Forecasting Multi-Wave Epidemics Through Bayesian Inference

Abstract

We present a simple, near-real-time Bayesian method to infer and forecast a multiwave outbreak, and demonstrate it on the COVID-19 pandemic. The approach uses timely epidemiological data that has been widely available for COVID-19. It provides short-term forecasts of the outbreak's evolution, which can then be used for medical resource planning. The method postulates one- and multiwave infection models, which are convolved with the incubation-period distribution to yield competing disease models. The disease models' parameters are estimated via Markov chain Monte Carlo sampling and information-theoretic criteria are used to select between them for use in forecasting. The method is demonstrated on two- and three-wave COVID-19 outbreaks in California, New Mexico and Florida, as observed during Summer-Winter 2020. We find that the method is robust to noise, provides useful forecasts (along with uncertainty bounds) and that it reliably detected when the initial single-wave COVID-19 outbreaks transformed into successive surges as containment efforts in these states failed by the end of Spring 2020.

Keywords: Bayesian framework; COVID-19; Incubation model; Infection rate; Markov Chain Monte Carlo; Pseudo-marginal MCMC.

Fig. 1

Daily confirmed cases of COVID-19 aggregated at state level, shown in black symbols, and the corresponding 7-day averaged data shown with red lines and symbols

Fig. 2

1D and 2D joint marginal distributions the components of $\Theta =\{t_0,N_1,k_1,{\theta }_1,\Delta t_2,N_2,k_2,{\theta }_2,log{\sigma }_a,log{\sigma }_m\}$ for data from California up to 2020-08-19. Distance correlations [24] for each pair of parameters is displayed about each joint marginal distribution

Fig. 3

Schematic showing new case data with three infection waves. The red box indicates a range of final dates for which one-wave model chain statistics have been used to generate priors for a two-wave model. The blue box indicates a range of final dates for which two-wave model chain statistics have been used to generate priors for a three-wave model

Fig. 4

One-wave model calibration and forecast for New Mexico on 2020-05-13

Fig. 5

Comparison of one-wave and two-wave model calibration and forecasts for New Mexico

Fig. 6

Comparison of information criteria (AIC, BIC) and CRPS for the single and two-wave model results for New Mexico

Fig. 7

Two-wave model results for California and Florida

Fig. 8

Comparison of information criteria (AIC, BIC) and CRPS for the single and two-wave model results for California

Fig. 9

Comparison of information criteria (AIC, BIC) and CRPS for the single and two-wave model results for Florida

Fig. 10

Three-wave model results for New Mexico on 2020-10-21 and 2020-12-21