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Arbovirus constitutes a group of virus that is transmitted by arthropod's bites. Examples of diseases produced by this kind of virus are Dengue, Yellow Fever, and West Nile Virus, among others. These diseases are a major health problem in the world. In this work we formulate a system of differential equations to study the dynamics of an infection produced by arbovirus. For this, we consider the population of host (humans, birds, mammals, etc.), and vectors (mosquitoes, ticks, etc.) The aim of this study is to understand and predict the formation of outbreaks from a variety of initial conditions. Control measures of the mosquito population are discussed in terms of threshold conditions, which govern the existence and stability of the endemic equilibrium.