Hindrances to bistable front propagation: application to Wolbachia invasion

TL;DR

This paper analyzes the factors influencing bistable front propagation in biological invasions, especially Wolbachia in mosquitoes, demonstrating how environmental heterogeneity can halt or facilitate invasion.

Contribution

It provides a rigorous mathematical framework for understanding how environmental heterogeneity affects bistable invasion fronts, including the existence of stable and unstable fronts.

Findings

Heterogeneous environments can stop invading fronts by creating stable fronts.

Existence of unstable fronts above stable fronts allows invasion to overcome obstacles.

Quantification of critical population jumps necessary for invasion success.

Abstract

We study the biological situation when an invading population propagates and replaces an existing population with different characteristics. For instance, this may occur in the presence of a vertically transmitted infection causing a cytoplasmic effect similar to the Allee effect (e.g. Wolbachia in Aedes mosquitoes): the invading dynamics we model is bistable. After quantification of the propagules, a second question of major interest is the invasive power. How far can such an invading front go, and what can stop it? We rigorously show that a heterogeneous environment inducing a strong enough population gradient can stop an invading front, which will converge in this case to a stable front. We characterize the critical population jump, and also prove the existence of unstable fronts above the stable (blocking) fronts. Being above the maximal unstable front enables an invading front to clear the obstacle and propagate further. We are particularly interested in the case of artificial Wolbachia infection, used as a tool to fight arboviruses.