Explaining the Bomb-Like Dynamics of COVID-19 with Modeling and the Implications for Policy

Gary Lin; Alexandra T Strauss; Maxwell Pinz; Diego A Martinez; Katie K Tseng; Emily Schueller; Oliver Gatalo; Yupeng Yang; Simon A Levin; Eili Y Klein

Our goal was to estimate the ranges of parameters that would fit the data of the beginning of an outbreak in a country, assuming that initially the effects of distancing and other measures to control the disease are largely absent and thus the data are largely representative of the transmission dynamics but that some proportion of the infected population is not observed. Data on outbreaks in Italy, Spain, and South Korea were obtained from the Center for Systems Science and Engineering at Johns Hopkins University [1] (Figure 1) . We fit the model to the observed data assuming that the first observed case was in the more severe group. We constrained our fit to the early part of the outbreak in each country, before widespread quarantines or extensive testing altered the path of the disease. For Italy this was from January 22, 2020 to March 20, 2020, for Spain this was from January 22, 2020 to March 30, 2020, and for South Korea this was from January 22, 2020 to March 5, 2020. To estimate the credibility of parameters, we used Monte Carlo (MC) to sample the parameter space with a uniform prior density with bounds and used acceptance and rejection sampling to approximate a posterior distribution of the parameters. The error between the results of the model yielding the expected number of observed cases and the observed number of cases is considered to be normally distributed with Norm (0, σ). The variance ( 2 ) is estimated as the difference between the model with the optimal parameter set and the observed number of cases. Reported parameter estimates are the medians of the posterior distributions, and 95% credible intervals from quantiles of the posterior distribution. The goal of the Bayesian parameter estimation is to approximate a posterior probability density function of the parameter. MC sampling of the parameter space was based on the number of reported active cases, recoveries and deaths. Specifically, we fit projected cases in the I compartment to active cases (confirmed cases minus recovered cases and deaths) and the R compartment to the sum of recovered and deaths. While traditional unbiased curve-fitting methods yield a set of parameter estimations that capture observed data, they do not account for known prior belief on parameter ranges. A Bayesian approach to parameter estimation allows us to quantify the credibility of one set of model parameters. This approach is extremely powerful as it provides a range of credible parameters in which the model can fit the observed data. Parameter bounds were based on disease dynamics literature and expert judgement (Table 1) .