Fractional-Order Modeling of Dengue Transmission Dynamics Using the Atangana–Baleanu Fractional Derivative

Dengue fever remains a significant global health threat, and mathematical models are crucial for understanding its transmission and devising control strategies. Traditional integer-order models often limit to capture the long-range memory and historical dependencies inherent in epidemiological systems. To address this limitation, this study introduces a novel fractional-order SEIR-SEI model for dengue transmission, which uniquely employs the Atangana–Baleanu (ABC) fractional derivative. The use of the ABC derivative, with its non-singular Mittag-Leffler kernel, provides a more realistic framework to account for the memory effects in the disease’s progression through both human and mosquito populations. The model’s mathematical integrity was established by proving the existence and uniqueness of its solution. We derived the basic reproduction number ([Formula: see text]) and performed a comprehensive stability analysis of the disease-free and endemic equilibria. Key findings from our sensitivity analysis reveal that the basic reproduction number is most sensitive to parameters related to vector control, such as the mosquito death rate from insecticides ([Formula: see text]), inter-species transmission rates ([Formula: see text], [Formula: see text]), and the mosquito recruitment rate ([Formula: see text]). This result has important public health implications, providing strong quantitative evidence that prioritizing vector control measures is the most effective strategy for mitigating dengue outbreaks. The study thus presents a robust and insightful tool for public health policy making and a significant advancement in the mathematical modeling of infectious diseases.