Wolbachia‐based biocontrol has recently emerged as a potential method for the prevention and control of dengue and other vector‐borne diseases. Major vector species, such as Aedes aegypti females, when deliberately infected with Wolbachia become far less capable of getting infected and transmitting the virus to human individuals. In this paper, we propose and qualitatively analyze a simplified model of Wolbachia invasion that describes an interaction and competition between Wolbachia‐infected and wild Aedes aegypti mosquitoes. This model not only facilitates better visualization of the Wolbachia invasion dynamics thanks to its bidimensionality, but it also possesses the noticeable property of monotonicity and exhibits the saddle‐point behavior. The latter helps to identify a threshold manifold consisting of points in that couple the minimum viable population sizes of wild and Wolbachia‐carrying insects and also regulate the survival and extinction of each population of mosquitoes.

中文翻译：

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Wolbachia入侵的简化单调模型，包括埃及伊蚊

基于Wolbachia的生物防治技术最近已成为预防和控制登革热和其他媒介传播疾病的潜在方法。当故意感染沃尔巴克氏菌时，主要的媒介物种，例如埃及伊蚊，就变得不容易被感染并将病毒传播给人类。在本文中，我们提出并定性分析了沃尔巴克氏菌入侵的简化模型，该模型描述了感染了沃尔巴克氏菌的埃及伊蚊和野生埃及伊蚊之间的相互作用和竞争。该模型不仅有助于更好地可视化沃尔巴克氏菌入侵动力学具有二维性，但它也具有单调性的显着特性并表现出鞍点行为。后者有助于确定阈值流形，该阈值流形由点组成，这些点耦合了携带野生和沃尔巴克氏菌的昆虫的最小可行种群大小，并且还调节了每个蚊子的生存和灭绝。