title: Disease elimination and re-emergence in differential-equation models.
abstract: Traditional differential equation models of disease transmission are often used to predict disease trajectories and evaluate the effectiveness of alternative intervention strategies. However, such models cannot account explicitly for probabilistic events, such as those that dominate dynamics when disease prevalence is low during the elimination and re-emergence phases of an outbreak. To account for the dynamics at low prevalence, i.e. the elimination and risk of disease re-emergence, without the added analytical and computational complexity of a stochastic model, we develop a novel application of control theory. We apply our approach to analyze historical data of measles elimination and re-emergence in Iceland from 1923 to 1938, predicting the temporal trajectory of local measles elimination and re-emerge as a result of disease migration from Copenhagen, Denmark.
authors.affiliation: Center for Infectious Disease Modeling and Analysis, School of Public Health, Yale University, 135 College Street, New Haven, CT 06510, USA. Electronic address: scottyg3@gmail.com.
authors.forename: Scott
authors.initials: S
authors.lastname: Greenhalgh
authors.affiliation: Center for Infectious Disease Modeling and Analysis, School of Public Health, Yale University, 135 College Street, New Haven, CT 06510, USA. Electronic address: alison.galvani@yale.edu.
authors.forename: Alison P
authors.initials: AP
authors.lastname: Galvani
authors.affiliation: Department of Biomedical Sciences, College of Veterinary Medicine, Oregon State University, 106 Dryden Hall, Corvallis, OR 97331, USA. Electronic address: jan.medlock@oregonstate.edu.
authors.forename: Jan
authors.initials: J
authors.lastname: Medlock
mesh_terms: D050936:Basic Reproduction Number; D060740:Disease Eradication; D006801:Humans; D007055:Iceland; D008457:Measles / Q000453:epidemiology* / Q000635:transmission; D008954:Models, Biological; D013997:Time Factors
keywords: Control theory; Dynamic modeling; Eradication; Infectious-disease modeling; Migration