Analysis and numerical simulation of a fractal-fractional Chikungunya model with saturated incidence

This study develops a mathematical model for the transmission dynamics of the Chikungunya (CHIK) virus using the Caputo-Fabrizio fractal-fractional derivative (CFFFD), which incorporates memory effects and complex transmission patterns not captured by traditional models. The fractal-fractional approach accounts for memory effects and long-range dependence in disease transmission, allowing more accurate representation of real-world dynamics in which current states depend on past history. This framework improves the prediction of outbreak patterns and supports a more thorough assessment of control measures such as vaccination and vector control. The existence and uniqueness of solutions are established using the Krasnoselskii and Banach fixed-point theorems. Numerical simulations are performed via the Adams-Bashforth method, together with stability and sensitivity analyses. Graphical results illustrate the effects of the fractional order ([Formula: see text]) and fractal dimension ([Formula: see text]) on CHIK transmission dynamics. The findings provide useful insights for public health policymakers.