  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.
