Chaotic Dynamics and Theoretical Modeling of Dengue Fever Transmission Using a Modified ABC Fractional Operator Enhanced by Machine Learning

Dengue fever remains a primary global health concern, particularly in tropical and subtropical regions. This study proposes a fractional-order mathematical model of dengue transmission based on a modified Atangana–Baleanu–Caputo (mABC) derivative, incorporating six epidemiological compartments. The existence of solutions is established, and a series solution is obtained using Laplace transforms and decomposition techniques. Stability is assessed via fixed point theory and the Picard approach. Numerical simulations under varying fractional orders confirm positivity and stability of solutions. To capture the system’s complexity, chaotic behavior is explored through phase-space reconstruction using time-delay embedding, revealing butterfly-like attractors that highlight sensitivity to initial conditions and nonlinear dynamics. Furthermore, artificial neural networks (ANN) are employed for predictive modeling, demonstrating high accuracy. This work highlights the importance of fractional-order and chaotic analysis in understanding dengue dynamics and provides a foundation for developing improved control strategies.