A simplified monotone model of Wolbachia invasion encompassing Aedes aegypti mosquitoes

Abstract

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.

Sex-structured model of Wolbachia invasion and design of sex-biased release strategies in Aedes spp mosquitoes populations

“…In this case, the dynamical system (2) exhibits bistability (both boundary equilibria E n and E w are LAS in Region V given in Figure 1), and the outcome of the inter-species competition depends on the frequency of Wolbachia infection in the total mosquito population. The latter fully agrees with previous results obtained for other models of Wolbachia invasion formulated either in terms of the infection frequency [2,21,24] or competitive population dynamics [1,3,7,11,12,13,16,26,27].…”

“…Several models have been developed and analyzed to study release strategies to ensure population replacement, thanks to different Wolbachia strains: see for instance [1,2,3,7,11,12,13,16,21,24,26,27]. In the present paper, we provide a sex-structured model allowing us to study and size in detail the release process, enabling in particular to assess different male/female compositions all capable of achieving successful infection by Wolbachia.…”