Adaptive Bayesian Learning and Forecasting of Epidemic Evolution-Data Analysis of the COVID-19 Outbreak

Abstract

Since the beginning of 2020, the outbreak of a new strain of Coronavirus has caused hundreds of thousands of deaths and put under heavy pressure the world's most advanced healthcare systems. In order to slow down the spread of the disease, known as COVID-19, and reduce the stress on healthcare structures and intensive care units, many governments have taken drastic and unprecedented measures, such as closure of schools, shops and entire industries, and enforced drastic social distancing regulations, including local and national lockdowns. To effectively address such pandemics in a systematic and informed manner in the future, it is of fundamental importance to develop mathematical models and algorithms to predict the evolution of the spread of the disease to support policy and decision making at the governmental level. There is a strong literature describing the application of Bayesian sequential and adaptive dynamic estimation to surveillance (tracking and prediction) of objects such as missiles and ships; and in this article, we transfer some of its key lessons to epidemiology. We show that we can reliably estimate and forecast the evolution of the infections from daily - and possibly uncertain - publicly available information provided by authorities, e.g., daily numbers of infected and recovered individuals. The proposed method is able to estimate infection and recovery parameters, and to track and predict the epidemiological curve with good accuracy when applied to real data from Lombardia region in Italy, and from the USA. In these scenarios, the mean absolute percentage error computed after the lockdown is on average below 5% when the forecast is at 7 days, and below 10% when the forecast horizon is 14 days.

Keywords: Bayesian sequential estimation; SARS-CoV-2; compartmental model; ensemble forecasting; pandemic prediction; pandemic tracking.

FIGURE 1.

Evolution of the infection rate in the simulated scenarios.

FIGURE 2.

Estimated (top) infection rate and (bottom) recovery rate in the first simulated scenario. The shaded areas represent the 90% confidence interval.

FIGURE 3.

Estimated (top) infection rate and (bottom) recovery rate in the second simulated scenario. The shaded areas represent the 90% confidence interval.

FIGURE 4.

Estimation and forecasting, respectively in solid and dashed lines, of (top) the infection rate and (bottom) the number of infected individuals in the first scenario; the superscripts E and F stand for estimate and forecast, respectively. The estimation is up to (marked by a vertical dotted line), and the forecast is up to . The shaded areas represent the 90% confidence interval.

FIGURE 5.

Estimation and forecasting, respectively in solid and dashed lines, of (top) the infection rate and (bottom) the number of infected individuals in the second scenario; the superscripts E and F stand for estimate and forecast, respectively. The estimation is up to (marked by a vertical dotted line), and the forecast is up to . The shaded areas represent the 90% confidence interval.

FIGURE 6.

Numbers of infected and recovered (i.e., hospital releases plus deaths) individuals in Lombardia, Italy, from February 24, 2020, to June 30, 2020 (data from Protezione Civile [38]). The vertical dashed line indicates March 8, 2020, the beginning of the lockdown. The large steps on May 6 are due to an inaccurate reporting of the data, as explained in Section V-B1.

FIGURE 7.

Estimated (top) infection rate and (bottom) recovery rate for Lombardia. The vertical dashed line indicates March 8, 2020, the beginning of the lockdown. The shaded areas represent the 90% confidence interval.

FIGURE 8.

Estimation and forecasting, respectively in solid and dashed lines, of the number of infected individuals in Lombardia, Italy (legend is reported in the bottom-right corner image; the superscript E stands for estimate, and the superscript F stands for forecast). The date corresponding to the end of the estimation and the beginning of the forecast is marked by a vertical dotted line (the leftmost vertical dashed line marks March 8, the beginning of the lockdown). In all the cases, the forecast horizon is June 30. The shaded area represents the 90% confidence interval. The poor forecasts made on April 28, and May 3, relate to the inaccurate data later provided on May 6, as explained in Section V-B1.

FIGURE 9.

Numbers of infected and recovered (i.e., hospital releases plus deaths) individuals in the USA, from March 1, 2020, to July 31, 2020 (data from JHU [41]).

FIGURE 10.

Estimated (top) infection rate and (bottom) recovery rate for the USA. The shaded areas represent the 90% confidence interval.

FIGURE 11.

Estimation and forecasting, respectively in solid and dashed lines, of the number of infected individuals in the USA (legend is reported in the bottom-right corner image; the superscript E stands for estimate, and the superscript F stands for forecast). The date corresponding to the end of the estimation and the beginning of the forecast is marked by a vertical dotted line. In all the cases, the forecast horizon is July 31. The shaded area represents the 90% confidence interval. The poor forecasts made on May 11 and 16, relate to the abrupt decrease of the estimated recovery rate that follows April 30 (cf. Fig. 10, bottom image).