Modeling spatial waves of Wolbachia invasion for controlling mosquito-borne diseases

TL;DR

This paper develops PDE models to understand how spatial heterogeneity influences Wolbachia invasion in mosquitoes, providing insights into threshold conditions and wave dynamics critical for disease control strategies.

Contribution

The study introduces reaction-diffusion PDE models capturing spatial heterogeneity and vertical transmission, analyzing invasion thresholds and wave propagation for Wolbachia in mosquitoes.

Findings

Identified a critical bubble profile as the invasion threshold.

Derived conditions for traveling wave solutions.

Numerical simulations inform optimal release strategies.

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, which is created by the local release of the infected mosquitoes. We develop and analyze partial differential equation (PDE) models to study the invasion dynamics of Wolbachia infection among mosquitoes in the field. Our reaction-diffusion-type models account for both the complex vertical transmission and the spatial mosquito dispersion. We characterize the threshold for a successful invasion, which is a bubble-shaped profile, 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.