A vector Allee effect in mosquito dynamics

J. Banasiak; Bime M. Ghakanyuy; Gideon A. Ngwa

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arXiv · 2411.06551

A vector Allee effect in mosquito dynamics

J. Banasiak·Bime M. Ghakanyuy·Gideon A. Ngwa

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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.

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J. Banasiak, Bime M. Ghakanyuy, Gideon A. Ngwa. 2024-11-10. A vector Allee effect in mosquito dynamics. https://arxiv.org/abs/2411.06551

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