Chronic hepatitis B virus and liver fibrosis: A mathematical model Avner Friedman Ohio State University MBI and Nourridine Siwie University of Tennessee, NIMBioS

Hapatitis B Virus Hepatitis B virus (HBV) is a viral infection that results in liver cirrhosis (a late stage of fibrosis), causing the destruction of the liver Chronic HBV affects 350 million people worldwide, with 600,000 deaths annually The disease is 50 time more infectious than HIV Infection occurs by contact with infected persons (sexual contact, sharing needles, toothbrush, nail clippers, razors, etc.) The symptoms do not show up immediately after infection: the delay time make take weeks, months, or even years Vaccination is effective 90%

Diameter 42 nm, ~3000 nucleotides the long strand, and ~2000 nucleotides the short strand

drugs Adefovir ----decreases viral load in the liver IFN- alpha -----decreases viremia (viral concentration in the blood) and inflammation Our aim Our aim is to develop a mathematical model to be used to evaluate the efficacy in combination therapy in terms of optimal proportions between the two agents, and optimal scheduling; The objective functions to be minimized are the scar density, and the viral load.

Model equations macrophages

macrophages hepatocytes

T cells Fibroblasts and myofibroblasts

ECM scar

Intracellular virus

Extracellular virus

Parameters

Control case---no drugs

PDEs vs ODEs --------------- ----------------------------------------------------

Efficacy---- for scar (S) and for intracellular viral load (Vi) The decrease in viral load by each of the drugs alone are in agreement with clinical results Definitions Efficacy---- for scar (S) and for intracellular viral load (Vi)

Synergy between the two drugs

Biological explanation of the synergy map

Conclusions 1. We have determined the proportion between the two drugs for which the combined treatment has maximal synergy, based on simple choice of 2. But this special choice needs to be adjusted to take into consideration negative side effects; these side effects will have to be incorporated into the model 3. The model can be used to explore intermittent treatment vs. continuous treatment with total amount of the drugs