(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Dengue fever is a mosquito-borne viral infection that poses significant health risks and contributes to severe social and economic burdens, particularly in low-resource communities. Understanding the complex transmission dynamics of dengue is essential for developing effective control strategies. In this study, we investigate the spread of dengue by incorporating the effects of vaccination and a saturated incidence rate into a compartmental model formulated within the framework of the fractal-fractional Caputo derivative. This advanced mathematical approach captures the memory and hereditary properties of the disease progression. We derive the basic reproduction number, R_0, using the next-generation matrix method to assess the potential for disease persistence or elimination. Numerical simulations are carried out using a reliable computational scheme to evaluate how different biological and intervention-related parameters influence the course of the outbreak. Our results reveal the pivotal role of vaccination coverage, transmission rates, and saturation effects in shaping the epidemic curve. The analysis identifies key parameters that most strongly affect disease dynamics, offering valuable insights for public health authorities to optimize intervention strategies aimed at reducing dengue transmission and mitigating outbreak severity.