Investigating non-local dynamics in Zika virus transmission: a fractal-fractional approach

The re-emergence of Zika virus remains a significant public-health concern because its transmission dynamics involve both symptomatic and asymptomatic infections. This paper develops a deterministic Zika virus transmission model using the fractal–fractional Caputo operator to incorporate memory effects and heterogeneous temporal scaling. The model includes susceptible, exposed, symptomatic infectious, asymptomatic infectious, clinically managed infectious, and recovered human classes, together with susceptible, exposed, and infectious vector classes. The Sterile Insect Technique is incorporated through a constant sterile-male mosquito density that suppresses the vector population. Positivity, boundedness, existence, and uniqueness of solutions are established under suitable assumptions. The disease-free equilibrium is obtained, and the basic reproduction number R₀ is derived using the next-generation matrix approach. A generalized Adams–Bashforth–Moulton scheme is used to approximate the resulting nonlinear fractal–fractional system. In the integer-order limit, the numerical solution is compared with a high-accuracy LSODA reference solution, and the observed convergence behavior supports the reliability of the proposed scheme for the selected parameter set. Sensitivity analysis shows that the mosquito biting rate is the dominant risk parameter, whereas sterile-male density contributes to reducing the disease threshold. Numerical simulations further indicate that the fractional order and fractal dimension influence the transient epidemic profile, including the timing and magnitude of infection peaks. The results suggest that SIT-based vector suppression, combined with conventional control measures, may help reduce Zika transmission under suitable parameter conditions.