Dengue is considered an emerging disease with an increasing prevalence especially in South America. In 2002, an epidemic of classic Dengue (DENV-1) occurred unexpectedly on Easter Island, where it had never been detected before. It reappeared in 2006-2007 and 2008, 2009 and 2011. The aim of this study was to estimate the most relevant parameters of the epidemiological dynamics of transmission of Dengue on Easter Island and to model the dynamics since 2002, comparing the predictions with the actual situation observed. Of the total cases, 52.27% were females and 47.73% men. The average age of infection was 31.38 ± 18.37 years, similar in men and women. We estimated the reproductive number R0 = 3.005 with an IC0,95 = [1.92, 4.61]. The inter-epidemic period reached an estimated T = 5.20 to 6.8 years. The case simulation showed recurrent epidemics with decreasing magnitude (damped oscillations), which is a known phenomenon in models of dengue and malaria. There was good qualitative fit to the epidemiological dynamics from 2002 onwards. It accurately predicted the rise in cases between 2006 and 2011. The predicted number of cases during the 2002 epidemic is greater than the confirmed cases and the predicted epidemic was faster than notified cases. Interepidemic period in the simulation was 6.72 years between 2002 and 2008 and 4.68 years between 2008 and 2013. From the theoretical perspective, the first epidemic had affected 94% of the population (approximately 3500 cases), but 639 were reported suggesting underreporting and a lot of sub-clinical cases occurred. Future epidemic of decreasing size are expected, although the main danger are epidemics of hemorrhagic dengue fever resulting from the introduction of different dengue virus serotypes.