Modeling Spatial Waves of Wolbachia Invasion for Controlling Mosquito-Borne Diseases
Zhuolin Qu, Tong Wu, James M. Hyman
Abstract
.Wolbachia is a natural bacterium that can infect mosquitoes and reduce their ability to transmit mosquito-borne diseases, such as dengue fever, Zika, and chikungunya. Field trials and modeling studies have shown that the fraction of infection among the mosquitoes must exceed a threshold level for the infection to persist. To capture this threshold, it is critical to consider the spatial heterogeneity in the distributions of the infected and uninfected mosquitoes created by a local release of the infected mosquitoes. We develop and analyze PDE models to study the invasion dynamics of Wolbachia infection among mosquitoes in the field. Our reaction-diffusion-type models account for the complex vertical transmission and the spatial mosquito dispersion. We characterize the threshold for a successful invasion with a bubble-shaped distribution, called the "critical bubble." The critical bubble is optimal in its release size compared to other spatial profiles in a one-dimensional landscape. The fraction of infection near the release center is higher than the threshold level for the corresponding homogeneously mixing ODE models. We show that the proposed spatial models give rise to the traveling waves of Wolbachia infection when above the threshold. We quantify how the threshold condition and traveling-wave velocity depend on the diffusion coefficients and other model parameters. Numerical studies for different scenarios are presented to inform the design of release strategies.Keywordsmosquito-borne diseasesWolbachiainvasionthreshold conditiontraveling wavemodel reductionMSC codes93A3035K5735C0792D30