Application de la théorie des Équations Différentielles Abstraites (EDA) à des problèmes de dynamique de population

Abstract

In this thesis, we consider the infestation of a village by the domestic species Triatoma. Dimidiata. The village adjoins a forest representing the habitat of vectors. The latter go to the village to eat. Food is a meal of blood from the humans or mammals they breed. The transmission of Trypanosoma Cruzi from vector to host takes place mainly during this phase. In this work, we consider a triatomic population structured in time and space. The processes of demography and spatial dispersion are captured by reaction-diffusion equations in two-dimensional space. In adequate functional spaces, the system of partial differential equations is transformed into an abstract differential equation. Our first objective is to show that the operator generates an analytical semi-group. We then prove the existence and uniqueness of a local solution to the corresponding Cauchy problem