ON A NETWORK MODEL OF TWO COMPETITORS WITH APPLICATIONS TO THE INVASION AND COMPETITION OF AEDES ALBOPICTUS AND AEDES AEGYPTI MOSQUITOES IN THE UNITED STATES

摘要

Based on the invasion of the Aedes albopictus mosquitoes and the competition between Ae. albopictus and Ae. aegypti mosquitoes in the United States, we consider a two-species competition model in a network, that is, with discrete Laplacian diffusion. In the case of weak-strong competition where the invasive competitor is stronger than the local one, it is shown that solutions converge uniformly to the semipositive equilibrium such that the invasive species survives while the local species becomes extinct, and vice versa. In the case of weak-weak competition, solutions converge uniformly to the positive equilibrium such that both invasive and local species coexist. By using numerical simulations, we apply the two-species competition model in a network to explain the invasion and competition of Ae. Albopictus and Ae. Aegypti mosquitoes in the United States. It also indicates that discrete Laplacian diffusion induces different spreading speeds in different invasive directions.