Plant disease control is often implemented at the private property level, and problems of cooperation and coordination between landowners can lead to social inefficiencies. Drawing on the private management problem of sharka on Prunus trees, we analyse an epidemic game and its outcomes according to initial infection levels. We show that, depending on the infection level in each farm, the nature of strategic interactions changes drastically, and a wide range of games can occur, including games with multiple or without pure strategy equilibria and games with coordination or anti-coordination patterns. We characterise the epidemic conditions for which private management produces social inefficiency and analyse the properties of uniform and differentiated subsidy schemes to solve it. We conclude with a discussion of the policy implications of the ongoing deregulation of sharka management in France.