SIAM Journal on Applied Mathematics, Volume 80, Issue 2, Page 929-950, January 2020.
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.

中文翻译：

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关于两个竞争对手的网络模型及其在美国伊蚊和伊蚊的入侵和竞争中的应用

SIAM应用数学杂志，第80卷，第2期，第929-950页，2020年1月。
基于白纹伊蚊的入侵和Ae之间的竞争。albopictus和Ae。在美国的埃及蚊中，我们考虑网络中的两种种群竞争模型，即具有离散的拉普拉斯扩散。在弱强竞争的情况下，入侵竞争者比本地竞争者强，这表明解决方案均匀地收敛到半正平衡，从而使入侵物种得以生存，而本地物种灭绝，反之亦然。在弱弱竞争的情况下，解决方案统一收敛到正平衡，从而使入侵物种和本地物种同时存在。通过数值模拟，我们在网络中应用两种种群竞争模型来解释Ae的入侵和竞争。Albopictus和Ae。美国的埃及伊蚊。这也表明离散的拉普拉斯扩散在不同的侵入方向上引起不同的扩散速度。