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.

Dynamics of a generalized viral infection model with adaptive immune response

“…Note that our model (1) extends the model [1] when f (x, y, v) = βx and the model [4] when f (x, y, v) = βx x + y . In addition, the hypotheses (H 1 ) − (H 3 ) are checked by other forms of incidence rates including the saturation incidence used by Li and Ma in [16] when f (x, y, v) = βx 1 + v , Beddington-DeAngelis incidence function used in [8,9,17] …”

“…This suggests that this model may not be a reasonable model for describing HCV virus infection since it implies that an individual with a smaller liver may be more resistant to the virus infection than an individual with a larger one. Therefore, the authors Yousfi et al [4] corrected this problem by replacing the mass action process βxv with a standard incidence function of the form βxv x + y in order to model the adaptive immune response in hepatitis B virus (HBV) infection. In addition, there are some models considered only one type of adaptive immunity.…”

Mathematical Modeling of the Adaptive Immune Responses in the Early Stage of the HBV Infection

“…To our knowledge, there is no study that investigates the adaptive immune response in the early stage of the infection and effect of the early treatment on the progress of the disease. In this work, we are aiming to investigate this issue by considering an augmented model of our recent works [18,19], and we consider the logistic growth only for the healthy hepatocyte cells and the infected hepatocyte cells [11]. This assumption is made to reflect the nature of the growth of these two types of cells in the early stage of the infection.…”

“…Mathematical modeling of the immune response to HBV is a subject that has been heavily investigated over the years by many authors [11][12][13][14][15][16][17][18], just to name a few. To our knowledge, there is no study that investigates the adaptive immune response in the early stage of the infection and effect of the early treatment on the progress of the disease.…”

Global Properties of General Viral Infection Models with Humoral Immune Response

“…Several works have been devoted to propose and analyze mathematical models of viral infectious dynamics such as human immunodeficiency virus (HIV) [1][2][3][4][5][6][7][8][9][10][11][12][13][14], hepatitis B virus (HBV) [15][16][17][18][19][20], hepatitis C virus (HCV) [21][22][23] and human T cell leukemia (HTLV) [24], etc. Mathematical models of viral infection can help for understanding the viral dynamics and developing antiviral drug therapies.…”