Non-exponential tolerance to infection in epidemic systems.modeling, inference, and assessment

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.