Impact of the impulsive releases and Allee effect on the dispersal behavior of the wild mosquitoes

We develop a mathematical model of the wild mosquito dispersal with impulsive releases of the sterile mosquitoes and obtain a threshold condition that determines the eradication and uniform persistence of the wild mosquitoes using Floquet theory and impulsive comparison theorem. The effect of the dispersal rate on dynamics is investigated by means of numerical simulation. Additionally, we investigate a three-dimensional dispersal model of mosquitoes with impulsive state feedback control to effectively control the abundance of the wild mosquitoes below the acceptable level when the density of the wild mosquitoes reaches a certain threshold. Dynamics of such state-dependent control is also presented by applying numerical simulations since it is difficult to implement theoretical analysis. Finally, a brief discussion is given.