  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.
