Dynamic models of epidemiology in discrete time taking into account processes with lag.

Models of epidemic dynamics in the form of systems of differential equations of the type SIR and its generalizations, for example SEIR and SIRS, have become widespread in epidemiology. Their coefficients are averages of some epidemic indicators, for example the time when a person is contagious. Statistical data about spreading of the epidemic are known in discrete periods of time, for example twenty-four hours. Therefore, adjustment of the differential equations system under such data comes across cleanly calculable difficulties. They can be avoided, initially to build a model in discrete time as a system of difference equations. Such initial consideration allows, as it shown in the article, to get a general model. On its basis, the models of development of epidemics can be built taking into account their specific. There is another way to obtain a model in discrete time. It consists in discretizing the original model in continuous time. The model obtained in this way is inaccurate, and it is only an approximation to the original one, which makes it possible to simplify calculations and increase the stability of the calculation process. This model is inappropriate, for example, for fitting the model to statistical data. Another argument against the use of systems of differential equations is that the coefficients of such a model may not be the same during a day. For example, the number of contacts of an infected person with susceptible people during a day differs from that at night. However, there is no such difference for daily data. It is possible depending on the day of the week.

Application of the Robust Methods for Estimation of Distribution Parameters with a Priori Constraints on Parameters in Economics and Engineering.

The approach to estimating distribution parameters with a priori constraints has been developed. The Lorentz six-sector model has been constructed. Based on this model, the authors have studied the relationships between food, energy, water resources, supply systems, epidemic, and social situations. They also have investigated the impact of the successive transitions of interconnected sectors to the deterministic chaos regime on the operation mode of the whole system. The method of risk assessment for food security and risk management has been elaborated.

Stochastic Models in the Problems of Predicting the Epidemiological Situation.

The paper investigates some stochastic models with discrete and continuous time to solve important problems of predicting the spread of epidemiological diseases in the population. Various factors of epidemic spread and the main parameters influencing the forecast assessment are taken into account. Some test calculations based on the proposed methods have been performed.

Statistical Analysis of the Dynamics of Coronavirus Cases using Stepwise Switching Regression.

The dynamics of coronavirus cases is proposed to be modeled using switching regression whose switching points are unknown. The stepwise process of constructing the regression in time is described. The dynamics of the number of coronavirus cases in Ukraine is analyzed.