Randomized machine learning and forecasting of nonlinear dynamic models applied to SIR epidemiological model

We propose an approach to estimation of the parameters of non-linear dynamic models using the concept of Randomized Machine Learning (RML), based on the transition from deterministic models to random ones (with random parameters), followed by estimation of the probability distributions of parameters and noises on real data. The main feature of this method is its efficiency in conditions of a small amount of real data. The paper considers models formulated in terms of ordinary differential equations, which are converted to a discrete form for setting and solving the problem of entropy optimization. The application of the proposed approach is demonstrated on the problem of predicting the total number of infected COVID-19 using a dynamic SIR epidemiological model. To do this, we construct a randomized SIR model (R-SIR) with one parameter, the entropy-optimal estimate of which is realized by its probability density function, as well as the probability density functions of the measurement noise at the points where training is performed. Next, the technique of randomized prediction with noise filtering is applied, based on the generation of the corresponding distributions and the construction of an ensemble of predictive trajectories with the calculation of the trajectory averaged over the ensemble. The paper implements a computational experiment using real operational data on the infection cases in the form of a comparative study with a well-known method for estimating model parameters based on the least squares method. The results obtained in the experiment demonstrate a significant decrease in the mean absolute percentage error (MAPE) with respect to real observations in the forecast interval, which shows the efficiency of the proposed method and its effectiveness in problems of the type considered in the work.