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STS506 L. Leticia R. et al.
            surrogate-ABC-MCMC  took  less  than  2  minutes  to  obtain  the  posterior
            sample.
                This ABC-MCMC modification becomes highly attractive not only because
            it is fast to compute, but because it only requires partial knowledge of the
            network, that is its first and second moment of its degree.

            3.3 Assessing surrogate model B: “RNN”
                The  proposed  RNN  architecture  allows  us  to  predict  the  dynamics  of
            epidemic outbreaks on contact networks with similar degree distributions (in
            the  experiments  depicted  in  Figure  3  we  used  networks  with  Poisson
            generated degree sequences). Although this model requires a considerable
            amount of time to train (approximately 5 minutes for two sets of simulations),
            it offers fast prediction as it took an average of 38.5ms per simulation on a i7-
            8650U processor.

















                    Figure 3: Predicted outbreaks with our augmented RNN architecture.

            4.  Discussion and Conclusion
                We  base  the  likelihood-free  inference  ABC-MCMC  on  more  realistic
            surveillance–like information, that report only the new infective in intervals of
            time. We emphasize on the inference for the SIR parameters  and , but using
            this same ABC methods, we can do the inference of any epidemic model from
            which  we  can  obtain  pseudo-observations.  The  ABC-MCMC  can  be  very
            computer expensive if it uses the agent-based simulation, but in this case,
            many other characteristics can be inferred, such as the degree of the initial
            infectious cases, the most exposed community, etc. This approach also allows
            doing inference for non-Markovian epidemic models.
                We explore the use of surrogate models to run more efficient ABC-MCMC.
            For the specific case of SIR (or SEIR) models, we propose harnessing model (1)
            but other alternatives must be used when the model has infectious (latent)
            periods are not exponentially distributed. In these more general scenarios, we
            propose  some  models  that  allows  for  fast  forecasting,  while  they  can
            incorporate the network topological features that are relevant for the outbreak

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