Mathematical modeling of tourism development in territorial communities

In this paper, the problems of development of associations of territorial communities in the tourism direction of economic development are considered. The object of research is the improvement of territorial communities on the example of Ukraine. One of the most problematic places is the lack of funds for the development of existing large tourist complexes and the creation of new ones. The study uses the idea that tourism development has a direct stimulating effect on the development of a number of important economic sectors. The use of a mathematical apparatus is also considered, which allows to analyze the main factors influencing the development of the tourism industry of territorial communities. A comprehensive solution of economic, social and environmental issues of sustainable tourism development is impossible without the development of mathematical models and supporting tools that allow predicting the main indicators of sustainable tourism development. The paper considers PLS-PM modeling using such internal consistency criteria as Cronbach’s Alpha coefficient, Dillon-Goldstein coefficient ρ, model reliability, mean variance. The purpose of the PLS-PM model is to obtain estimates of latent variables for further forecasting procedures for the development of the system. The processes taking place in the tourism industry are characterized by a complex interaction of economic, environmental and social factors. Their influence should be taken into account for the implementation of the sustainable tourism development strategy. The analysis of the model was also carried out with the help of a single coefficient of quality of the correspondence of the data model, which characterizes the quality of the internal and external models of the system. Thanks to the listed tools, the statement is formed that the regulation of key factors of the tourism sector of the economic sector can have a positive impact on the development of national culture and economy in the united territorial communities. The created mathematical model clearly forms the conclusion that the development of tourism in local communities can become the engine of their sustainable economic development, given the available regional conditions