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The on-going African swine fever pandemic has been devastating to affected nations, with continued spread observed despite aggressive interventions. Suspected interspecific transmission among wild and domestic hosts further complicates control efforts, yet its role in epidemic propagation remains poorly understood. Here, we develop and calibrate a multi-host mechanistic transmission model to the first wave of the epidemic in Romania (June-December 2018), quantifying these dynamics and evaluating counterfactual management scenarios. We estimated that 60% (95% credible interval: 27-83%) of outbreak farms were linked to other outbreak farms, 27% (5.3-67%) to infected wild boar populations, and 13% (1.9-27%) to external sources. For wild boar, 39% (3.8-93%) of infected populations were estimated to have originated from outbreak farms, and 61% (7.3-96%) from other infected wild boar populations, with favorable habitat exhibiting higher susceptibility and infectivity than unfavorable habitat. Among alternative control strategies, reactive and preventive culling of domestic pig herds yielded the greatest decrease in median final epidemic size among domestic pigs. These findings provide quantitative evidence that interspecific transmission was a critical epidemic driver, and a necessary target for achieving holistic control. Our model offers a flexible, rapidly-deployable framework for informing surveillance and response policy in at-risk regions.