Multistage spatial model for informing release of Wolbachia-infected mosquitoes as disease control

Abstract: Wolbachia is a naturally occurring bacterium that can infect Aedes mosquitoes and reduce the transmission of mosquito-borne diseases, including dengue fever, Zika, and chikungunya. Field trials have been conducted worldwide to suppress local epidemics. We introduce a novel partial differential equation model to simulate the spread of Wolbachia infection in mosquito populations. Our model incorporates the intricate Wolbachia maternal transmission cycle and detailed mosquito life stages, while also accounting for the spatial heterogeneity induced by mosquito dispersion across a two-dimensional domain. Prior modeling studies and field data indicate that a critical threshold of Wolbachia-infected mosquitoes is necessary for infection to persist among the mosquito population. Through our spatial model, we identify a threshold condition, termed the ``critical bubble'', for having a self-sustainable Wolbachia infection in the field. When releasing beyond this threshold, the model predicts a spatial wave of Wolbachia infection. We further quantify how this threshold and infection wave velocity depend on the diffusion process and other parameters. We numerically study various intervention scenarios to inform efficient Wolbachia release strategies. Our findings suggest that: (1) integrating Wolbachia release with pre-release mitigations targeting the adult mosquitoes, rather than the aquatic stages, better reduces the threshold for Wolbachia establishment; Habitats modification before the release may increase the threshold; (2) releases in the dry regions lower the threshold, though the infection waves may slow down or stall at the dry-wet interfaces due to the difference in carrying capacities; and (3) initiating releases just before the wet season further reduces the release threshold.