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

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.

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.

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.

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.