Modelling, analysis and optimal control of Zika virus transmission dynamics based on sterile insect technique

The sterile insect technique (SIT) has emerged as a promising tool for suppressing mosquito-borne diseases. This study develops a Zika virus transmission model integrating SIT, emphasizing both mosquito-borne and environmental aquatic transmission pathways. Unlike eradication-focused approaches, the model targets population suppression through sterile male releases, allowing controlled coexistence of sterile and wild mosquitoes. Dynamical analysis reveals critical thresholds: when the sterile insect release rate b < b_p and Allee effects are weak (r < r_p), the system stabilizes at a coexistence equilibrium; exceeding these thresholds drives population collapse. While low wild mosquito densities may theoretically risk extinction, such levels are epidemiologically insufficient to trigger outbreaks, as viral resurgence requires a critical population density. The basic reproduction number R₀ was derived under coexistence conditions, demonstrating that R₀ > 1 ensures viral persistence. Additionally, a multi-objective optimal control framework prioritizes cost minimization over infection reduction, offering resource-efficient strategies. Environmental transmission, a hallmark of Zika virus, accelerates early infection spread but is effectively mitigated by SIT. These results establish actionable thresholds (b_p, r_p) for balancing mosquito suppression and disease control, while providing theoretical insights applicable to dengue, malaria, and other arboviral diseases.