In recent years, animal epidemics – such as African swine fever and bird flu – break out more frequently in both developed and developing economies, causing serious economic losses and animal product shortages. To restore animal product supply, many governments offer two agricultural subsidies to farms: (i) the culling compensating subsidy (CCS), which guarantees a floor price for culled animals, and (ii) the scaled construction subsidy (SCS), which supports large-scale farms to enhance their production capacities. We develop a three-stage Stackelberg game framework to capture the strategic interactions among the government, large- and small-scale farms. In particular, the two types of farms differ in their epidemic prevention and control capabilities and must operate under yield uncertainty. We study two cases regarding whether the government requires a minimum BS for the SCS. In each case, we analyze the equilibrium decisions of the profit-seeking farms and characterize the structure of the government’s optimal subsidy programs with an earmarked budget to maximize social welfare. Moreover, we identify the conditions under which the government should adopt the “SCS only strategy”, “CCS only strategy”, or offer the two subsidies simultaneously. Furthermore, we examine the effectiveness of the subsidy programs in terms of consumer surplus, farms payoffs, and social welfare. We show that in both cases, these programs can make the three stakeholders achieve a win–win–win situation by prioritizing a reasonable CCS according to the subsidy budget. We leverage our analyses to offer insights that can help generate policy recommendations for stakeholders in countries suffering from animal epidemics.