A Hybrid Fractal-Fractional and Machine Learning Framework for Zika Virus Spread Prediction

We develop and analyze a Zika transmission model that couples mosquito-borne and sexual pathways with host awareness and vector control interventions, assuming no disease-induced mortality. The dynamics are formulated in a fractal-fractional framework with order ℘ and fractal dimension ς, allowing memory and nonlocal effects. Existence and uniqueness of solutions are established via compactness and a Banach fixed-point argument, and Ulam–Hyers stability is derived for the integral equation representing the system. For computation, we design a fractional Adams–Bashforth scheme and report simulations using baseline parameters from the literature. One at a time, sensitivity experiments identify the dominant amplifiers of infection (mosquito biting b2 and transmission probabilities, together with sexual contact c and α2) and show that awareness a and vector control b suppress prevalence; the fractional parameters modulate persistence, with larger ℘/ς prolonging transients. We further employ a feedforward artificial neural network as a surrogate to approximate the numerical solution, using a training, validation, testing split, and standard performance diagnostics. Finally, we compare operator choices integer, Caputo, Hilfer, Atangana–Baleanu in Caputo sense, and FF under identical settings; all memory-bearing models decay more slowly than the classical system, with ABC/FF exhibiting the strongest persistence. Future research will extend this framework to spatially structured and seasonally varying settings, calibrated with surveillance data, to support optimal intervention design and real-time decision-making.