The dynamics of a delay model of hepatitis B virus infection with logistic hepatocyte growth
Chronic HBV affects 350 million people and can lead to death through cirrhosis-inducedliver failure or hepatocellular carcinoma. We analyze the dynamics of a model consideringlogistic hepatocyte growth and a standard incidence function governing viral infection.This model also considers an explicit...
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AIMS Press
2009-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.283 |
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| author | Steffen Eikenberry Sarah Hews John D. Nagy Yang Kuang |
| author_facet | Steffen Eikenberry Sarah Hews John D. Nagy Yang Kuang |
| author_sort | Steffen Eikenberry |
| collection | DOAJ |
| description | Chronic HBV affects 350 million people and can lead to death through cirrhosis-inducedliver failure or hepatocellular carcinoma. We analyze the dynamics of a model consideringlogistic hepatocyte growth and a standard incidence function governing viral infection.This model also considers an explicit time delay in virus production. With this modelformulation all model parameters can be estimated from biological data; we also simulatea course of lamivudine therapy and find that the model gives good agreement with clinicaldata. Previous models considering constant hepatocyte growth have permitted only twodynamical possibilities: convergence to a virus free or a chronic steady state. Ourmodel admits a third possibility of sustained oscillations. We show that when thebasic reproductive number is greater than 1 there exists a biologically meaningfulchronic steady state, and the stability of this steady state is dependent upon boththe rate of hepatocyte regeneration and the virulence of the disease. When thechronic steady state is unstable, simulations show the existence of an attractingperiodic orbit. Minimum hepatocyte populations are very small in the periodicorbit, and such a state likely represents acute liver failure. Therefore, theoften sudden onset of liver failure in chronic HBV patients can be explained asa switch in stability caused by the gradual evolution of parameters representingthe disease state. |
| format | Article |
| id | doaj-art-8520ae4e60f34eee8a3042dd3f19aa83 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-8520ae4e60f34eee8a3042dd3f19aa832025-01-24T01:59:06ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-02-016228329910.3934/mbe.2009.6.283The dynamics of a delay model of hepatitis B virus infection with logistic hepatocyte growthSteffen Eikenberry0Sarah Hews1John D. Nagy2Yang Kuang3Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287Chronic HBV affects 350 million people and can lead to death through cirrhosis-inducedliver failure or hepatocellular carcinoma. We analyze the dynamics of a model consideringlogistic hepatocyte growth and a standard incidence function governing viral infection.This model also considers an explicit time delay in virus production. With this modelformulation all model parameters can be estimated from biological data; we also simulatea course of lamivudine therapy and find that the model gives good agreement with clinicaldata. Previous models considering constant hepatocyte growth have permitted only twodynamical possibilities: convergence to a virus free or a chronic steady state. Ourmodel admits a third possibility of sustained oscillations. We show that when thebasic reproductive number is greater than 1 there exists a biologically meaningfulchronic steady state, and the stability of this steady state is dependent upon boththe rate of hepatocyte regeneration and the virulence of the disease. When thechronic steady state is unstable, simulations show the existence of an attractingperiodic orbit. Minimum hepatocyte populations are very small in the periodicorbit, and such a state likely represents acute liver failure. Therefore, theoften sudden onset of liver failure in chronic HBV patients can be explained asa switch in stability caused by the gradual evolution of parameters representingthe disease state.https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.283delayacute liver failure.hbvhepatitis bmathematical model |
| spellingShingle | 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 and Engineering delay acute liver failure. hbv hepatitis b mathematical model |
| title | The dynamics of a delay model of hepatitis B virus infection with logistic hepatocyte growth |
| title_full | The dynamics of a delay model of hepatitis B virus infection with logistic hepatocyte growth |
| title_fullStr | The dynamics of a delay model of hepatitis B virus infection with logistic hepatocyte growth |
| title_full_unstemmed | The dynamics of a delay model of hepatitis B virus infection with logistic hepatocyte growth |
| title_short | The dynamics of a delay model of hepatitis B virus infection with logistic hepatocyte growth |
| title_sort | dynamics of a delay model of hepatitis b virus infection with logistic hepatocyte growth |
| topic | delay acute liver failure. hbv hepatitis b mathematical model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.283 |
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