New strains of influenza spread around the globe via the movement of infected individuals. The global dynamics of influenza are complicated by different patterns of influenza seasonality in different regions of the world. We have released an open-source stochastic mathematical model of the spread of influenza across 321 major, strategically located cities of the world. Influenza is transmitted between cities via infected airline passengers. Seasonality is simulated by increasing the transmissibility in each city at the times of the year when influenza has been observed to be most prevalent. The spatiotemporal spread of pandemic influenza can be understood through clusters of global transmission and links between them, which we identify using the epidemic percolation network (EPN) of the model. We use the model to explain the observed global pattern of spread for pandemic influenza A(H1N1) 2009-2010 (pandemic H1N1 2009) and to examine possible global patterns of spread for future pandemics depending on the origin of pandemic spread, time of year of emergence, and basic reproductive number (). We also use the model to investigate the effectiveness of a plausible global distribution of vaccine for various pandemic scenarios. For pandemic H1N1 2009, we show that the biggest impact of vaccination was in the temperate northern hemisphere. For pandemics starting in the temperate northern hemisphere in May or April, vaccination would have little effect in the temperate southern hemisphere and a small effect in the tropics. With the increasing interconnectedness of the world's population, we must take a global view of infectious disease transmission. Our open-source, computationally simple model can help public health officials plan for the next pandemic as well as deal with interpandemic influenza.