Sustainable animal disease management requires to design and implement control policies at the regional scale. However, for diseases which are not regulated, individual farmers are responsible for the adoption and successful application of control policies at the farm scale. Organizations (groups of farmers, health institutions...) may try to influence farmers' control actions through financial incentives, in order to ensure sustainable (from the health and economical point of views) disease management policies. Economics / Operations Research frameworks have been proposed for modeling the effect of incentives on agents. The Leader-Follower Markov Decision Processes framework is one such framework, that combines Markov Decision Processes (MDP) and stochastic games frameworks. However, since finding equilibrium policies in stochastic games is hard when the number of players is large, LF-MDP problems are intractable. Our contribution, in this article, is to propose a tractable model of the animal disease management problem. The tractable model is obtained through a few simple modeling approximations which are acceptable when the problem is viewed from the organization side. As a result, we design a polynomial-time algorithm for animal disease management, which we evaluate on a case study inspired from the problem of controlling the spread of the Porcine Reproductive and Respiratory Syndrome (PRRS).