We present a model for allocation of epidemic control resources among a set of interventions. We assume that the epidemic is modeled by a general compartmental epidemic model, and that interventions change one or more of the parameters that describe the epidemic. Associated with each intervention is a 'production function' that relates the amount invested in the intervention to values of parameters in the epidemic model. The goal is to maximize quality-adjusted life years gained or the number of new infections averted over a fixed time horizon, subject to a budget constraint. Unlike previous models, our model allows for interacting populations and non-linear interacting production functions and does not require a long time horizon. We show that an analytical solution to the model may be difficult or impossible to derive, even for simple cases. Therefore, we derive a method of approximating the objective functions. We use the approximations to gain insight into the optimal resource allocation for three problem instances. We also develop heuristics for solving the general resource allocation problem. We present results of numerical studies using our approximations and heuristics. Finally, we discuss implications and applications of this work.