This website contains prediction of the number of new cases and daily deaths for the Corona virus COVID-19 outbreak obtained using 2 variations of a parameter-varying stochastic SIR model.

Starting from the first Wednesday for which we had 21 days of past data, we performed system identification for the stochastic SIR model and computed forecasts for 7, 14, and 21 days ahead; which can eventually be compared with the actual values. We repeated this procedure for every subsequent Wednesday, resulting in updated forecasts. To obtain true validation, the model identified with data up to a particular Wednesday, does not use any subsequent data, either as measurements or to help initialize the numerical solver. This procedure was carried out on 144 regions around the globe for every week for which we had, at least, 21 days of data, resulting in over 4,500 identification/forecasting experiments for each model.

Model

The forecasts are based on a SIR model of the form $$\begin{aligned} R(t+1)&=R(t)+\gamma I(t)+d_\rho(t),\\ U(t+1)&=U(t)+\beta(t) I(t)\Big(1-\frac{U(t)}{N_0}\Big)+d_\nu(t),\\ y_\nu(t)&= \phi(t) \Big(\beta(t) I(t)\Big(1-\frac{U(t)}{N_0}\Big)+d_\nu(t)\Big)+w_\nu(t),\\ y_D(t)&= \omega(t) I(t)+w_D(t),\end{aligned}$$ where $R(t)$ denote the number of removed patients, $I(t)$ the number of infective patients, and $U(t)=R(t)+I(t)$ the number of unsusceptible patients. This model is trained based on two measurements: the daily reported number of new cases $y_\nu(t)$ and the daily reported number of deaths $y_D(t)$. The additive terms $d_\rho(t)$, $d_\nu(t)$, $w_\nu(t)$, $w_D(t)$ account for stochastic variability.

This model depends on a number of key parameters that include the infection rate $\beta(t)$ that can be interpreted as the probability that a susceptible individual will become infected due to interactions with infected individuals; the removal rate $\gamma$ that can be regarded as the probability that an individual leaves the infective state; the death rate $\omega(t)$ that can be regarded as the probability that a new death is reported; and the testing rate $\phi(t)$ that can be regarded as the probability that a new infection is reported.

Forecasts

We provide forecasts obtained using two instances of the model above:

1. A model in which the infection rate $\beta(t)$ and the testing rate $\phi(t)$ are allowed to vary, but the death rate $\omega(t)$ is assumed constant.

   For most regions, we have observed that this model produces more accurate forecasts and tighter confidence intervals.

   The resulting forecasts can be seen at https://web.ece.ucsb.edu/~hespanha/covid19/index2phi.html.

2. A model in which the infection rate $\beta(t)$, the testing rate $\phi(t)$, and the death rate $\omega(t)$ are all allowed to vary.

   The resulting forecasts can be seen at https://web.ece.ucsb.edu/~hespanha/covid19/index3.html.

Data

The data used to train out model include times series of COVID-19 daily cases and daily deaths obtained from the following sources:

1. the European Center for Disease Prevention and Control (ECDPC) for worldwide data outside the United States of America, Brazil, and Portugal;

2. the COVID-19 Data Repository by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University for State and City data within the United States of America;

3. the Portuguese Direção-Geral de Saúde for data in Portugal .

4. Brasil.IO based on data collected from the Secretarias Estaduais de Saúde for State and City data within Brazil .

We produced forecasts for every country represented in the ECDPC dataset that, at some point in time, reported more than 10 new COVID-19 cases in one day. For a few countries, including the United States of America and Brazil, we had available data at the state/province/city level and produced forecasts at finer regional levels. The ECDPC and CSSE time series go as far back as February 2020 and contain daily results up to the present.

Acknowledgments

This research was supported by the National Science Foundation under Grant No. ECCS-2029985.

Authors

• João P. Hespanha, hespanha@ece.ucsb.edu, University of California, Santa Barbara, USA

• Raphael Chincilla, raphaelchinchilla@ucsb.edu, University of California, Santa Barbara, USA

• Ramon R. Costa, ramon@coep.ufrj.br, Federal University of Rio de Janeiro, Brazil,

• Murat K. Erdal, m_erdal@ucsb.edu, University of California, Santa Barbara, USA

• Guosong Yang, guosongyang@ucsb.edu, University of California, Santa Barbara, USA