The aim of this thesis is the mathematical analysis and the estimation of the parameters of some metapopulation models for bilharzia transmission. We explain how the metapopulation models are built and give a full analysis of their stability. We compute the basic reproduction number R0. We show that if R0 is less than 1 then the Disease Free Equilibrium(DFE) is globally asymptotically stable. In case R0 is higher than 1, we prove the existence and the uniqueness of an endemic equilibrium which is globally asymptotically stable. At last,we suggest methods for the estimation of the states and the parameters for models. We build a numerical observer using the Moving Horizon State Estimation(MHSE) and an analitic one by the High Gain observer method. Applications of these methods will be done on the Macdonald transmission model of bilharzia.
