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We study the biological situation when an invading population propagates andreplaces an existing population with different characteristics. For instance,this may occur in the presence of a vertically transmitted infection causing acytoplasmic effect similar to the Allee effect (e.g. Wolbachia in Aedesmosquitoes): the invading dynamics we model is bistable. After quantificationof 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 showthat a heterogeneous environment inducing a strong enough population gradientcan 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 ofunstable fronts above the stable (blocking) fronts. Being above the maximalunstable front enables an invading front to clear the obstacle and propagatefurther. We are particularly interested in the case of artificial Wolbachiainfection, used as a tool to fight arboviruses.

Hindrances to bistable front propagation: application to Wolbachia invasion