Recent breakthroughs in gene-editing technologies that can render individual animals fully resistant to infections may offer unprecedented opportunities for controlling future epidemics in farm animals. Yet, their potential for reducing disease spread is poorly understood as the necessary theoretical framework for estimating epidemiological effects arising from gene editing applications is currently lacking. Here, we develop semi-stochastic modelling approaches to investigate how the adoption of gene editing may affect infectious disease prevalence in farmed animal populations and the prospects and timescale for disease elimination. We apply our models to the Porcine Reproductive and Respiratory Syndrome PRRS, one of the most persistent global livestock diseases to date. Whereas extensive control efforts have shown limited success, recent production of gene-edited pigs that are fully resistant to the PRRS virus have raised expectations for eliminating this deadly disease. Our models predict that disease elimination on a national scale would be difficult to achieve if gene editing was used as the only disease control. However, from a pure epidemiological perspective, disease elimination may be achievable within 3-6 years, if gene editing was complemented with widespread and sufficiently effective vaccination. Besides strategic distribution of genetically resistant animals, several other key determinants underpinning the epidemiological impact of gene-editing were identified.