Mosquito suppression via Filippov incompatible insect technique

Mosquito-borne diseases persist as a global health challenge despite ongoing control efforts, necessitating the exploration of alternative control approaches. This research proposes a Filippov incompatible insect technique (IIT) model with a threshold policy control for suppressing mosquito population. The model implements biological and chemical control strategies only when wild mosquito density surpasses an economic threshold. The biological strategy involves releasing Wolbachia-infected male mosquitoes, offering advantages such as a shortened lifespan and disease blocking. Simultaneously, moderate insecticide and larvicide spraying serve as a chemical approach to expedite the control process. The model provides economic advantages by minimizing control costs and environmental benefits through the integration of biological strategies, thus reducing reliance on chemicals. By employing Filippov's convex method, we identify necessary conditions for the existence of sliding segments and determine the dynamics of the switching line. Theoretical analysis reveals the model's long-term dynamics, including sliding bifurcations, pseudo-equilibria, and their stability. The model exhibits boundary equilibrium bifurcations and transcritical bifurcations in both free and controlled systems. Varying threshold values significantly impact the control outcomes effectiveness. The main findings demonstrate that integrated strategies efficiently decrease the population density of wild mosquitoes.