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

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.