Optimization in the Model of Control over a Socio-economic System in Conditions of a Mass Disease

Abstract

This article considers further development of the mathematical model that allows predicting the socio-economic situation and choosing the optimal management strategy in conditions of a mass disease. The model is a dynamic optimal control problem with a delay in phase variables. It takes into account social, biological and economic factors. The proposed modification of the model consists in simultaneous use of several quality criteria for evaluating management strategies, for which two approaches are proposed. The first approach is based on the reduction of criteria to same unit of measurement, which is the value of a statistical life. The second one consists of normalization of the criteria. Computational experiments were carried out using both modifications of the model; in particular, for the second approach, a series of calculations with different combinations of criteria significance was performed. The experiments used the values of the model parameters estimated on the basis of statistical data on the COVID-19 pandemic in the Russian Federation and the Ulyanovsk region. A modification of the numerical parameterization method developed by the authors was used to find a solution. The optimal solutions obtained for the Russian Federation and the Ulyanovsk region do not coincide when using the same objective functional. Such a result may indicate that it is desirable to choose a specific management strategy for each region.

Keywords

• optimal control
• optimal solution analysis
• economic system
• mass disease
• covid-19