| Mathematical models in epidemiology seek to understand the progress of infectious diseases. These models can be used to predict outbreaks and can give us some answers on how to manage them by means of vaccination campaigns. In this thesis we study the existence of traveling wave solutions for a nonlocal reaction-diffusion model of Influenza A. We present results for the existence of the traveling wave solutions for the integro-differential system of equations for the kernel K(x) = 1 - e -ax, where a is a crossprotection parameter. The proof for the existence of the traveling waves take advantage of the different time scales between the evolution of the mutation and the evolution of the disease in the population. First, we prove the existence of the solution for the unperturbed case, that is when epsilon = 0. The proof for the existence of the solution to the perturbed system follows by Contraction Principle. |
