Travelling Waves in Wolbachia Spread Dynamics

TL;DR

This paper models the spatial spread of Wolbachia in mosquito populations using integro-difference equations, analyzing how different dispersal kernels influence invasion speed and success, with implications for disease control strategies.

Contribution

It introduces a novel IDE framework incorporating various dispersal kernels to analyze Wolbachia invasion dynamics in heterogeneous landscapes.

Findings

Fat-tailed kernels lead to faster, broader invasions.

Existence and uniqueness of monotone traveling waves are established.

Numerical simulations confirm theoretical invasion speed estimates.

Abstract

Wolbachia, a maternally transmitted endosymbiont, offers a powerful biological control strategy for mosquito-borne diseases such as dengue, Zika, and malaria. We develop an integro-difference equation (IDE) model that integrates Wolbachia's nonlinear growth with spatially explicit mosquito dispersal kernels to study invasion dynamics in heterogeneous landscapes. Analytical results establish the existence and uniqueness of monotone traveling waves and provide explicit estimates of invasion speeds as functions of dispersal and growth parameters. Four kernels: Gaussian, Laplace, exponential square-root, and Cauchy, represent a continuum from short- to long-range movement. Fat-tailed kernels generate faster, broader wavefronts, while compact ones limit spread. We also identify a critical bubble, the minimal localized profile required for sustained invasion. Numerical simulations in one- and two-dimensional domains confirm theoretical predictions and reveal parameter regimes governing invasion success. This framework quantifies how dispersal mechanisms shape Wolbachia's spread, thus informing targeted and efficient vector-control strategies.