<p>The global spread of the Zika virus (ZIKV), compounded by the absence of effective antiviral drugs or widely available vaccines, highlights the importance of understanding its transmission dynamics to implement effective public health strategies. The transmission of the Zika virus is attributable to the heterogeneity of sexual contacts and the lack of miracle drugs or vaccines. We develop a degree-based mathematical network model which takes account of heterogeneity of sexual contacts and the adoption of preventive measures. We derive analytical expressions for the basic reproduction number for three scenarios: mosquito-borne transmission only, sexual transmission only, and a combined scenario where both transmission routes coexist. In particular, we demonstrate that the basic reproduction number is proportional to the degree of network heterogeneity when the Zika virus transmission is solely driven by sexual contacts. Our proposed model possesses infinitely many disease-free equilibrium points, and we prove that these collectively form a locally attracting set under specified conditions. Finally, we present numerical simulations, calibrated with Zika epidemic data from Brazil (2015-2016), which indicate that increasing the number of individuals who take comprehensive protective measures (using screens, mosquito nets, insect repellent, condoms, etc.) can significantly reduce the final epidemic size.</p>