A vector Allee effect in mosquito dynamics

TL;DR

This paper introduces a simplified monotone model of mosquito dynamics that exhibits an Allee effect, revealing critical thresholds for mosquito population persistence or extinction.

Contribution

The authors derive a simplified monotone model from a complex mosquito dynamics system and demonstrate it exhibits an Allee effect using monotone dynamical systems theory.

Findings

The simplified model has one extinction and two positive equilibria.

The original complex model also displays Allee-type dynamics.

The model's dynamics depend on parameter ranges.

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.