Page 379 - Special Topic Session (STS) - Volume 2

STS506 L. Leticia R. et al.

On the use of surrogate models to speed the ABC
inference for epidemic models in networks
2
1
L. Leticia Ramírez-Ramírez , Rocío Maribel Ávila-Ayala , Arturo Márquez-
3
Cerda
1 Centro de Investigación en Matemáticas, Guanajuato, Gto. Mexico
2 Universidad Nacional Autónoma de México, Mexico City, Mexico
3 Universidad de Guanajuato, Guanajuato, Gto, Mexico

Abstract
In order to explain outbreak evolutions that largely deviate from the results
provided by epidemic models based on the law of mass action, the epidemic
models in a network of contacts have been introduced to generalize them.
These models directly incorporate a population contact pattern that dictates
the potential infections between individuals and can be modeled based on
geographical distance and some other social patterns in the population. The
epidemic model increases its complexity with this pairwise contact network
structure and in most cases, obtaining its likelihood function is extremely
expensive or impossible. In this work, we present a statistical inference of
epidemic compartmental models based on the Approximate Bayesian
Computation (ABC) that is likelihood-free and we propose some surrogate
versions to reduce the required computing time for inference. We illustrate
this proposal with computational experiments of epidemic outbreaks in
simulated networks.

Keywords
Epidemic models; Networks of contacts; Likelihood-free method; MCMC;
Surrogate models; Recurrent Neural Networks.

1. Introduction
The SIR epidemic model considers that an individual can transit
through different status when infected during an outbreak. Let (), ()
and () be the number of susceptible infected and removed individuals
at time t, respectively. In a closed population, the population size
remains constant ( ≡ (), > and the state space {(); (); ()}
0
can be monitored using only {(); ()}. Let (,) () be its corresponding
() = (() = , () = ), where (, ) is a
joint probability function (,)
vector of possible ((), ()) states.
If the population is well-mixed, we can assume that the interactions
between infective and susceptible individuals are fully dictated by their
number, and the transmission and removal (recovery) rates β and .

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