[@paty2014large] from November 2013 to June 2014, and these cases are reportedly traced back to travelers returning from the French Caribbean islands where chikungunya and Dengue are endemic [@paty2014large]. The 2012 Portugal’s Dengue outbreak was reported to be imported by a traveler from Venezuela [@wilder20142012]. It is therefore important the gauge the impacts of infected immigrants of the dynamics of vector-borne diseases.\
Typically, modeling the dynamics of directly transmitted or vector-borne diseases have often been based on the assumption that the recruitment into the considered population is completely susceptible, and thereby sweeping the effects of global movement of individuals across the world at unprecedented levels under the rug. To the best of our knowledge, Brauer and van den Driessche [@BraVdd01] were the to first propose a mathematical model that accounts for immigration that includes infected individuals using an SIS structure in an attempt to study HIV in prisons. Subsequently, McCluskey and van den Driessche [@1056.92052] proposed a model studied with the same features where both immigration of latent and infective are considered, in the context tuberculosis. These two papers [@BraVdd01; @1056.92052] showed that there is no disease-free equilibrium and that the endemic equilibrium (EE) is globally asymptotically stable. Indeed, the 