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Missing data is a recurrent issue in epidemiology where the infection processmay be partially observed. Approximate Bayesian Computation, an alternative todata imputation methods such as Markov Chain Monte Carlo integration, isproposed for making inference in epidemiological models. It is alikelihood-free method that relies exclusively on numerical simulations. ABCconsists in computing a distance between simulated and observed summarystatistics and weighting the simulations according to this distance. We proposean original extension of ABC to path-valued summary statistics, correspondingto the cumulated number of detections as a function of time. For a standardcompartmental model with Suceptible, Infectious and Recovered individuals(SIR), we show that the posterior distributions obtained with ABC and MCMC aresimilar. In a refined SIR model well-suited to the HIV contact-tracing data inCuba, we perform a comparison between ABC with full and binned detection times.For the Cuban data, we evaluate the efficiency of the detection system andpredict the evolution of the HIV-AIDS disease. In particular, the percentage ofundetected infectious individuals is found to be of the order of 40%.

HIV with contact-tracing: a case study in Approximate Bayesian Computation