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For modeling the number of visits in Stopi\'{c}a cave (Serbia) we consider the classical Auto-regressive Integrated Moving Average (ARIMA) model, Machine Learning (ML) method Support Vector Regression (SVR), and hybrid NeuralPropeth method which combines classical and ML concepts. The most accurate predictions were obtained with NeuralPropeth which includes the seasonal component and growing trend of time-series. In addition, non-linearity is modeled by shallow Neural Network (NN), and Google Trend is incorporated as an exogenous variable. Modeling tourist demand represents great importance for management structures and decision-makers due to its applicability in establishing sustainable tourism utilization strategies in environmentally vulnerable destinations such as caves. The data provided insights into the tourist demand in Stopi\'{c}a cave and preliminary data for addressing the issues of carrying capacity within the most visited cave in Serbia.