Intermittent releases: a modelling approach for sterile insect technique in mosquito control

An unconventional and environmentally friendly mosquito management approach offers a sustainable solution that protects both the environment and human health. One such method is the Sterile Insect Technique (SIT), which holds promise as a mosquito control strategy by releasing sterilized male mosquitoes into the wild-type (WT) mosquito population. Since the success of SIT depends on the strategic planning of sterile mosquito releases, this paper examines a stage-structured model for mosquito populations with a density-dependent threshold for sterile male mosquito release, where releases occur only when the ratio of WT to sterile mosquito populations exceeds a critical threshold. Using intermittent releases, the proposed SIT model is designed to optimally align the release of sterile male mosquitoes with WT and sterile mosquito population densities, maintaining WT mosquito suppression at a predefined threshold and offering a more effective alternative to continuous release strategies. We employ Filippov's modelling approach to investigate how intermittent releases, represented by piecewise-smooth functions, affect the dynamics of the system, particularly when mosquito populations exceed the predefined threshold. To explore the dynamical complexities, we employ Filippov's convex method by defining the vector field in the discontinuous region as convex combinations of adjacent fields, allowing for the analysis of sliding motion and the identification of discontinuity-induced bifurcations through differential inclusions. Our findings identify the minimum release rate of sterile mosquitoes required to achieve the desired suppression level, highlighting the need to increase this rate due to increased WT mosquito immigration, reduced survival and mating fitness of sterile mosquitoes, and limitations in mosquito surveillance accuracy.