Mathematical Modelling of Dengue Transmission with Adaptive Fuzzy Backstepping Control and RK-5 Numerical Method

Abstract

The aim of this research is to create an adaptive nonlinear fuzzy backstepping robust controller for a dengue disease outbreak model. We use an SIR-SI compartmental mathematical model to analyse the diffusion mechanism of dengue disease. A nonlinear adaptive controller regulates prevention strategies for susceptible human beings and enhances hospitalization-based treatment for the infected people. Besides, the spraying of chemical insecticides will reduce the infected mosquito population. Adaptation laws are used to derive fuzzy system parameters, enhancing the system's adaptability. Then we construct a suitable Lyapunov function, which guarantees convergence, robustness, and stability for a closed-loop system. Finally, we plot all the system's control variables graphically and calculate their numerical approximations using the Runge–Kutta technique of fifth order. These simulations demonstrate that the proposed adaptive controllers can effectively control the dengue disease and ensure the stability of the system. Hence, we conclude that adaptive backstepping control measures can protect more people from dengue infection.