关键词: stochastic norovirus model, stochastic transmission, stochastic perturbation, stochastic stability, stochastic optimal control

Abstract: Norovirus is one of the most common causes of viral gastroenteritis in the world, causing significant morbidity, deaths, and medical costs. In this work, we look at stochastic modelling methodologies for norovirus transmission by water, human to human transmission and food. To begin, the proposed stochastic model is shown to have a single global positive solution. Second, we demonstrate adequate criteria for the existence of a unique ergodic stationary distribution $\mathfrak{R_s^0}>1$ by developing a Lyapunov function. Thirdly, we find sufficient criteria $\mathfrak{R_s}<1$ for disease extinction. Finally, two simulation examples are used to exemplify the analytical results. We employed optimal control theory and examined stochastic control problems to regulate the spread of the disease using some external measures. Additional graphical solutions have been produced to further verify the acquired analytical results. This research could give a solid theoretical foundation for understanding chronic communicable diseases around the world. Our approach also focuses on offering a way of generating Lyapunov functions that can be utilized to investigate the stationary distribution of epidemic models with nonlinear stochastic disturbances.

Key words: stochastic norovirus model, stochastic transmission, stochastic perturbation, stochastic stability, stochastic optimal control