The objective of this thesis is modelling the transmission of hepatitis B in Africa in general and, Senegal in particular. We propose new models based on the state of art and the epidemiology currently known from the transmission of the hepatitis B virus. Thus, we present two models of the transmission of HBV2, a model without vertical transmission and another in which the vertical transmission of the disease is taken into account. This second model is justi ed by the controversy, with regard to the incidence of the vertical and perinatal transmission of the virus in some parts of Africa ; between the World Health Organization on one hand and hepatitis B's specialists in Senegal on the other hand. These models helped us to analyse epidemiological models with a di erential susceptibility of the population, and stagged progression of infectious. We present a thorough analysis of the stability of the models using the Lyapunov techniques and obtain the basic reproduction ratio, R0 which allows into the study of general epidemiological models including those proposed for the transmission of the hepatitis B virus. Numerical simulations are done to illustrate the behaviour of the model, using data collected during the campaign against epidemic hepatitis B in Senegal and from published literature. These models enable the evaluation of the incidence of the vertical and perinatal transmission of the hepatitis B virus on the policies of Public health.
