1. Mathematics Institute, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
2. School of Life Sciences, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
3. Department of Epidemiology and Population Health, Institute of Infection and Global Health, University of Liverpool, Leahurst Campus, Neston CH64 7TE, UK