The Past Helps the Future: Coupling Differential Equations with Machine Learning Methods to Model Epidemic Outbreaks

The aim of the research is to assess the applicability of methods of artificial intelligence to the analysis and prediction of infectious disease dynamics, with an aim to increase the speed of obtaining predictions along with enhancing quality of the results. To ensure the compliance of the forecasts with the natural laws governing the epidemic transmission, we employ Physics-Informed Neural Networks (PINN) as our main tool for the forecasting experiments. With the help of numerical experiments, we show the applicability of the approach to infectious disease modeling based on coupling classic approaches, namely, SIR models, and the cutting-edge research related to machine learning techniques. We compare the accuracy of different implementations of PINN along with the statistical models in the task of forecasting COVID incidence in Saint Petersburg, thus choosing the best modeling approach for this challenge. The results of the research could be incorporated into surveillance systems monitoring the advance of COVID and influenza incidence in Russian cities.