Modeling the population effects of escape mutations in SARS-CoV-2 to guide vaccination strategies

•This model is the first to integrate both antigenic drifting from escape mutations and immunity waning in continuous time.•Low levels only of waning or only of escape mutation drifting have small or no effects. Together, though, these low levels have large joint effects that change across increasing parameter values.•There are no or few escape mutations during the first epidemic peak and no effect of drifting parameters on the size of that wave.•After the first epidemic peak, escape mutations accumulate rapidly. They increase with increases in waning rates and with increases in the drifting rate. Escape mutations then amplify other escape mutations because these raise the frequency of reinfections.•Escape mutations can negate the effects of vaccines and lead to more infections with vaccination than without.•The model generates population level cross-neutralization patterns that enable the model to be fitted to population level serological data.•The model can be modified to use laboratory data that determine the epitope specific effects of mutations on ACE2 attachment strength or escape from antibody effects.•The model, although currently unable to predict the effects of escape mutations in the real world, opens a path that can guide model incorporation of molecularly studied escape mutations and improve predictive value. We describe that path.•Model analysis indicates that vaccine trials and serological surveys are needed now to detect the effects of epitope specific escape mutations that could cause the loss of vaccine efficacy. SARS-Cov-2 escape mutations (EM) have been detected and are spreading. Vaccines may need adjustment to respond to these or future mutations. We designed a population level model integrating both waning immunity and EM. We also designed a set of criteria for elaborating and fitting this model to cross-neutralization and other data with a goal of minimizing vaccine decision errors. We formulated four related models. These differ regarding which strains can drift to escape immunity in the host when that immunity was elicited by different strains. Across changing waning and escape mutation parameter values, these model variations led to patterns where: 1) EM are rare in the first epidemic, 2) rebound outbreaks after the first outbreak are accelerated by increasing waning and by increasing drifting, 3) the long term endemic level of infection is determined mostly by waning rates with small effects of the drifting parameter, 4) EM caus