# American Institue of Mathematical Sciences

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

 1 Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, United States, United States 2 Department of Biology, Scottsdale Community College, Scottsdale, AZ 85256, United States 3 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
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