Modeling of periodic input Ornstein-Uhlenbeck temperature-tick-borne disease transmission coupling mechanism under climate change.

Given the rapid increase in climate change, investigating the impact of climate change on the transmission mechanism of tick-borne diseases is imperative. In order to fully capture the influence of the seasonal variation of temperature, environmental disturbances and the co-feeding transmission on the spread of tick-borne diseases, we propose a novel stochastic dynamical model that couples the mean-reverting Ornstein-Uhlenbeck temperature equation with periodic input to the tick-borne disease model. Through theoretical analysis, we derive sufficient conditions for the extinction of tick populations and the eradication of tick-borne diseases, as well as the stochastic persistence conditions of the system. In numerical simulations, we find that the periodic Ornstein-Uhlenbeck temperature equation can effectively fit the actual temperature data in low, medium, and high latitude regions of China. In risk assessment, we find that at the spatial perspective, low-latitude areas have a higher risk of tick-borne diseases, requiring enhanced control measures; from a temporal perspective, compared to the past, the current stage presents a greater risk of tick-borne diseases when preventive measures are not implemented. Additionally, we observe that larger noise of environment for tick populations favors the extinction of tick populations, while smaller temperature fluctuations, noise on infected hosts and ticks, as well as higher temperature regression rate, are more likely to lead to the extinction of tick-borne diseases. These findings provide crucial insights into understanding the impact of climate change on the transmission mechanism of tick-borne diseases.