2009, 6(2): 283-299. doi: 10.3934/mbe.2009.6.283

The dynamics of a delay model of hepatitis B virus infection with logistic hepatocyte growth


Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, United States, United States


Department of Biology, Scottsdale Community College, Scottsdale, AZ 85256, United States


Department of Math & Statistics, College of Liberal Arts and Sciences, Arizona State University, Tempe, AZ 85287 - 1804

Received  May 2008 Revised  July 2008 Published  March 2009

Chronic HBV affects 350 million people and can lead to death through cirrhosis-induced liver failure or hepatocellular carcinoma. We analyze the dynamics of a model considering logistic hepatocyte growth and a standard incidence function governing viral infection. This model also considers an explicit time delay in virus production. With this model formulation all model parameters can be estimated from biological data; we also simulate a course of lamivudine therapy and find that the model gives good agreement with clinical data. Previous models considering constant hepatocyte growth have permitted only two dynamical possibilities: convergence to a virus free or a chronic steady state. Our model admits a third possibility of sustained oscillations. We show that when the basic reproductive number is greater than 1 there exists a biologically meaningful chronic steady state, and the stability of this steady state is dependent upon both the rate of hepatocyte regeneration and the virulence of the disease. When the chronic steady state is unstable, simulations show the existence of an attracting periodic orbit. Minimum hepatocyte populations are very small in the periodic orbit, and such a state likely represents acute liver failure. Therefore, the often sudden onset of liver failure in chronic HBV patients can be explained as a switch in stability caused by the gradual evolution of parameters representing the disease state.
Citation: Steffen Eikenberry, Sarah Hews, John D. Nagy, Yang Kuang. The dynamics of a delay model of hepatitis B virus infection with logistic hepatocyte growth. Mathematical Biosciences & Engineering, 2009, 6 (2) : 283-299. doi: 10.3934/mbe.2009.6.283

Suxia Zhang, Xiaxia Xu. A mathematical model for hepatitis B with infection-age structure. Discrete and Continuous Dynamical Systems - B, 2016, 21 (4) : 1329-1346. doi: 10.3934/dcdsb.2016.21.1329


Bao-Zhu Guo, Li-Ming Cai. A note for the global stability of a delay differential equation of hepatitis B virus infection. Mathematical Biosciences & Engineering, 2011, 8 (3) : 689-694. doi: 10.3934/mbe.2011.8.689


Avner Friedman, Wenrui Hao. Mathematical modeling of liver fibrosis. Mathematical Biosciences & Engineering, 2017, 14 (1) : 143-164. doi: 10.3934/mbe.2017010


Suxia Zhang, Hongbin Guo, Robert Smith?. Dynamical analysis for a hepatitis B transmission model with immigration and infection age. Mathematical Biosciences & Engineering, 2018, 15 (6) : 1291-1313. doi: 10.3934/mbe.2018060


Saif Ullah, Muhammad Altaf Khan, Muhammad Farooq, Taza Gul, Fawad Hussain. A fractional order HBV model with hospitalization. Discrete and Continuous Dynamical Systems - S, 2020, 13 (3) : 957-974. doi: 10.3934/dcdss.2020056


Elamin H. Elbasha. Model for hepatitis C virus transmissions. Mathematical Biosciences & Engineering, 2013, 10 (4) : 1045-1065. doi: 10.3934/mbe.2013.10.1045


Meihong Qiao, Anping Liu, Qing Tang. The dynamics of an HBV epidemic model on complex heterogeneous networks. Discrete and Continuous Dynamical Systems - B, 2015, 20 (5) : 1393-1404. doi: 10.3934/dcdsb.2015.20.1393


Tadas Telksnys, Zenonas Navickas, Miguel A. F. Sanjuán, Romas Marcinkevicius, Minvydas Ragulskis. Kink solitary solutions to a hepatitis C evolution model. Discrete and Continuous Dynamical Systems - B, 2020, 25 (11) : 4427-4447. doi: 10.3934/dcdsb.2020106


Ting Guo, Haihong Liu, Chenglin Xu, Fang Yan. Global stability of a diffusive and delayed HBV infection model with HBV DNA-containing capsids and general incidence rate. Discrete and Continuous Dynamical Systems - B, 2018, 23 (10) : 4223-4242. doi: 10.3934/dcdsb.2018134


Junyoung Jang, Kihoon Jang, Hee-Dae Kwon, Jeehyun Lee. Feedback control of an HBV model based on ensemble kalman filter and differential evolution. Mathematical Biosciences & Engineering, 2018, 15 (3) : 667-691. doi: 10.3934/mbe.2018030


Xichao Duan, Sanling Yuan, Kaifa Wang. Dynamics of a diffusive age-structured HBV model with saturating incidence. Mathematical Biosciences & Engineering, 2016, 13 (5) : 935-968. doi: 10.3934/mbe.2016024


Yuan Yuan, Xianlong Fu. Mathematical analysis of an age-structured HIV model with intracellular delay. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 2077-2106. doi: 10.3934/dcdsb.2021123


Gregory Zitelli, Seddik M. Djouadi, Judy D. Day. Combining robust state estimation with nonlinear model predictive control to regulate the acute inflammatory response to pathogen. Mathematical Biosciences & Engineering, 2015, 12 (5) : 1127-1139. doi: 10.3934/mbe.2015.12.1127


Mostafa Karimi, Noor Akma Ibrahim, Mohd Rizam Abu Bakar, Jayanthi Arasan. Rank-based inference for the accelerated failure time model in the presence of interval censored data. Numerical Algebra, Control and Optimization, 2017, 7 (1) : 107-112. doi: 10.3934/naco.2017007


Samitha Samaranayake, Axel Parmentier, Ethan Xuan, Alexandre Bayen. A mathematical framework for delay analysis in single source networks. Networks and Heterogeneous Media, 2017, 12 (1) : 113-145. doi: 10.3934/nhm.2017005


Avner Friedman, Chuan Xue. A mathematical model for chronic wounds. Mathematical Biosciences & Engineering, 2011, 8 (2) : 253-261. doi: 10.3934/mbe.2011.8.253


José Ignacio Tello. Mathematical analysis of a model of morphogenesis. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 343-361. doi: 10.3934/dcds.2009.25.343


Seema Nanda, Lisette dePillis, Ami Radunskaya. B cell chronic lymphocytic leukemia - A model with immune response. Discrete and Continuous Dynamical Systems - B, 2013, 18 (4) : 1053-1076. doi: 10.3934/dcdsb.2013.18.1053


Chengzhi Li, Jianquan Li, Zhien Ma. Codimension 3 B-T bifurcations in an epidemic model with a nonlinear incidence. Discrete and Continuous Dynamical Systems - B, 2015, 20 (4) : 1107-1116. doi: 10.3934/dcdsb.2015.20.1107


Ata Allah Taleizadeh, Biswajit Sarkar, Mohammad Hasani. Delayed payment policy in multi-product single-machine economic production quantity model with repair failure and partial backordering. Journal of Industrial and Management Optimization, 2020, 16 (3) : 1273-1296. doi: 10.3934/jimo.2019002

2018 Impact Factor: 1.313


  • PDF downloads (126)
  • HTML views (0)
  • Cited by (50)

[Back to Top]