The aim: Is to build a forecast of the COVID-19 disease course, considering the vaccination of the population from particular countries. Materials and methods: Based on the analysis of statistical data, the article deals with the topical issue of the impact made by vaccination on the prevention of the COVID-19 pandemic. The time series, showing the dynamics of changes in the number of infected in Chile, Latvia, Japan, Israel, Australia, Finland, India, United States of America, New Zealand, Czech Republic, Venezuela, Poland, Ukraine, Brazil, Georgia for the period 07.08. 2020–09.09.2021, are analyzed. Trend-cyclic models of time series are obtained using fast Fourier transform. The predicted values of the COVID-19 incidence rate for different countries in the period from September 10, 2021 to February 2, 2022 were calculated using the constructed models. Results and conclusions: The results of the study show that vaccination of the population is one of the most effective methods to prevent the COVID-19 pandemic. The proposed method of modeling the dynamics of the incidence rate based on statistical data can be used to build further predictions of the incidence rate dynamics. The study of behavioral aspects of trust in vaccination is proposed to be conducted within the theory regarding the self-organization of complex systems.

The paper emphasizes the importance of human health as the most valuable, most important resource at the individual and national level, affecting the country’s socio-economic development and competitiveness. It states that it is necessary for the actors ensuring the public health system to form a new concept for the functioning of the health system, taking into account the current state of public health, the functioning of medical institutions, and the resource support of the healthcare industry. The primary purpose is to conduct a bibliometric analysis of scientific publications dealing with the global behavioral and social dimension of the public health system. The systematization of literary achievements and approaches to solving this problem has been carried out, which indicates the need for proper attention and high-quality, conceptual, international research by world scientists on issues related to the state and level of public health, satisfaction with the healthcare system. The relevance of the analysis of research on the behavioral and social dimension of the public health system of the world implies that the further development of the healthcare industry necessitates research, intensive development, and dissemination of available scientific and methodological international experience in solving this issue of the public health system in different countries worldwide. The research consisted of four stages. A map of the interrelationships of key concepts with other scientific categories has been constructed; a content-contextual study of the constructed blocks of bibliometric analysis has been implemented; an inter-cluster analysis has been carried out. A map of the interrelationships of the key concepts under study with other scientific categories has been constructed, reflecting the dynamics in the form of a contextual-time block; the evolutionary-time prospects of the study have been determined. A geographically extensive map of the scientific bibliography of the categories under study has been constructed; the spatial component of the study has been analyzed. A territorially branched map of the spatio-temporal dimension of the category under the study in dynamics has been constructed. The methodological tools of the research are theoretical (grouping, abstraction, synthesis) and empirical methods (observation, description), research methods, services of the Scopus information platform, and VOSViewers tools.1.6.15. The study was conducted based on the publications indexed by the Scopus database for 2000-2020. The objects of research were the following scientific categories: “health care system, medical services, behavioral aspect, social aspect,” the countries United States, Germany, Norway, Greece, United Kingdom, Australia, Canada, India, Netherlands, China, Brazil, Switzerland, Denmark, Belgium, Iran, Japan, Italy, Spain, because these two groups of objects allowed to conduct two-directional analysis of the problem under study. The results of the bibliometric analysis presented in the paper showed that the aspect of the behavioral and social dimension of the public health system was relatively young and insufficiently developed; the attention of the scientific community for a long time on this issue was mainly concentrated in the United States and the United Kingdom. China, Iran, and Japan were less involved in this process at an earlier time interval, but this research became relevant for them in recent years. The study results can be used to identify the most potential priority areas for forming the policy and strategy of the state health system, based on determining the main significant, modern, relevant characteristics of the healthcare industry.

