Modeling of processes of sustainable tourism development

The article deals with mathematical modeling of sustainable tourism development. The proposed approach allows for a more cost-effective manner, as compared with other instruments, to prove effective management options in tourism development in the regions. Described are the interaction and interrelationship between main factors determining the state and dynamic characteristics of sustainable tourism on a regional scale. It is shown that the construction of models of sustainable tourism in a particular region should take into account the parameters of its economic development, environmental conditions, characteristics of social relations, as well as natural and cultural potential of a specific area. It is noted that a special importance for the formation parameters of sustainable tourism has an effective organization of destination management. Based on the regulations of UNWTO, the following main criteria management are suggested: sustainable management of destinations, maximizing social and economic benefits for the local population with minimal impact on it, maximizing benefits for traveling and cultural heritage sites with minimal impact on them, maximizing the benefits for the natural environment and minimizing the negative impact on it. On the basis of these criteria, the basic principles of modeling are highlighted: a systematic account of interacting factors that determine the development of sustainable tourism, the use of integrated criteria when evaluating options for sustainable tourism, the direction of the modeling of process as a basis for effective management for destinations. Based on the research, the author concluds that the development of a mathematical model for sustainable tourism in a particular region should take into account two groups of factors affecting its development: interpersonal contacts between the "experienced" tourists and newcomers on the one hand, and the impact of advertising and travel agencies, on the other. The author provides an aggregated view of a model of sustainable tourism as a nonlinear differential equation of diffusion of innovations tourist. Qualitative solution of the equation in the form of an S-shaped curve is suggested. To understand the impact of innovation processes in the development of tourism, the author suggests an analysis of the statistical distribution of the individuals involved in innovation related to sustainable tourism.