Vol 26, No 134 (2021)

We propose multicompartmental models of infectious diseases dynamics for numerical study of the spread parameters of the new coronavirus infection SARS-CoV-2, which take into account the delay effects associated with the presence of the latent period of the infection, as well as the possibility of an asymptomatic course of the disease. The dynamics of the spread of COVID-19 in the Russian Federation was investigated, using these models with distributed parameters that formalize the interactions of the models’ compartments. The paper provides numerical estimates of the spread dynamics of the new coronavirus infection in various age groups of the population. We also investigate possible consequences of the mask regime and quarantine measures. We obtain an explicit estimate allowing to assess the necessary scope of these measures for the epidemy extinction.

A system of first-order partial differential-algebraic equations in a Banach space with constant degenerate operators in the case of a regular operator pencil is considered. In this case, under some additional condition, the original system splits into two subsystems in disjoint subspaces in order to search for the projections of the original unknown function in the subspaces. The matching conditions for the parameters of the systems are identified. A solution of the considered system of differential-algebraic equations is constructed.

The paper is devoted to the regularization of the classical optimality conditions (COC) - the Lagrange principle and the Pontryagin maximum principle in a convex optimal control problem for a parabolic equation with an operator (pointwise state) equality-constraint at the final time. The problem contains distributed, initial and boundary controls, and the set of its admissible controls is not assumed to be bounded. In the case of a specific form of the quadratic quality functional, it is natural to interpret the problem as the inverse problem of the final observation to find the perturbing effect that caused this observation. The main purpose of regularized COCs is stable generation of minimizing approximate solutions (MAS) in the sense of J. Warga. Regularized COCs are: 1) formulated as existence theorems of the MASs in the original problem with a simultaneous constructive representation of specific MASs; 2) expressed in terms of regular classical Lagrange and Hamilton-Pontryagin functions; 3) are sequential generalizations of the COCs and retain the general structure of the latter; 4) “overcome” the ill-posedness of the COCs, are regularizing algorithms for solving optimization problems, and form the theoretical basis for the stable solving modern meaningful ill-posed optimization and inverse problems.

Maximal linked systems (MLS) of sets on widely understood measurable spaces (MS) are considered; in addition, every such MS is realized by equipment of a nonempty set with a π -system of its subsets with «zero» and «unit» (π -system is a nonempty family of sets closed with respect to finite intersections). Constructions of the MS product connected with two variants of measurable (in wide sense) rectangles are investigated. Families of MLS are equipped with topologies of the Stone type. The connection of product of above-mentioned topologies considered for box and Tychonoff variants and the corresponding (to every variant) topology of the Stone type on the MLS set for the MS product is studied. The properties of condensation and homeomorphism for resulting variants of topological equipment are obtained.