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.
Highlights
Gaglione et al.: Adaptive Bayesian Learning and Forecasting of Epidemic Evolution—Data Analysis of the COVID-19 Outbreak have pushed many governments to take extraordinary social measures. These events include the lack of effective cures and vaccines, the exponentially increasing number of individuals requiring recovery in intensive care units, and the announcement by the World Health Organization (WHO) of a Coronavirus pandemic on March 11, 2020 [2]
Where uk is a random vector — whose dimension depends on S, M, and f(·) — with known distribution modeling the stochastic variation of the epidemic state in the time interval t
We proposed a Bayesian sequential estimation and forecasting algorithm that, based on the information that authorities provide on a daily basis, is able to estimate the state of the epidemic and the parameters of the underlying model, as well as to forecast the evolution of the epidemiological curve
Summary
Gaglione et al.: Adaptive Bayesian Learning and Forecasting of Epidemic Evolution—Data Analysis of the COVID-19 Outbreak have pushed many governments to take extraordinary social measures These events include the lack of effective cures and vaccines, the exponentially increasing number of individuals requiring recovery in intensive care units, and the announcement by the World Health Organization (WHO) of a Coronavirus pandemic on March 11, 2020 [2]. In order to capture the effects of mitigation strategies (e.g., mobility restriction, lockdown, wearing masks, and social distancing), the marginal posterior distributions of both the variable states (number of infected and recovered people) and model parameters (infection rate β and recovery rate γ ), are calculated at each time by means of recursive prediction and update formulae. N (x; μ, C) refers to a multivariate Gaussian pdf of random vector x with mean μ and covariance matrix C
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