A spatial transmission model for enhancing the effectiveness of Wolbachia in controlling the spread of mosquito-borne diseases

Wolbachia is a natural bacterium that can infect mosquitoes and reduce their ability to transmit mosquito-borne diseases, such as dengue fever, malaria, Zika, and chikungunya. Field trials and modeling studies have shown that the fraction of infection among mosquitoes must exceed a threshold level for the infection to persist. To capture this threshold condition, 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 a partial differential equation (PDE) model 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. 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.

Bio
https:/sse.tulane.edu/math/faculty/hyman
Mac Hyman is the Evelyn and John G. Phillips Distinguished Chair in Mathematics at Tulane University, past President of the Society of Industrial and Applied Mathematics, and an AAAS Fellow. He is the former group leader of the Los Alamos National Laboratory Mathematical Modeling and Analysis Group and coordinated the Los Alamos Applied Mathematics summer student internship program for twenty years.