Stochastic Compartmental Modelling of SARS-CoV-2 with Approximate Bayesian Computation

Vedant Chandra

Armed with the ability to generate stochastic infection and recovery curves from starting parameters, we turn to fitting the starting parameters from real-world epidemic data. Since the models are stochastic in nature, there isn't a simple analytical form that we can minimize. Additionally, rather than fitting for only the parameters themselves, we would also like to quantify how certain we are about those parameters. We therefore employ an approximate Bayesian computation (ABC) technique to compare our simulations to observations and recover the posterior distributions of β and γ (Figure 1 ). This technique was previously used to fit initial mass functions to nearby galaxies (Gennaro et al. 2018) . The general goal of ABC is to sample the posterior distributions of simulation parameters such that the simulations match the observed data. In practice, it is impossible for simulations to exactly match data due to noise and ill-posed models. Additionally, if the observable space is continuous, then the probability of simulations exactly matching observations is exactly zero. Therefore, we define some distance d between simulations and observations, as well as a tolerance . We accept those parameters who produce simulations are d < away from the observed data. By initially sampling from the prior distributions of the parameters and iteratively shrinking the tolerance up to some stopping criterion, we 'shrink' the prior into the posterior.