Infectious disease is the main thing that kills people. Some of the greatest improvements to human health have involved improvements in our understanding and control of germs - from John Snow's pioneering work on cholera in the 19th century to the eradication of smallpox in the 20th century. The 21st century sees a new set of challenges in the understanding and control of infections - while the eradication of polio progresses, we see new influenza strains causing or threatening pandemics, the continued progression of HIV and a massive health burden of often simply but expensively preventable diseases in the developing world.Epidemiology - the science of looking for significant patterns in cases of disease - has always been at the heart of controlling infectious diseases, and mathematics has always been central epidemiology.This project applies advanced mathematics to the science of epidemiology, making use of the large datasets and modern computational resources that are available. New insights about the structure of complex systems offer the promise of making massive advances in this field, through enhanced understanding of transmission routes of infection, risk factors and changes in the disease over time. These insights can in turn be combined with mathematical methods to design optimised interventions against infection so that diseases can be controlled in the most effective way.