Genetic selection is an inexpensive and complementary strategy to traditional methods of improving animal health and welfare. Nonetheless, endeavors to incorporate animal health and welfare traits in international breeding programs have been hampered by the availability of informative phenotypes. The recent eradication program for bovine viral diarrhea (BVD) in the Republic of Ireland has provided an opportunity to quantify the potential benefits that genetic selection could offer BVD eradication programs elsewhere, as well as inform possible eradication programs for other diseases in the Republic of Ireland. Using a dataset of 188,085 Irish calves, the estimated direct and maternal heritability estimates for the birth of persistently infected calves following likely in utero exposure to BVD virus ranged from not different from zero (linear model) to 0.29 (SE = 0.075; threshold model) and from essentially zero (linear model) to 0.04 (SE = 0.033; threshold model), respectively. The corresponding genetic SD for the direct and maternal effect of the binary trait (0, 1) ranged from 0.005 (linear model) to 0.56 (threshold model) units and ranged from 0.00008 (linear model) to 0.20 (threshold model) units, respectively. The coefficient of direct genetic variation based on the linear model was 2.56% indicating considerable genetic variation could be exploited. Based on results from the linear model in the present study, there is the potential to reduce the incidence of persistent infection in cattle by on average 0.11 percentage units per year which is cumulative and permanent. Therefore, genetic selection can contribute to reducing the incidence of persistent infection in cattle. Moreover, where populations are free from persistent infection, inclusion of the estimated genetic merit for BVD in national breeding indexes could contribute to a preservation of a BVD-free status. Results from the present study can be used to inform breeding programs of the potential genetic gains achievable. Moreover, the approaches used in the present study can be applied to other diseases when data become available.