On a reaction-diffusion system modeling strong competition between two mosquito populations

Nicolas Vauchelet

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arXiv · 2506.15202

On a reaction-diffusion system modeling strong competition between two mosquito populations

Nicolas Vauchelet

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Abstract

This paper is devoted to the analysis of a reaction-diffusion system with strong competition and spatial heterogeneities modelling the interaction between two species of mosquitoes. In particular, we propose a mathematical model that accounts for the spatial segregation observed between two species of mosquito vectors of numerous viruses. Indeed, it has been observed that, in tropical regions, Aedes aegypti mosquitoes are well established in urban areas whereas Aedes albopictus mosquitoes spread widely in forest regions. Moreover, these species of mosquitoes compete with each other in the larval stage. Based on these observations, we introduce a simple mathematical model to account for this phenomenon. This model consists of a system of reaction-diffusion equations describing the dynamics of the aquatic and aerial phases of each species in a spatially heterogeneous environment. The competition takes place at the aquatic phase and is assumed to be strong which allows us to reduce the dimensionality of the system. We first establish a sufficient condition on the parameters to prevent one species from invading another in a homogeneous environment. Next, using this sufficient condition, we show that spatial segregation may be observed in a spatially heterogeneous environment. Our theoretical results are also illustrated by some numerical simulations.

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Nicolas Vauchelet. 2025-06-18. On a reaction-diffusion system modeling strong competition between two mosquito populations. https://arxiv.org/abs/2506.15202

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