1 Center for Communicable Disease Dynamics, Department of Epidemiology and Department of Immunology and Infectious Diseases, Harvard T H Chan School of Public Health and Department of Pathology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.
2 Nuffield Department of Medicine, University of Oxford, Oxford, UK.
3 Institute of Population Health, University of Liverpool, Liverpool L36 3GF, UK.
4 Institute of Infection, Veterinary and Ecological Sciences, University of Liverpool, Liverpool, UK.
5 Institute of Population Health, University of Liverpool, Liverpool L36 3GF, UK. Electronic address: buchan@liverpool.ac.uk.