Chronic hepatitis B virus (HBV) infection is a major cause of human suffering, and a number of mathematical models have examined within-host dynamics of the disease. Most previous HBV infection models have assumed that: (a) hepatocytes regenerate at a constant rate from a source outside the liver; and/or (b) the infection takes place via a mass action process. Assumption (a) contradicts experimental data showing that healthy hepatocytes proliferate at a rate that depends on current liver size relative to some equilibrium mass, while assumption (b) produces a problematic basic reproduction number. Here we replace the constant infusion of healthy hepatocytes with a logistic growth term and the mass action infection term by a standard incidence function; these modifications enrich the dynamics of a well-studied model of HBV pathogenesis. In particular, in addition to disease free and endemic steady states, the system also allows a stable periodic orbit and a steady state at the origin. Since the system is not differentiable at the origin, we use a ratio-dependent transformation to show that there is a region in parameter space where the origin is globally stable. When the basic reproduction number, R (0), is less than 1, the disease free steady state is stable. When R (0) > 1 the system can either converge to the chronic steady state, experience sustained oscillations, or approach the origin. We characterize parameter regions for all three situations, identify a Hopf and a homoclinic bifurcation point, and show how they depend on the basic reproduction number and the intrinsic growth rate of hepatocytes.

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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We develop mathematical models for the role of hepatitis B e-antigen in creating immunological tolerance during hepatitis B virus infection and propose mechanisms for hepatitis B e-antigen clearance, subsequent emergence of a potent cellular immune response, and the effect of these on liver damage. We investigate the dynamics of virus-immune cells interactions, and derive parameter regimes that allow for viral persistence. We modify the model to account for mechanisms responsible for hepatitis B e-antigen loss, such as seroconversion and virus mutations that lead to emergence of cellular immune response to the mutant virus. Our models demonstrate that either seroconversion or mutations can induce immune activation and that instantaneous loss of e-antigen by either mechanism is associated with least liver damage and is therefore more beneficial for disease outcomes.

This work presents a technique termed as "electrophoretic exclusion" that is capable of differentiation and concentration of proteins in bulk solution. In this method, a hydrodynamic flow is countered by the electrophoretic velocity to prevent a species from entering into a channel. The separation can be controlled by changing the flow rate or applied electric potential in order to exclude a certain species selectively while allowing others to pass through the capillary. The exclusion of various proteins is investigated using a flow-injection regime of the method. Concentration of myoglobin of up to 1200 times the background concentration in 60 s was demonstrated. Additionally, negatively charged myoglobin was separated from a solution containing negatively charged allophycocyanin. Cationic cytochrome c was also differentiated from a solution with allophycocyanin. The ability to differentially transport species in bulk solution enables parallel and serial separation modes not available with other separations schemes.