Dynamic Study of a Class of Stochastic Marine Viruses with Ornstein-Uhlenbeck Process
摘要
This study investigates the stochastic dynamics of marine viral infections by incorporating Ornstein-Uhlenbeck processes into epidemic models to account for environmental fluctuations such as temperature and nutrient concentrations. Through the construction of auxiliary functions, application of Itô’s formula, estimation of drift terms, integration, and limit calculation, it is shown that when Rn<1, disease transmission decays exponentially to extinction. Near the steady state, a multidimensional Taylor expansion is employed to linearize the nonlinear system and examine its local behavior. To quantify uncertainty, an integral transform method is used to derive analytical expressions for the expected prevalence and variance of infection, thereby highlighting how environmental autocorrelation influences viral persistence. Finally, this study analyzed the behavior of the system over extended time scales and further examined its limits to understand long-term trends and stability. Numerical simulation results indicate that a lower decay rate leads to fewer fluctuations before the system reaches equilibrium, while a higher recovery rate allows the system to return to equilibrium more quickly.