Infectious diseases pose a serious threat to humans, plants, and animals. Though vaccines can help control outbreaks of infectious diseases, there is typically not enough vaccine available for the entire population. In this case, certain vaccination strategies can be employed to maximize the benefits for the entire population. Using results from graph theory and the simulation tool lONTW (Infections On NeTWorks), we investigated various vaccination strategies on certain types of so-called contact networks that model the patterns of interactions within a population. In particular, we focused on a certain class of contact networks known as small world models, where individuals are randomly connected, i.e., can transmit and/or contract an infectious disease, along paths that are relatively small in relation to the overall population size. These types of networks tend to provide good estimations of the interactions of real populations when the exact contact network is unknown. However, the complexity and stochasticity of such networks create challenges in determining the best vaccination strategy. Here we discuss our preliminary results for vaccination strategies on small world models, including how many vaccines are needed (a notion related to a concept called the herd immunity threshold) and, for a given amount of vaccine, which individuals should be vaccinated in order to prevent major outbreaks
