The Zika Virus (ZIKV) is a virus transmitted by Aedes aegypti mosquitoes (same as the one transmitting dengue and chikungunya fever) and Aedes albopictus. The main way of contagion by the ZIKV is caused by the bite of a mosquito that, after feeding from someone contaminated, can transport the ZIKV throughout its life, transmitting the disease to a population that does not have the immunity. It can also be transmitted through a person s sexual relationship with ZIKV to their partners, even if the infected person does not have the symptoms of the disease. In this work, we present two mathematical models for the ZIKV epidemic by using (1) ordinary differential equations and, (2) ordinary differential equations with temporal delay, which is the time it takes mosquitoes to develop the virus. We make a comparison between the two modeling variants and, to facilitate the work with the models, we provide a graphical user interface. Computational simulations are performed for Suriname and El Salvador, which are countries that are prone to develop the epidemic in an endemic manner. In order to study the spatial diffusion of ZIKV, we propose a model based on advection-diffusion equations and create a numerical scheme with finite elements and finite differences to resolve it.