived. Furthermore, an exact expression of probability density function near the quasi-endemic equilibrium is obtained by solving the corresponding four-dimensional matrix equation. Finally, some numerical simulations are carried out to illustrate the theoretical results.

Keywords: SEIV model; Ornstein–Uhlenbeck process; Stationary distribution; Extinction; Density function (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:615:y:2023:i:c:s0378437123001607

DOI: 10.1016/j.physa.2023.128605

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