title: Five challenges for stochastic epidemic models involving global transmission.
abstract: The most basic stochastic epidemic models are those involving global transmission, meaning that infection rates depend only on the type and state of the individuals involved, and not on their location in the population. Simple as they are, there are still several open problems for such models. For example, when will such an epidemic go extinct and with what probability (questions depending on the population being fixed, changing or growing)? How can a model be defined explaining the sometimes observed scenario of frequent mid-sized epidemic outbreaks? How can evolution of the infectious agent transmission rates be modelled and fitted to data in a robust way?
authors.affiliation: Department of Mathematics, Stockholm University, Stockholm 106 91, Sweden. Electronic address: tom.britton@math.su.se.
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 Mathematics and Biomathematics Graduate Program, North Carolina State University, Raleigh, NC 27695, USA; Fogarty International Center, National Institutes of Health, Bethesda, MD, USA.
authors.forename: Alun L
authors.initials: AL
authors.lastname: Lloyd
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: MRC Centre for Outbreak Analysis and Modelling, Department of Infectious Disease Epidemiology, School of Public Health, Imperial College London, London, UK; Department of Community Medicine and School of Public Health, The University of Hong Kong, 21 Sassoon Road, Pokfulam, Hong Kong, China.
authors.forename: Steven
authors.initials: S
authors.lastname: Riley
authors.affiliation: Department of Mathematics, Stockholm University, Stockholm 106 91, Sweden.
authors.forename: Pieter
authors.initials: P
authors.lastname: Trapman
mesh_terms: D005075:Biological Evolution; D003141:Communicable Diseases / Q000453:epidemiology / Q000635:transmission; D019353:Endemic Diseases / Q000706:statistics & numerical data; D058872:Epidemics / Q000706:statistics & numerical data*; D053476:Extinction, Biological; D014943:Global Health / Q000706:statistics & numerical data; D006801:Humans; D015233:Models, Statistical; D013269:Stochastic Processes
keywords: Endemicity; Extinction; Genetic evolution; Global transmission; Stochastic epidemics
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