We consider models for control of epidemics on local, global, small-world and scale-free networks, with only partial information accessible about the status of individuals and their connections. The effectiveness of local (e.g. ring vaccination or culling) vs global (e.g. random vaccination) control measures is evaluated, with the aim of minimising the total cost of an epidemic. The costs include direct costs of treating infected individuals as well as costs of treatment. We first consider a random (global) vaccination strategy designed to stop any potential outbreak. We show that if the costs of the preventive vaccination are ignored, the optimal strategy is to vaccinate the whole population, although most of the resources are wasted on preventing a small number of cases. If the vaccination costs are included, or if a local strategy (within a certain neighbourhood of a symptomatic individual) is chosen, there is an optimum number of treated individuals. Inclusion of non-local contacts (,small-worlds' or scale-free networks) increases the levels of preventive (random) vaccination and radius of local treatment necessary for stopping the outbreak at a minimal cost. The number of initial foci also influences our choice of optimal strategy. The size of epidemics and the number of treated individuals increase for outbreaks that are initiated from a larger number of initial foci, but the optimal radius of local control actually decreases. The results are important for designing control strategies based on cost effectiveness.