Adams–Bashforth Moulton Numerical Approach on Dengue Fractional Atangana Baleanu Caputo Model and Stability Analysis

This study presents a comprehensive dengue disease model that accounts for recovery with low immunity and progression to severe dengue within a traditional SIR-SI framework. The population is divided into three subpopulations, including suspected, infected, and recovered individuals. The human population is represented as the host while the mosquito population is represented as the vector. A fractional order operator known as ABC (Atangana Baleanu Caputo) is applied to extract some qualitative data about dengue disease. This research evaluates an essential model attributes and the reproduction rate, identifying local asymptotic stability states. Furthermore, the Adams–Bashforth–Moulton predictor corrector technique is employed to find approximate solutions to the proposed model. Numerical simulations reveal a significant impact of fractional order on dengue dynamics. These findings indicate that reproductive number \({R}_{0}\) $R_0$ can be reduced under certain conditions, thereby highlighting the potential for effective disease control strategies.