A vector Allee effect in mosquito dynamics

Abstract

We consider a recently introduced model of mosquito dynamics that includes mating and progression through breeding, questing and egg-laying stages of mosquitoes using human and other vertebrate sources for blood meals. By exploiting a multiscale character of the model and recent results on their uniform-in-time asymptotics, we derive a simplified monotone model with the same long-term dynamics. Using the theory of monotone dynamical systems, we show that for a range of parameters, the latter displays Allee-type dynamics; that is, it has one extinction and two positive equilibria ordered with respect to the positive cone $\mathbb R_+^7$, with the extinction and the larger equilibrium being attractive and the middle one unstable. Using asymptotic analysis, we show that the original system also displays this pattern.