Mathematical Population Studies, 18:122–149, 2011 Copyright © Taylor & Francis Group, LLC ISSN: 0889-8480 print/1547-724X online DOI: 10.1080/08898480.2011.564566 Modelling Mutation to a Cytotoxic T-lymphocyte HIV Vaccine Bernhard P. Konrad Faculty of Mathematics, Karlsruhe Institute of Technology, Germany Naveen K. Vaidya Theoretical Biology and Biophysics, Los Alamos National Laboratory, New Mexico, USA Robert J. Smith? Department of Mathematics and Faculty of Medicine, The University of Ottawa, Canada Resistance to a postinfection HIV vaccine that stimulates cytotoxic T-lymphocytes (CTLs) depends on the relationship between the vaccine strength, the fitness cost of the mutant strain, and the rate of mutant escape. If the vaccine is strong enough, both strains of the virus should be controlled by administering the vaccine sufficiently often. However, if escape mutation to the vaccine occurs, then either the wild type or the mutant can outcompete the other strain. Imperfect adherence may result in the persistence of the mutant, while fluctuations in the vaccination time—even if no vaccines are missed—may result in the mutant outcompeting the wild type. Keywords: adherence; cytotoxic T-lymphocytes; escape mutation; fitness cost; impulsive differential equations; vaccination 1. INTRODUCTION Virus-specific cytotoxic T-lymphocytes (CTLs) control HIV-1 repli- cation in humans and SIV replication in rhesus monkeys, thereby delaying the onset of disease and progression to AIDS (Klein et al., 1998; Jin et al., 1999; Schmitz et al., 1999; Amara et al., 2002; Barouch et al., 2003). Controls against SIV during trials of vaccines that elicit CTL responses (Barouch et al., 2000; Amara et al., 2001, 2002) Address correspondence to Robert J. Smith?, Department of Mathematics and Faculty of Medicine, The University of Ottawa, 585 King Edward Ave, Ottawa K1N 6N5, Canada. E-mail: rsmith43@uottawa.ca 122 Downloaded By: [Canadian Research Knowledge Network] At: 03:06 10 May 2011