Research on stochastic SVITR epidemic model driven by log-normal Ornstein-Uhlenbeck process

Abstract In this paper, a stochastic SVITR epidemic model including the mechanism of reinfection after vaccination and rehabilitation is studied to analyze the transmission dynamics of highly infectious diseases such as COVID-19. In order to describe the influence of environmental uncertainty on the infection rate, the lognormal Ornstein-Uhlenbeck process is introduced as a random disturbance in the model. We first prove the existence and uniqueness of the solution of the model, and then establish the criterion for the extinction of the disease and the existence of a stationary distribution of the system by the Lyapunov method, and reveal the threshold effect of the random basic reproduction number. Furthermore, we derive the analytical expression of the probability density function near the endemic equilibrium point under the SVITR framework for the first time, and clarify the influence of random disturbance on the epidemic steady state from the perspective of probability. Numerical experiments verify the effectiveness of the theoretical results. This study provides a theoretical basis for infectious disease modeling and prevention and control strategy evaluation in a random environment.