Existence and stability of spike solutions in a mosquito suppression model with directional movement

The goal of this paper is to investigate the impact of the directional movement of wild-type mosquitoes on mosquito control strategies using the Sterile Insect Technique (SIT). A reaction–advection–diffusion model is developed to describe the population dynamics of wild-type mosquitoes, incorporating both the SIT and their directional movement. The existence of interior spikes in wild-type mosquito population has been strictly proved when the directional movement of wild-type mosquitoes is sufficiently strong. Using spectral theory, the stability of these interior spikes is established. Numerical simulations have been conducted to validate and support the theoretical analysis. The obtained results indicate that the amplitudes of the interior spikes are depending on the releasing numbers of sterile mosquitoes. Our findings also suggest that the directional movement of wild-type mosquitoes could induce the aggregation phenomena of wild-type mosquitoes, which may offer valuable insights for the implementation of mosquito control strategies.