The influence of ionic strength on the electrostatic interaction of viruses with environmentally relevant surfaces was determined for three viruses, MS2, Q beta, and Norwalk. The virus is modeled as a particle comprised of ionizable amino acid residues in a shell surrounding a spherical RNA core of negative charge, these charges being compensated for by a Coulomb screening due to intercalated ions. A second model of the virus involving surface charges only is included for comparison. Surface potential calculations for each of the viruses show excellent agreement with electrophoretic mobility and zeta potential measurements as a function of pH. The environmental surface is modeled as a homogeneous plane held at constant potential with and without a finite region (patch) of opposite potential. The results indicate that the electrostatic interaction between the virus and the oppositely charged patch is significantly influenced by the conditions of ionic strength, pH and size of the patch. Specifically, at pH 7, the Norwalk virus interacts more strongly with the patch than MS2 (approximately 51 vs approximately 9kT) but at pH 5, the Norwalk-surface interaction is negligible while that of MS2 is approximately 5.9kT. The resulting ramifications for the use of MS2 as a surrogate for Norwalk are discussed.