Efficacy of Wolbachia-based mosquito control: Predictions of a spatially discrete mathematical model

Wolbachia is an endosymbiont bacterium present in many insect species. When Wolbachia-carrying male Aedes aegypti mosquitoes mate with non-carrier females, their embryos are not viable due to cytoplasmic incompatibility. This phenomenon has been exploited successfully for the purpose of controlling mosquito populations and the spread of mosquito-borne illnesses: Wolbachia carriers are bred and released into the environment. Because Wolbachia is not harmful to humans, this method of mosquito control is regarded as a safer alternative to pesticide spraying. In this article, we introduce a mathematical framework for exploring (i) whether a one-time release of Wolbachia carriers can elicit a sustained presence of carriers near the release site, and (ii) the extent to which spatial propagation of carriers may allow them to establish fixation in other territories. While some prior studies have formulated mosquito dispersal models using advection-reaction-diffusion PDEs, the predictive power of such models requires careful ecological mapping: advection and diffusion coefficients exhibit significant spatial dependence due to heterogeneity of resources and topography. Here, we adopt a courser-grained view, regarding the environment as a network of discrete, diffusively-coupled "habitats"-distinct zones of high mosquito density such as stagnant ponds. We extend two previously published single-habitat mosquito models to multiple habitats, and calculate rates of migration between pairs of habitats using dispersal kernels. Our primary results are quantitative estimates regarding how the success of carrier fixation in one or more habitats is determined by: the number of carriers released, sizes of habitats, distances between habitats, and the rate of migration between habitats. Besides yielding sensible and potentially useful predictions regarding the success of Wolbachia-based control, our framework applies to other approaches (e.g., gene drives) and contexts beyond the realm of insect pest control.