<p>Zika virus primarily spreads through the bites of Aedes aegypti mosquitoes and may also be transmitted from an infected woman to her fetus, through human contact, and from humans to mosquitoes. Traditional non-fractional models and bilinear incidence rates fail to account for memory-dependent dynamics and the psychological effects resulting from delayed immune responses and interventions. Therefore, we propose a Caputo fractional-order model that incorporates saturated incidence, multiple transmission pathways, and vertical transmission of the Zika virus. The existence and uniqueness of solutions are established by fixed-point theory. We explore the equilibrium states with their stability. The model is validated on weekly data from the 2018 Zika outbreak in Brazil. Numerical simulations performed using the Adams predictor-corrector method to show the effect of memory, vertical transmission, and multiple transmission routes on the spread of disease. Local and global sensitivity analyses identify the key parameter that influences the reproduction number. Numerical simulations and sensitivity reveal that transmission rate, medical treatment, and vector control are key sensitive parameters. We introduce a fractional-order optimal control model that incorporates prevention, treatment, and vector control. An efficiency and cost-effective analysis of seven different policies revealed that the policy with all three controls is the most effective, with the highest efficiency index of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(92.19\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>92.19</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>. In comparison, a policy focused exclusively on prevention measures is the most cost-effective. These insights will help public health authorities develop effective strategies to combat Zika outbreaks.</p>