title: Non-exponential tolerance to infection in epidemic systems--modeling, inference, and assessment.
abstract: The transmission dynamics of infectious diseases have been traditionally described through a time-inhomogeneous Poisson process, thus assuming exponentially distributed levels of disease tolerance following the Sellke construction. Here we focus on a generalization using Weibull individual tolerance thresholds under the susceptible-exposed-infectious-removed class of models which is widely employed in epidemics. Applications with experimental foot-and-mouth disease and historical smallpox data are discussed, and simulation results are presented. Inference is carried out using Markov chain Monte Carlo methods following a Bayesian approach. Model evaluation is performed, where the adequacy of the models is assessed using methodology based on the properties of Bayesian latent residuals, and comparison between 2 candidate models is also considered using a latent likelihood ratio-type test that avoids problems encountered with relevant methods based on Bayes factors.
authors.affiliation: School of Mathematical and Computer Sciences, Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK. g.streftaris@hw.ac.uk
authors.forename: George
authors.initials: G
authors.lastname: Streftaris
authors.forename: Gavin J
authors.initials: GJ
authors.lastname: Gibson
mesh_terms: D000818:Animals; D001499:Bayes Theorem; D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission*; D003198:Computer Simulation; D004196:Disease Outbreaks; D005536:Foot-and-Mouth Disease / Q000453:epidemiology / Q000635:transmission; D006801:Humans; D008390:Markov Chains; D015233:Models, Statistical; D009010:Monte Carlo Method; D012756:Sheep; D012757:Sheep Diseases / Q000453:epidemiology / Q000635:transmission; D012899:Smallpox / Q000453:epidemiology / Q000635:transmission