Wolbachia spread dynamics in multi-regimes of environmental conditions

Mosquito-borne diseases such as dengue fever and Zika kill more than 700,000 people each year in the world. A novel strategy to control these diseases employs the bacterium Wolbachia whose infection in mosquitoes blocks virus replication. The prerequisite for this measure is to release Wolbachia -infected mosquitoes to replace wild population. Due to the fluctuation of environmental conditions for mosquito growth, we develop and analyze a model of differential equations with parameters randomly changing over multiple environmental regimes. By comparing the dynamics between the stochastic system and constructed auxiliary systems, combined with other techniques, we provide sharp estimates on the threshold releasing level for Wolbachia fixation. We define the alarm period of disease transmission to measure the risk of mosquito-borne diseases. Our numerical simulations suggest that more frequent inter-regime transitions help reduce the alarm period, and the disease transmission is more sensitive to the average climatic conditions than the number of sub-regimes over a given time period. Further numerical examples also indicate that the reduction in the waiting time to suppress 95% of wild population is more evident when the releasing amount is increased up to a double of the wild population.