• 1 Université Alioune Diop de Bambey
• 2 Unité de modélisation mathématique et informatique des systèmes complexes [Bondy]

For more than one century, Aedes species are supposed to be a reservoir in dengue, yellow fever, rift valley fever and west nile viruses transmission. In this article, we study an infinite dimension ordinary differential equations system that models arbovirus vertical transmission in \textit{Aedes} mosquito. Relying of the positive semigroup theory, we show that the model is well-posed and compute a threshold parameter known as the basic reproduction ratio $R0$. This parameter describes "the average rate of secondary new cases of infected adult females from emergences in a breeding habitat that are produced by an infected adult female via transovarial transmission during its lifetime." In addition, we prove that the solution of the model goes to zero asymptotically if R0<1$, else it has the property of balanced exponential growth. Finally, a climate-environment effects Index on model parameters and a diagram depicting the conditions of arboviruses persistence via Aedes in nature is derived.