Impact of releasing period and magnitude on mosquito population in a sterile release model with delay

Mirrored dynamics of a wild mosquito population suppression model with Ricker-type survival probability and time delay

Here, we formulated a delayed mosquito population suppression model including two switching sub-equations, in which we assumed that the growth of the wild mosquito population obeys the Ricker-type density-dependent survival function and the release period of sterile males equals the maturation period of wild mosquitoes. For the time-switched delay model, to tackle with the difficulties brought by the non-monotonicity of its growth term to its dynamical analysis, we employed an essential transformation, derived an auxiliary function and obtained some expected analytical results. Finally, we proved that under certain conditions, the number of periodic solutions and their global attractivities for the delay model mirror that of the corresponding delay-free model. The findings can boost a better understanding of the impact of the time delay on the creation/suppression of oscillations harbored by the mosquito population dynamics and enhance the success of real-world mosquito control programs.

A mosquito population suppression model with a saturated Wolbachia release strategy in seasonal succession

Releasing Wolbachia-infected male mosquitoes to suppress wild female mosquitoes through cytoplasmic incompatibility has shown great promise in controlling and preventing mosquito-borne diseases. To make the release logistically and economically feasible, we propose a saturated release strategy, which is only implemented during the epidemic season of mosquito-borne diseases. Under this assumption, the model becomes a seasonally switching ordinary differential equation model. The seasonal switch brings rich dynamics, including the existence of a unique periodic solution or exactly two periodic solutions, which are proved by using the qualitative property of the Poincaré map. Sufficient conditions are also obtained for determining the stability of the periodic solutions.