A Simplified Monotone Model Of Wolbachia Invasion Encompassing Aedes Aegypti Mosquitoes

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 R+2 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.