## 3 Materials and Methods
### Theory of the Suggested Model  
The following model is an example of a stock and flow diagram, exploring the system behavior where essential variables enter the system, determining the supply and demand for transport in a location (e.g., municipality). This simplified model ignores other crucial factors, such as generators of local travels. Based on the research, we included interconnected elements in the dynamic model. Its logical background allows for an extension to other constituents or input subsystems, which yields more accurate results. The model contains only two transport modes: passenger car transport (_PCT_) and public transport (_PT_). The reduced design includes an element quantifying the state of the transport system by comparing supply and demand in the sector. The transport supply means an immediate daily capacity of means of transport, whereas the transport demand involves a sum of all possible journeys that residents can take daily. For both kinds of transport, the comparative estimate of supply and demand can be expressed as follows:  
\[\textit{the ratio of the supply and demand in transport capacity supply} \tag{4}\]  
The transport supply and demand ratio refers to the state of a local transport sector. Higher values reflect greater flexibility, satisfying the demand without problems. By applying this ratio to each transport mode, we obtain an acceptable level of sustainable transport (_PT_) in the model and can compare it with the situation in car transport. Figure 2 depicts one part of the model structure with individual variables connected with generating car travels within the region. Figure 2: Supply and demand estimation model in CT and PT-first part of the model (source: Authors). The model describes basic stocks, flows, variables, and measurable interrelationships. In this case, the stocks involve the total population in the locality, _GDP_ rates in the region, the number of means of transport in _PT_, and the number of registered cars. These stocks are susceptible to flows and other variables analyzed below. For measuring initial variable values, the model involved partly factual data (statistical data from the South Bohemian Region in the CZ) and partly expertly estimated data upon consulting with relevant professionals. For that reason, we could not validate the model, suggesting only an applied theory of system dynamics from the transport sector. The regional population stock comprises hard data on the population, natural population growth/decline and migration increase/decrease. The formula for exploring the relationships between the population, natural change, and migration are as follows:  
\[population(t_{n})=\int_{t_{0}}^{t_{n}}natural\ change(x)+migration(x)dx+ population(t_{0})\ [population] \tag{5}\]  
The population in time (\(t_{0}\)) represents the initial value of the data-checked population in the model. This simplified submodel of the population stock in time allows for an annual population increase. The 'inflow' of the stock displayed as a natural population change reflects the average annual population growth. The degree of the change is as follows:  
\[natural\ change=\frac{population\times average\ annual\ population\ growth}{100}\ [population] \tag{6}\]  
A percentage constant derived from the local statistical data represents the average annual growth. As applied by analogy, if the migration triggers the population change, it is reflected in the average year-to-year migration increase. A percentage constant from the statistical data again reflects the increment in our simplified model. The _GDP_ stock involves the initial _GDP_ value and 'inflow' levels expressed by the _GDP_ annual growth in CZK. The formula for quantified relationships between _GDP_ rates and _GDP_ growth is as follows:  
\[GDP(t_{n})=\int_{t_{0}}^{t_{n}}GDP\ growth(x)dx+GDP(t_{0})\ [CZK] \tag{7}\]  
The simplified submodel contains a percentage constant that reflects the average annual _GDP_ growth. We again rely on the statistical data over a period.