We develop a mathematical model for the interaction between two competing equine infectious anemia virus strains and neutralizing antibodies. We predict that elimination of one or both virus strains depends on the initial antibody levels, the strength of antibody mediated neutralization, and the persistence of antibody over time. We further show that the ability of a subdominant, neutralization resistant virus to dominate the infection transiently or permanently is dependent on the antibody-mediated neutralization effect. Finally, we determine conditions for persistence of both virus strains. We fit our models to virus titers from horses (foals) with severe combined immunodeficiency to estimate virus-host parameters and to validate analytical results.