title: Nine challenges for deterministic epidemic models.
abstract: Deterministic models have a long history of being applied to the study of infectious disease epidemiology. We highlight and discuss nine challenges in this area. The first two concern the endemic equilibrium and its stability. We indicate the need for models that describe multi-strain infections, infections with time-varying infectivity, and those where superinfection is possible. We then consider the need for advances in spatial epidemic models, and draw attention to the lack of models that explore the relationship between communicable and non-communicable diseases. The final two challenges concern the uses and limitations of deterministic models as approximations to stochastic systems.
authors.affiliation: Infectious Disease Research Centre, Institute of Natural and Mathematical Sciences, and New Zealand Institute for Advanced Study, Massey University, Private Bag 102 904, North Shore Mail Centre, 1311 Auckland, New Zealand. Electronic address: m.g.roberts@massey.ac.nz.
authors.forename: Mick
authors.initials: M
authors.lastname: Roberts
authors.affiliation: Department of Science, Roskilde University, 4000 Roskilde, Denmark.
authors.forename: Viggo
authors.initials: V
authors.lastname: Andreasen
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 20892, USA.
authors.forename: Alun
authors.initials: A
authors.lastname: Lloyd
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
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology / Q000635:transmission; D019353:Endemic Diseases / Q000706:statistics & numerical data; D058872:Epidemics / Q000706:statistics & numerical data*; D015981:Epidemiologic Factors; D006801:Humans; D015233:Models, Statistical; D013269:Stochastic Processes; D015163:Superinfection
keywords: Deterministic models; Endemic equilibrium; Multi-strain systems; Non-communicable diseases; Spatial models
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