Determining the parameters of the age-dependent model of infectious diseases, applied to modeling the COVID-19 epidemic in Ukraine.

Abstract

In December 2019, an outbreak of severe acute respiratory syndrome, now known as SARS-CoV-2, began in Wuhan, China. The virus soon spread around the world, becoming a pandemic. Since the early days of the pandemic, many mathematical models have been proposed to predict the spread of the disease. Since the outbreak, various measures have been introduced to contain and control the spread of the virus, and these measures have been largely based on the results of these models. All the applied models require model parameter refinement to improve forecast accuracy. SEIR-AGE allows for forecasting the spread of the COVID-19 virus infection, taking into account the age groups of the population and their spatial heterogeneity. SEIR-AGE is a system of ordinary differential equations. To numerically solve this system of ordinary differential equations, an explicit Runge-Kutta method of 8th order of accuracy with 5th order error estimation and control of the choice of integration step is used in the paper. The model parameters are refined by comparing the predicted results with the observed ones by solving a nonlinear least squares problem with constraints. The DQED procedure is used to solve the nonlinear least squares problem with constraints. The algorithm is based on the approximation of nonlinear functions using a quadratic tensor model. It uses a confidence region defined by a parallelepiped containing the current values of the unknowns. The objective function is allowed to increase at intermediate steps. This increase is allowed as long as the predictor indicates that a new set of the best values exists in the confidence region. If necessary, it is possible to return to the current best values. Numerical examples of refining the parameters of the SEIR-AGE model are presented in the paper.