Visiting Scholar Long term

Mathematical Biosciences Institute

The Ohio State University (Columbus, OH)

Avner Friedman, Gauthier Sallet

mathematical epidemiology, Modeling the infectious disease transmission between host (HIV, Hepatitis B virus HBV, optimal control of the spread of this diseases, impact of vaccination, changing behiavor policy)

During my PhD thesis, 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 HBV, 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 dierential susceptibility of the population, and stagged 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.
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.