Сучасний світ-це світ постійних змін, багатоваріантності, невизначеності та малопередбачуваності. Кардинальні зміни відбуваються як у науковій парадигмі, так і в різних сферах життєдіяльності людини. У науковому просторі все більше поширюється методологія синергетики-теорії самоорганізації, яка орієнтована на пошук певних універсальних законів еволюції та самоорганізації складних систем, законів еволюції відкритих, нерівноважних систем будь-якої природи-від фізичних і біологічних до економічних та соціальних. У межах теорії управління соціально-економічними системами вчені все частіше звертаються до синергетичної методології. У роботі досліджується актуальне питання зміни управлінської парадигми в сучасних умовах, розкрито суть однієї з основних категорій синергетики-нелінійності, акцентується увага на необхідності врахування методології синергетики в процесі управління соціально-економічними системами. Ключові слова: самоорганізація, синергетика, соціально-економічні системи, синергетичні методи, управління, нелінійність. Современный мир-это мир постоянных изменений, многовариантности, неопределенности, непредсказуемости. Кардинальные изменения происходят как в научной парадигме, так и в различных сферах жизнедеятельности человека. В научном пространстве все больше используется методология синергетики-теории самоорганизации, направленной на поиск универсальных законов эволюции и самоорганизации сложных систем, открытых, неравновесных систем любой природыот физических и биологических до экономических и социальных. В рамках теории управления социально-экономическими системами ученые все чаще обращаются к синергетической методологии. В работе исследуется актуальный вопрос изменения управленческой парадигмы в современных условиях, раскрыта суть одной из основных категорий синергетики-нелинейности, акцентируется внимание на необходимости применения методологии синергетики в процессе управления социальноэкономическими системами. Ключевые слова: самоорганизация, синергетика, социально-экономические системы, синергетические методы, управление, нелинейность. The modern world is a world of constant change, uncertainty, unpredictability. Fundamental changes occur in the scientific paradigm (understanding of the world and its laws of development). Under such conditions, unambiguous determinism is a special case, and forecasting is fundamentally limited. The classical scientific paradigm studied mainly stability, balance, order, closed systems, linear relationships. Modern nonlinear science includes nonlinear thermodynamics, catastrophe theory, dynamic chaos theory, fractal mathematics, synergetics. Synergetics has arisen in the natural sciences, it has broad prospects for application in economic, social sciences and processes. Synergetics studies general principles, guidelines for life, for the development of companies, for scientific research in an unstable and unpredictable world. In the theory of managing socioeconomic systems, scientists are increasingly turning to a synergistic methodology. According to the conclusions...

Modern socio-economic systems demonstrate instability, chaos, and unpredictability. What methodology should be used to modeling modern socio-economic systems? Constant changes and crises in the development of socio-economic systems require new approaches to the research of these systems. The feature of the approach to the study of socio-economic systems in modern conditions is the conversion from a linear to a nonlinear paradigm. The models of socio-economic systems are systems of nonlinear differential equations. Nonlinear differential equations demonstrate different modes of functioning of complex socio-economic systems. Nonlinear equations can have several qualitatively different solutions. This explains the existence of different ways of evolution of nonlinear socio-economic systems. Nonlinearity is a fundamental position of new paradigm of cognition and development. Nonlinearity is a general law of nature and means, first of all, non-observance of the principle of superposition. The whole cannot be the sum of its parts; the result cannot be the sum of efforts, the quality of the whole is not determined by the sum of the qualities of its parts, the reaction of the system is not proportional to the influence. For nonlinear phenomena, knowledge about the behavior of a part of an object does not yet guarantee correct ideas about the behavior of the object as a whole, and its response to changes in conditions may qualitatively depend on the magnitude of these changes. Non-linearity is the multivariance of the evolutionary paths, the presence of a choice of alternative paths and determining the rate of evolution. Nonlinearity is the irreversibility of evolutionary processes; nonlinear, indirect dependence of evolutionary processes on external influences. The article examines the topical issue of changing the paradigm of modeling and forecasting socio-economic systems. The necessity of transition from linear to nonlinear paradigm in economic research is theoretically substantiated. The features of the application of methods of nonlinear dynamics to the modeling of socio-economic systems are considered. The phenomenon of nonlinearity of socio-economic systems is studied.

In the modern society, public healthcare and safe life are key tasks of any country worldwide. Social health and security are the highest and the most desired values. They are integral conditions to reach sustainable development goals. Healthcare is an important policy component of separate states and supernational communities worldwide. The issue of global approaches to healthcare and environment protection is one of the most outstanding scientific achievements of the 20th century. The current article reviews arguments in researching the public healthcare system. The main study purpose is a detailed analysis of the social-economic public healthcare determinants and their transparency in the 2013-2023 Scopus sources. The research object is public healthcare. The research topic is bibliometric analysis of the 2013-2023 Scopus sources about public healthcare. The bibliometric analysis of big data provides us with those necessary research results that cannot be obtained without special tools. To conduct the public healthcare bibliometric analysis, we applied the VOSviewer computer software. It engages wide functional possibilities of smart text processing, which generates and visualises joint networks of the most significant terms and notions in a certain branch. A thorough bibliometric analysis of the social-economic public healthcare determinants and their transparency in the 2013-2023 Scopus sources is conducted stepwise. Firstly, we select a list of keywords for the studied issue. Secondly, the Scopus search engine is activated. Thirdly, a range of sources is defined. Fourthly, we analyse a sample of Scopus publications. Fifthly, we conduct the VOSviewer cluster analysis of the Scopus sources (arranged by citation number, co-authorship frequency, countries with the given problem). Sixthly, we examine bibliometric maps with visualised clusters. The obtained research results may definitely contribute to further healthcare studies and bibliometric analysis of indexed scientific sources.