In this talk, we consider epidemic models with a continuum of agents where the evolution of the epidemics is represented by an ODE system. In contrast with most of the existing literature, we allow the agents to make decisions and we incorporate game theoretical ideas in the model such as the notion of Nash equilibrium. When the population is homogeneous, this leads to a continuous time, finite state mean field game. We consider, from a mathematical viewpoint, mainly two questions: (1) How to find optimal public policies to reduce the impact of the epidemics while taking into account the agents' rational choices? (2) How to handle heterogeneities among the population while keeping a continuum of agents? For the first point, we use a Stackelberg mean field game model, while for the second point, we rely on the framework of graphon games. In each case, we develop numerical methods based on machine learning tools to efficiently compute approximately optimal solutions.