title: Seven challenges for metapopulation models of epidemics, including households models.
abstract: This paper considers metapopulation models in the general sense, i.e. where the population is partitioned into sub-populations (groups, patches,...), irrespective of the biological interpretation they have, e.g. spatially segregated large sub-populations, small households or hosts themselves modelled as populations of pathogens. This framework has traditionally provided an attractive approach to incorporating more realistic contact structure into epidemic models, since it often preserves analytic tractability (in stochastic as well as deterministic models) but also captures the most salient structural inhomogeneity in contact patterns in many applied contexts. Despite the progress that has been made in both the theory and application of such metapopulation models, we present here several major challenges that remain for future work, focusing on models that, in contrast to agent-based ones, are amenable to mathematical analysis. The challenges range from clarifying the usefulness of systems of weakly-coupled large sub-populations in modelling the spread of specific diseases to developing a theory for endemic models with household structure. They include also developing inferential methods for data on the emerging phase of epidemics, extending metapopulation models to more complex forms of human social structure, developing metapopulation models to reflect spatial population structure, developing computationally efficient methods for calculating key epidemiological model quantities, and integrating within- and between-host dynamics in models.
authors.affiliation: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK. Electronic address: frank.ball@nottingham.ac.uk.
authors.forename: Frank
authors.initials: F
authors.lastname: Ball
authors.affiliation: Department of Mathematics, Stockholm University, Stockholm 106 91, Sweden.
authors.forename: Tom
authors.initials: T
authors.lastname: Britton
authors.affiliation: Warwick Infectious Disease Epidemiology Research Centre (WIDER) and Warwick Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK.
authors.forename: Thomas
authors.initials: T
authors.lastname: House
authors.affiliation: Department of Statistical Science, University College London, London WC1E 6BT, UK.
authors.forename: Valerie
authors.initials: V
authors.lastname: Isham
authors.affiliation: Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, UK.
authors.forename: Denis
authors.initials: D
authors.lastname: Mollison
authors.affiliation: Warwick Infectious Disease Epidemiology Research Centre (WIDER) and Warwick Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK.
authors.forename: Lorenzo
authors.initials: L
authors.lastname: Pellis
authors.affiliation: Department of Mathematics, University of Rome Tor Vergata, Rome 00133, Italy.
authors.forename: Gianpaolo
authors.initials: G
authors.lastname: Scalia Tomba
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology / Q000635:transmission; D058872:Epidemics / Q000706:statistics & numerical data*; D005191:Family Characteristics; D006801:Humans; D015233:Models, Statistical; D011157:Population Dynamics; D062206:Spatial Analysis
keywords: Households; Large sub-populations; Metapopulations