Fractional Modeling of Dengue Transmission with Vaccination and Vector Control Strategies

Dengue remains a major public health problem in tropical countries, particularly in Brazil, where the mosquito \textit{Aedes aegypti} is widely distributed in urban environments. In this work, we propose a fractional-order mathematical model to describe the transmission dynamics of dengue incorporating vaccination and vector control strategies. The model considers human and mosquito populations, including the aquatic phase of the vector life cycle, as well as mechanical and chemical control measures acting on the mosquito population. Analytical expressions for the basic reproduction number are derived for different control scenarios, allowing the evaluation of the combined effects of vector control and vaccination. Model parameters are estimated using reported dengue case data from the city of Bauru, São Paulo, Brazil. Numerical simulations indicate that increasing mosquito mortality significantly reduces the transmission potential of dengue. The results also show that fractional derivatives introduce memory effects into the epidemic dynamics, producing smoother epidemic curves and slower temporal evolution compared to classical integer-order models.