Releasing Wolbachia-infected mosquitos to mitigate the transmission of Zika virus

Abstract

Although many people infected with Zika virus do not get sick or only have mild symptoms, pregnant women infected with Zika virus may have babies with severe birth defects. To understand the transmission dynamics of Zika virus, we develop deterministic and stochastic models, taking into account mosquito-human transmission, sexual transmission, and the release of Wolbachia-infected male mosquitoes. For the deterministic model, we analyze the stability of the disease-free equilibrium and evaluate the impact of the parameters on the basic reproduction number by sensitivity analysis. We found the upper and lower bounds for the release rate of Wolbachia-infected male mosquitoes to be cost effective. Since the transmission of infectious diseases is affected by many stochastic factors, we incorporate the impact of environmental white noise on death rates of adult mosquitoes, mosquitoes at aquatic stages, and humans to develop a stochastic model for Zika. We proved that the stochastic model has a unique and bounded global solution and derived the sufficient conditions for the extinction of Zika. We also proved the existence of a unique ergodic stationary distribution of the solutions. Numerical simulations show that the stochasticity may drive the disease to extinction when the intensity of the white noise is large enough, and the release of Wolbachia-infected mosquitoes shortens the time it takes for the wild mosquitoes to become extinct.