Marian Petrica

Marian Petrica, Ionel Popescu

In this paper, we propose a parameter identification methodology of the SIRD model, an extension of the classical SIR model, that considers the deceased as a separate category. In addition, our model includes one parameter which is the ratio between the real total number of infected and the number of infected that were documented in the official statistics. Due to many factors, like governmental decisions, several variants circulating, opening and closing of schools, the typical assumption that the parameters of the model stay constant for long periods of time is not realistic. Thus our objective is to create a method which works for short periods of time. In this scope, we approach the estimation relying on the previous 7 days of data and then use the identified parameters to make predictions. To perform the estimation of the parameters we propose the average of an ensemble of neural networks. Each neural network is constructed based on a database built by solving the SIRD for 7 days, with random parameters. In this way, the networks learn the parameters from the solution of the SIRD model. Lastly we use the ensemble to get estimates of the parameters from the real data of Covid19 in Romania and then we illustrate the predictions for different periods of time, from 10 up to 45 days, for the number of deaths. The main goal was to apply this approach on the analysis of COVID-19 evolution in Romania, but this was also exemplified on other countries like Hungary, Czech Republic and Poland with similar results. The results are backed by a theorem which guarantees that we can recover the parameters of the model from the reported data. We believe this methodology can be used as a general tool for dealing with short term predictions of infectious diseases or in other compartmental models.

Marian Petrica, Radu D. Stochitoiu, Marius Leordeanu et al.

In this paper we propose a three stages analysis of the evolution of Covid19 in Romania. There are two main issues when it comes to pandemic prediction. The first one is the fact that the numbers reported of infected and recovered are unreliable, however the number of deaths is more accurate. The second issue is that there were many factors which affected the evolution of the pandemic. In this paper we propose an analysis in three stages. The first stage is based on the classical SIR model which we do using a neural network. This provides a first set of daily parameters. In the second stage we propose a refinement of the SIR model in which we separate the deceased into a distinct category. By using the first estimate and a grid search, we give a daily estimation of the parameters. The third stage is used to define a notion of turning points (local extremes) for the parameters. We call a regime the time between these points. We outline a general way based on time varying parameters of SIRD to make predictions.

Radu D. Stochiţoiu, Marian Petrica, Traian Rebedea et al.

Analysing and understanding the transmission and evolution of the COVID-19 pandemic is mandatory to be able to design the best social and medical policies, foresee their outcomes and deal with all the subsequent socio-economic effects. We address this important problem from a computational and machine learning perspective. More specifically, we want to statistically estimate all the relevant parameters for the new coronavirus COVID-19, such as the reproduction number, fatality rate or length of infectiousness period, based on Romanian patients, as well as be able to predict future outcomes. This endeavor is important, since it is well known that these factors vary across the globe, and might be dependent on many causes, including social, medical, age and genetic factors. We use a recently published improved version of SEIR, which is the classic, established model for infectious diseases. We want to infer all the parameters of the model, which govern the evolution of the pandemic in Romania, based on the only reliable, true measurement, which is the number of deaths. Once the model parameters are estimated, we are able to predict all the other relevant measures, such as the number of exposed and infectious people. To this end, we propose a self-supervised approach to train a deep convolutional network to guess the correct set of Modified-SEIR model parameters, given the observed number of daily fatalities. Then, we refine the solution with a stochastic coordinate descent approach. We compare our deep learning optimization scheme with the classic grid search approach and show great improvement in both computational time and prediction accuracy. We find an optimistic result in the case fatality rate for Romania which may be around 0.3% and we also demonstrate that our model is able to correctly predict the number of daily fatalities for up to three weeks in the future.