Bulletin of Mathematical Biology

, Volume 74, Issue 8, pp 1789–1817

# Modeling Quasispecies and Drug Resistance in Hepatitis C Patients Treated with a Protease Inhibitor

Original Article

DOI: 10.1007/s11538-012-9736-y

Rong, L., Ribeiro, R.M. & Perelson, A.S. Bull Math Biol (2012) 74: 1789. doi:10.1007/s11538-012-9736-y

## Abstract

Telaprevir, a novel hepatitis C virus (HCV) NS3-4A serine protease inhibitor, has demonstrated substantial antiviral activity in patients infected with HCV. However, drug-resistant HCV variants were detected in vivo at relatively high frequency a few days after drug administration. Here we use a two-strain mathematical model to explain the rapid emergence of drug resistance in HCV patients treated with telaprevir monotherapy. We examine the effects of backward mutation and liver cell proliferation on the preexistence of the mutant virus and the competition between wild-type and drug-resistant virus during therapy. We also extend the two-strain model to a general model with multiple viral strains. Mutations during therapy only have a minor effect on the dynamics of various viral strains, although they are capable of generating low levels of HCV variants that would otherwise be completely suppressed because of fitness disadvantages. Liver cell proliferation may not affect the pretreatment frequency of mutant variants, but is able to influence the quasispecies dynamics during therapy. It is the relative fitness of each mutant strain compared with wild-type that determines which strain(s) will dominate the virus population. This study provides a theoretical framework for exploring the prevalence of preexisting mutant variants and the evolution of drug resistance during treatment with other HCV protease inhibitors or polymerase inhibitors.

### Keywords

Telaprevir Mutation Fitness Quasispecies Direct-acting antiviral agents Mathematical model

© Society for Mathematical Biology 2012

## Authors and Affiliations

• Libin Rong
• 1
• 2
• Ruy M. Ribeiro
• 2
• Alan S. Perelson
• 2
1. 1.Department of Mathematics and Statistics and Center for Biomedical ResearchOakland UniversityRochesterUSA
2. 2.Theoretical Biology and BiophysicsLos Alamos National LaboratoryLos AlamosUSA