A two-species competition model on a compact metric graph for the invasion and competition of <i> Aedes Aegypti </i> and <i> Aedes Albopictus </i> mosquitoes in Florida

Abstract

Motivated by the invasion of Aedes albopictus mosquitoes and the interspecific competition between Aedes aegypti and Aedes albopictus in Florida, we formulate a two-species competition model on a compact metric graph. This model accounts for the species’ ability to inhabit and traverse along the graph’s edges. In the scenario of weak-strong competition, we prove that solutions of the competition model converge uniformly to a semi-positive equilibrium, where either Aedes albopictus survives while Aedes aegypti goes extinct, or vice versa. Whereas for weak-weak competition, the solutions converge uniformly to a positive equilibrium, enabling the coexistence of both Aedes aegypti and Aedes albopictus. We conduct numerical simulations on the two-species competition model along Route 441 in Florida, aiming to illustrate the invasion dynamics and competitive interactions of Aedes aegypti and Aedes albopictus.