Dynamics of a stochastic multi-host cystic echinococcosis model with log-normal Ornstein-Uhlenbeck process

Cystic echinococcosis (CE) is a parasitic disease that poses a significant threat to animal husbandry. To investigate the transmission dynamics of CE under external disturbances, a stochastic livestock-dog CE model incorporating two log-normal Ornstein-Uhlenbeck processes was formulated. This model is more biologically and mathematically reasonable, and extending stochastic epidemiological models to integrate within-host and between-host frameworks. To explore the dynamics of stochastic CE model, the existence and uniqueness of its global positive solution were first verified. By means of appropriate Lyapunov functions, compact sets, and Fatou’s lemma, sufficient conditions for the existence of a stationary distribution indicative of disease persistence were established, and the sufficient condition for CE extinction was derived. Specifically, through solving the corresponding seven-dimensional algebraic equations of the model, the exact probability density function near the quasi-endemic equilibrium was obtained, which provides valuable insights into the stationary distribution. Finally, numerical simulations were conducted to validate the theoretical conclusions.