School of Mathematics and Statistics, Northeast Petroleum University, Daqing, Heilongjiang, China.
PLoS One. 2024 Oct 23;19(10):e0310175. doi: 10.1371/journal.pone.0310175. eCollection 2024.
In this paper, we study a stochastic SIVS infectious disease model with the Ornstein-Uhlenbeck process and newborns with vaccination. First, we demonstrate the theoretical existence of a unique global positive solution in accordance with this model. Second, adequate conditions are inferred for the infectious disease to die out and persist. Then, by classic Lynapunov function method, the stochastic model is allowed to obtain the sufficient condition so that the stochastic model has a stationary distribution represents illness persistence in the absence of endemic equilibrium. Calculating the associated Fokker-Planck equations yields the precise expression of the probability density function for the linearized system surrounding the quasi-endemic equilibrium. In the end, the theoretical findings are shown by numerical simulations.
本文研究了一类具有 Ornstein-Uhlenbeck 过程和新生儿接种的随机 SIVS 传染病模型。首先,根据该模型证明了唯一全局正解的存在性。其次,推断出传染病灭绝和持续存在的充分条件。然后,通过经典的 Lyapunov 函数方法,使得随机模型获得了在不存在地方病平衡点的情况下疾病持续存在的充分条件。计算相关的 Fokker-Planck 方程得出了拟地方病平衡点附近线性系统的概率密度函数的精确表达式。最后,通过数值模拟验证了理论结果。