This thesis investigates the optimal use of intervention strategies to mitigate the spread of infectious diseases. Three main problems are addressed: (i) The optimal use vaccination and isolation resources under the assumption that these resources are limited. Specifically we address the problem of minimizing the outbreak size and we determine the optimal vaccination-only, isolation-only and mixed vaccination-isolation strategies. (ii) The optimal use of a single antiviral drug to minimize the total outbreak size, under the assumption that treatment causes de novo resistance. (iii) The optimal use of two antiviral drugs to minimize the total infectious burden. Specifically we address the situation where there are two different strains and each strain is effectively treated by only one drug.