A Fractional-Order Framework for Dengue Transmission Dynamics with Human-to-Human and Mosquito-to-Mosquito Pathways

BACKGROUND OBJECTIVES: Dengue fever remains a major global public health threat, responsible for millions of infections annually across tropical and subtropical regions. Despite extensive modeling efforts, most existing studies focus exclusively on mosquito-mediated transmission and overlook additional non-vectorial pathways that may influence outbreak persistence. METHODS: This study addresses this gap by developing the first fractional-order dengue transmission model that simultaneously integrates human-to-human, mosquito-to-mosquito, human-to-mosquito, and mosquito-to-human transmission routes. The Caputo fractional derivative is applied to capture memory effects and nonlocal temporal behavior inherent in real epidemic processes. RESULTS: Analytical results demonstrate that the model exhibits backward bifurcation when the mosquito-to-mosquito reproduction number exceeds unity, implying that dengue may persist even when the basic reproduction number falls below one. Numerical simulations reveal that fractional-order dynamics slow epidemic decay, delay infection peaks, and prolong outbreak duration compared with classical integer-order models. These findings indicate that memory effects significantly influence disease persistence and the effectiveness of control measures. INTERPRETATION CONCLUSION: By bridging an important gap in dengue modeling, this framework highlights the combined epidemiological impact of multi-route transmission and fractional dynamics. The results provide insight into designing integrated and sustainable dengue control strategies that account for vectorial, non-vectorial, and memory-dependent transmission processes.