Optimal control of a delayed hepatitis B viral infection model with cytotoxic T-lymphocyte and antibody responses

2016 ◽  
Vol 5 (3) ◽  
pp. 893-902 ◽  
Author(s):  
Adil Meskaf ◽  
Karam Allali ◽  
Youssef Tabit
Keyword(s):  
Optimal Control ◽  
Hepatitis B ◽  
Viral Infection ◽  
T Lymphocyte ◽  
Cytotoxic T Lymphocyte ◽  
Antibody Responses ◽  
Infection Model ◽  
Hepatitis B Viral Infection ◽  
Viral Infection Model

Analysis of a hepatitis B viral infection model with immune response delay

2017 ◽  
Vol 10 (02) ◽  
pp. 1750020 ◽  
Author(s):  
Jianhua Pang ◽  
Jing-An Cui
Keyword(s):  
Immune Response ◽  
Time Delay ◽  
Hepatitis B ◽  
Viral Infection ◽  
Endemic Equilibrium ◽  
Infection Model ◽  
Response Delay ◽  
The Stability ◽  
Hepatitis B Viral Infection ◽  
Viral Infection Model

In this paper, a hepatitis B viral infection model with a density-dependent proliferation rate of cytotoxic T lymphocyte (CTL) cells and immune response delay is investigated. By analyzing the model, we show that the virus-free equilibrium is globally asymptotically stable, if the basic reproductive ratio is less than one and an endemic equilibrium exists if the basic reproductive ratio is greater than one. By using the stability switches criterion in the delay-differential system with delay-dependent parameters, we present that the stability of endemic equilibrium changes and eventually become stable as time delay increases. This means majority of hepatitis B infection would eventually become a chronic infection due to the immune response time delay is fairly long. Numerical simulations are carried out to explain the mathematical conclusions and biological implications.

scholarly journals Antibody Responses during Hepatitis B Viral Infection

2014 ◽  
Vol 10 (7) ◽  
pp. e1003730 ◽  
Author(s):  
Stanca M. Ciupe ◽  
Ruy M. Ribeiro ◽  
Alan S. Perelson
Keyword(s):  
Hepatitis B ◽  
Viral Infection ◽  
Antibody Responses ◽  
Hepatitis B Viral Infection

scholarly journals Mathematical Analysis and Treatment for a Delayed Hepatitis B Viral Infection Model with the Adaptive Immune Response and DNA-Containing Capsids

2018 ◽  
Vol 7 (4) ◽  
pp. 35 ◽  
Author(s):  
Jaouad Danane ◽  
Karam Allali
Keyword(s):  
Hepatitis B ◽  
Cytotoxic T Lymphocyte ◽  
Minimum Principle ◽  
Adaptive Immune Response ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Infection Model ◽  
Control Pair ◽  
B Virus ◽  
Hepatitis B Viral Infection

We model the transmission of the hepatitis B virus (HBV) by six differential equations that represent the reactions between HBV with DNA-containing capsids, the hepatocytes, the antibodies and the cytotoxic T-lymphocyte (CTL) cells. The intracellular delay and treatment are integrated into the model. The existence of the optimal control pair is supported and the characterization of this pair is given by the Pontryagin’s minimum principle. Note that one of them describes the effectiveness of medical treatment in restraining viral production, while the second stands for the success of drug treatment in blocking new infections. Using the finite difference approximation, the optimality system is derived and solved numerically. Finally, the numerical simulations are illustrated in order to determine the role of optimal treatment in preventing viral replication.

scholarly journals Spatiotemporal Dynamics of a Generalized Viral Infection Model with Distributed Delays and CTL Immune Response

Computation ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 21 ◽  
Author(s):  
Khalid Hattaf
Keyword(s):  
Immune Response ◽  
Viral Infection ◽  
Cytotoxic T Lymphocyte ◽  
Distributed Delays ◽  
Infection Model ◽  
Cell Infection ◽  
Incidence Functions ◽  
Dynamics Models ◽  
Ctl Immune Response ◽  
Viral Infection Model

In this paper, we propose and investigate a diffusive viral infection model with distributed delays and cytotoxic T lymphocyte (CTL) immune response. Also, both routes of infection that are virus-to-cell infection and cell-to-cell transmission are modeled by two general nonlinear incidence functions. The well-posedness of the proposed model is also proved by establishing the global existence, uniqueness, nonnegativity and boundedness of solutions. Moreover, the threshold parameters and the global asymptotic stability of equilibria are obtained. Furthermore, diffusive and delayed virus dynamics models presented in many previous studies are improved and generalized.

Sign in / Sign up

Export Citation Format

Share Document