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Secretory immunoglobulin A (sIgA), a dimeric antibody found in high quantities in the gastrointestinal mucosa, is broadly associated with mucosal immune protection. A distinguishing feature of sIgA is its ability to crosslink pathogens, thereby creating pathogen/sIgA aggregates that are too large to traverse the dense matrix of mucin fibers in mucus layers overlying epithelial cells and consequently reducing infectivity. Here, we use modeling to investigate this mechanism of “immune exclusion” based on sIgA-mediated agglutination, in particular the potential use of sIgA to agglutinate HIV in cervicovaginal mucus (CVM) and prevent HIV transmission. Utilizing reported data on HIV diffusion in CVM and semen, we simulate HIV collision kinetics in physiologically-thick mucus layers–a necessary first step for sIgA-induced aggregation. We find that even at the median HIV load in semen of acutely infected individuals possessing high viral titers, over 99% of HIV virions will penetrate CVM and reach the vaginal epithelium without colliding with another virion. These findings imply that agglutination is unlikely to be the dominant mechanism of sIgA-mediated protection against HIV or other sexually transmitted pathogens. Rather, we surmise that agglutination is most effective against pathogens either present at exceedingly high concentrations or that possess motility mechanisms other than Brownian diffusion that significantly enhance encounter rates.