Discrete dynamical models on Wolbachia infection frequency in mosquito populations with biased release ratios

Modelling the ecological dynamics of mosquito populations with multiple co-circulating Wolbachia strains

Wolbachia intracellular bacteria successfully reduce the transmissibility of arthropod-borne viruses (arboviruses) when introduced into virus-carrying vectors such as mosquitoes. Despite the progress made by introducing Wolbachia bacteria into the Aedes aegypti wild-type population to control arboviral infections, reports suggest that heat-induced loss-of-Wolbachia-infection as a result of climate change may reverse these gains. Novel, supplemental Wolbachia strains that are more resilient to increased temperatures may circumvent these concerns, and could potentially act synergistically with existing variants. In this article, we model the ecological dynamics among three distinct mosquito (sub)populations: a wild-type population free of any Wolbachia infection; an invading population infected with a particular Wolbachia strain; and a second invading population infected with a distinct Wolbachia strain from that of the first invader. We explore how the range of possible characteristics of each Wolbachia strain impacts mosquito prevalence. Further, we analyse the differential system governing the mosquito populations and the Wolbachia infection dynamics by computing the full set of basic and invasive reproduction numbers and use these to establish stability of identified equilibria. Our results show that releasing mosquitoes with two different strains of Wolbachia did not increase their prevalence, compared with a single-strain Wolbachia-infected mosquito introduction and only delayed Wolbachia dominance.

Existence and stability of two periodic solutions for an interactive wild and sterile mosquitoes model

In this paper, we study the periodic and stable dynamics of an interactive wild and sterile mosquito population model with density-dependent survival probability. We find a release amount upper bound G∗, depending on the release waiting period T, such that the model has exactly two periodic solutions, with one stable and another unstable, provided that the release amount does not exceed G∗. A numerical example is also given to illustrate our results.

Periodic Orbits of a Mosquito Suppression Model Based on Sterile Mosquitoes

In this work, we investigate the existence and stability of periodic orbits of a mosquito population suppression model based on sterile mosquitoes. The model switches between two sub-equations as the actual number of sterile mosquitoes in the wild is assumed to take two constant values alternately. Employing the Poincaré map method, we show that the model has at most two T-periodic solutions when the release amount is not sufficient to eradicate the wild mosquitoes, and then obtain some sufficient conditions for the model to admit a unique or exactly two T-periodic solutions. In particular, we observe that the model displays bistability when it admits exactly two T-periodic solutions: the origin and the larger periodic solution are asymptotically stable, and the smaller periodic solution is unstable. Finally, we give two numerical examples to support our lemmas and theorems.