Title: A Hepatitis C Virus Infection Model with Time-Varying Drug Effectiveness: Solution and Analysis

Abstract

Simple models of therapy for viral diseases such as hepatitis C virus (HCV) or human immunodeficiency virus assume that, once therapy is started, the drug has a constant effectiveness. More realistic models have assumed either that the drug effectiveness depends on the drug concentration or that the effectiveness varies over time. Here a previously introduced varying-effectiveness (VE) model is studied mathematically in the context of HCV infection. We show that while the model is linear, it has no closed-form solution due to the time-varying nature of the effectiveness. We then show that the model can be transformed into a Bessel equation and derive an analytic solution in terms of modified Bessel functions, which are defined as infinite series, with time-varying arguments. Fitting the solution to data from HCV infected patients under therapy has yielded values for the parameters in the model. We show that for biologically realistic parameters, the predicted viral decay on therapy is generally biphasic and resembles that predicted by constant-effectiveness (CE) models. We introduce a general method for determining the time at which the transition between decay phases occurs based on calculating the point of maximum curvature of the viral decay curve. For the parameter regimes ofmore » interest, we also find approximate solutions for the VE model and establish the asymptotic behavior of the system. We show that the rate of second phase decay is determined by the death rate of infected cells multiplied by the maximum effectiveness of therapy, whereas the rate of first phase decline depends on multiple parameters including the rate of increase of drug effectiveness with time.« less

Authors:

Conway, Jessica M. ^[1]; Perelson, Alan S. ^[1]

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+ Show Author Affiliations

1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:

Thu Aug 07 00:00:00 EDT 2014

Research Org.:

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Biological and Environmental Research (BER). Biological Systems Science Division; National Institutes of Health (NIH)

OSTI Identifier:

1627237

Grant/Contract Number:  

AC52-06NA25396; R01-OD011095; R01-AI078881; R34-HL109334; P20-GM103452; R01-AI028433

Resource Type:

Accepted Manuscript

Journal Name:

PLoS Computational Biology (Online)

Additional Journal Information:

Journal Name: PLoS Computational Biology (Online); Journal Volume: 10; Journal Issue: 8; Journal ID: ISSN 1553-7358

Publisher:

Public Library of Science

Country of Publication:

United States

Language:

English

Subject:

59 BASIC BIOLOGICAL SCIENCES; Biochemistry & Molecular Biology; Mathematical & Computational Biology