A Fractional‐Order Dengue Transmission Model Incorporating Density‐Dependent Mosquito Recruitment and Control Interventions

Dengue fever remains a major global public health challenge, driven by urbanization, climate change, and the complex dynamics of mosquito‐borne transmission. In this study, we propose a fractional‐order host‐vector compartmental model to capture the transmission dynamics of dengue, incorporating density‐dependent mosquito recruitment, personal protection measures, and vector control interventions. The Caputo fractional derivative is employed to account for memory effects and hereditary properties inherent in biological systems, which are often neglected in classical integer–order models. We perform a rigorous qualitative analysis, including the positivity and boundedness of solutions, existence and uniqueness, and the derivation of the effective reproduction number . Local stability of the disease‐free equilibrium (DFE) is established under the condition , while Hyers–Ulam stability is also demonstrated. Using monthly dengue case data from Burkina Faso (2024) obtained from the OpenDengue project, we estimate key transmission parameters via nonlinear least squares. Numerical simulations explore the influence of the fractional order α and control intervention effectiveness on disease dynamics. Our results indicate that lower fractional orders ( α < 1) enhance strong memory‐dependent and that increasing personal protection efficacy significantly reduces peak infectious cases. The proposed framework provides a more realistic and flexible tool for evaluating intervention strategies in dengue‐endemic regions.