Article

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.
Mathematical biosciences and engineering: MBE (Impact Factor: 0.87). 05/2009; 6(2):283-99. DOI: 10.3934/mbe.2009.6.283
Source: PubMed

ABSTRACT 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.

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    • "it can be detected in non hepatic tissues (kidney, pancreas or skin). Hepatitis B is endemic in Africa [8] [32] [1] [23] [49] (see also the references cited therein) and some models have been constructed in order to understand its dynamic with Ordinary Differential Equations (with or without time delay) or based on stochastic processes [5] [10] [20] [32] [16] [45] [30] [56] or using partial differential equations models [55] [53]. "
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    • "Hepatitis B is endemic in Africa [4] [14] [18] (see also the references cited therein) and some models have been constructed in order to understand its dynamic with ODE deterministic (with delay or not) or stochastic processes [1] [2] [5] [6] [7] [14] [21] or partial differential equations [19] [20]. Studies like [11] [12] [16] [19] [20] recognized the importance of the age factor in the dynamics of infectious diseases like hepatitis B (see [20] for a good description). "
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    ABSTRACT: We construct and study a differential infectivity model with chronological and infection ages. The application is done on hepatitis B in Cameroon. We prove the global stability of the disease free equilibrium when the basic reproduction number R0 is less than one and the existence and uniqueness of an endemic equilibrium when R0 > 1 .
    Applied Mathematical Sciences 12/2013; 7(120):5977 - 5993. · 0.47 Impact Factor
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    • "it can be detected in non hepatic tissues (kidney, pancreas or skin). Hepatitis B is endemic in Africa [8] [32] [1] [23] [49] (see also the references cited therein) and some models have been constructed in order to understand its dynamic with Ordinary Differential Equations (with or without time delay) or based on stochastic processes [5] [10] [20] [32] [16] [45] [30] [56] or using partial differential equations models [55] [53]. "
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    ABSTRACT: We are studiying in this manuscript, the hepatitis B dynamic in a closed population without vertical transmission. Then we shed some light on the asymptotic behaviour of a SEI PDE model. Under suitable (biological and mathematical) assumptions, it is shown that the disease free equilibrium is globally asymptotically stable (GAS) if R0 < 1. On the other hand R0 > 1 induces (through a perturbation result of Magal [2009]) that endemic equilibrium is GAS and the system is uniformly persistent.
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