HIV with contact-tracing: a case study in Approximate Bayesian ComputationReport as inadecuate




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* Corresponding author 1 TIMB TIMC-IMAG - Techniques de l-Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications Grenoble 2 LPP - Laboratoire Paul Painlevé 3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

Abstract : Missing data is a recurrent issue in epidemiology where the infection process may be partially observed. Approximate Bayesian Computation, an alternative to data imputation methods such as Markov Chain Monte Carlo integration, is proposed for making inference in epidemiological models. It is a likelihood-free method that relies exclusively on numerical simulations. ABC consists in computing a distance between simulated and observed summary statistics and weighting the simulations according to this distance. We propose an original extension of ABC to path-valued summary statistics, corresponding to the cumulated number of detections as a function of time. For a standard compartmental model with Suceptible, Infectious and Recovered individuals SIR, we show that the posterior distributions obtained with ABC and MCMC are similar. In a refined SIR model well-suited to the HIV contact-tracing data in Cuba, we perform a comparison between ABC with full and binned detection times. For the Cuban data, we evaluate the efficiency of the detection system and predict the evolution of the HIV-AIDS disease. In particular, the percentage of undetected infectious individuals is found to be of the order of $40\%$.

Keywords : Mathematical epidemiology stochastic SIR model unobserved infectious population simulation-based inference likelihood-free inference





Author: Michael G B Blum - Viet Chi Tran -

Source: https://hal.archives-ouvertes.fr/



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