In this paper, we analyze the Zika virus transmission dynamics on human and mosquito populations. Mosquitoes play a role of infectious agents and vector of the Zika virus (ZIKV). In this sense, we set out a mathematical model assuming constant size population for the evolution of the infected humans with ZIKV and analyze its qualitative dynamics. The epidemic threshold parameter for the extinction of disease is computed. Numerical simulations of the model varying the numerical values of the parameters corroborate the theoretical results regarding . The values of the parameters related to the mathematical model of the Zika epidemic are estimated using real data from Zika prevalence in Colombia for year 2016. We find a for this particular case which allows us to understand and explain some aspects of the Zika epidemic in Colombia. These results are valuable since they can be compared with Zika epidemics in other countries and from other years, and enrich the knowledge about the dynamics of the spread of Zika virus.