Nonlinear Robust Adaptive Sliding Mode Control Strategies Involve a Fractional Ordered Approach to Reducing Dengue Vectors

Abstract

This study presents an innovative approach by integrating adaptive sliding mode control strategies with fractional order modeling to address the challenge of reducing Aedes aegypti mosquito populations, the primary vector of Dengue - a widespread and debilitating disease. By employing the Atangana-Baleanu-Caputo fractional operator to model the dynamics of the mosquito population, we achieve a more precise representation of complex and non-linear behaviors. The motivation behind adopting the Adaptive Sliding Mode Control (ASMC) approach lies in the critical need to efficiently control Aedes aegypti mosquito populations, a key step in combating the prevalence of dengue. The ASMC method dynamically adjusts control parameters based on evolving conditions, enhancing its adaptability to the changing dynamics of mosquito populations.The Lyapunov stability theorem ensures the reliability of tracking convergence and control structure. Additionally, we implement the Toufik Atangana method to solve both state and adjoint fractional differential equations using the ABC derivative operator. This incorporation adds a novel dimension to the study, providing a comprehensive framework for addressing the intricate dynamics inherent in the Aedes aegypti mosquito population. To assess the effectiveness of the proposed strategy, a numerical performance index is introduced at the end of the abstract. This index justifies the controller’s efficacy by comparing it to other conventional controllers. The inclusion of this quantitative measure reinforces the significance of the proposed strategy in the context of dengue prevention and control efforts.