title: Modeling the adaptive immune response in HBV infection.
abstract: The aim of this work is to investigate a new mathematical model that describes the interactions between Hepatitis B virus (HBV), liver cells (hepatocytes), and the adaptive immune response. The qualitative analysis of this as cytotoxic T lymphocytes (CTL) cells and the antibodies. These outcomes are (1) a disease free steady state, which its local stability is characterized as usual by R                         (0) < 1, (2) and the existence of four endemic steady states when R                         (0) > 1. The local stability of these steady states depends on functions of R                         (0). Our study shows that although we give conditions of stability of these steady states, not all conditions are feasible. This rules out the local stability of two steady states. The conditions of stability of the two other steady states (which represent the complete failure of the adaptive immunity and the persistence of the disease) are formulated based on the domination of CTL cells response or the antibody response.
authors.affiliation: Department of Mathematics and Computer Science, Hassan II University, Casablanca, Morocco. nourayousfi@gmail.com
authors.forename: Noura
authors.initials: N
authors.lastname: Yousfi
authors.forename: Khalid
authors.initials: K
authors.lastname: Hattaf
authors.forename: Abdessamad
authors.initials: A
authors.lastname: Tridane
mesh_terms: D056704:Adaptive Immunity; D000914:Antibodies, Viral / Q000276:immunology; D005260:Female; D006515:Hepatitis B virus; D019694:Hepatitis B, Chronic / Q000276:immunology*; D022781:Hepatocytes / Q000276:immunology; D006801:Humans; D008297:Male; D018448:Models, Immunological; D013602:T-Lymphocytes, Cytotoxic / Q000276:immunology
chemical_list: D000914:Antibodies, Viral