The purpose of the article is to analyze the parameters of the educational sector on a global scale, to summarize and present the differences in investments, Internet penetration in the educational sphere in different countries, and to show the impact of COVID-19 on global education. The article highlights educational digital transformations and innovations in different countries, the development of e-learning and new tools and means that have been developed during the COVID waves. The article offers the basic concepts and characteristics for e-learning management of Ukrainian educational companies using effective management and mathematical tools and means. Methodology. To analyze relevant quantitative and qualitative data on e-learning management, a literature review, observation and research methodology, and comparison were used. Stratification and decomposition approaches are used to develop a model for assessing the competitiveness of e-learning educational enterprises. Research results show that the educational field requires new technologies, tools and equipment. Various e-learning platforms and massive open online courses have shown significant effectiveness during the pandemic. At the same time, a significant number of challenges remain: Internet penetration in different countries, investment in the development of learning equipment, the quality of e-learning materials, the ability to teach and learn with all the necessary tools and equipment, and access to devices. Educational companies that understood the trends in time and were able to change their products accordingly have gained additional profits. This study contributes to the evaluation of the competitiveness of e-learning educational companies and organizations. The results of the study were used to further develop the proposed model. The proposed model has six functions that describe the main aspects of a typical domestic educational enterprise. Practical implications. In the context of digital transformation and innovation, companies and countries must understand what tasks they need to solve, what problems to avoid, and find the best way to develop their own activities. These ideas have been developed into a model, which in this study is based on mathematical fuzzy logic and the Hopfield neural network. Value/originality. The model can be implemented in the Ukrainian domestic educational market by companies in order to develop and improve their competitive strategy.