# Health Care Accessibility Analysis Considering Behavioral Preferences for Hospital Choice
## 2 Method
### Combined 2 SFCA Method
#### 2.2.1 Gravity Model for Travel Time and Distance  
Based on a previous gravity model [25], two gravity models \(G_{ijt}\) and \(G_{ijs}\) for travel time and travel distance were built, as shown in Equations (1) and (2).  
\[G_{ijt}=\left\{\begin{array}{rl}0,&d_{ijt}>d_{t}\\ \frac{e^{-\frac{1}{2}\frac{d_{ijt}}{d_{t}}}-e^{-\frac{1}{2}}}{1-e^{-\frac{1}{ 2}}},&d_{ijt}\leq d_{t}\end{array}\right. \tag{1}\]  
\[G_{ijs}=\left\{\begin{array}{rl}0,&d_{ijs}>d_{s}\\ \frac{e^{-\frac{1}{2}\frac{d_{ijs}}{d_{s}}}-e^{-\frac{1}{2}}}{1-e^{-\frac{1}{ 2}}},&d_{ijs}\leq d_{s}\end{array}\right. \tag{2}\]where \(d_{ijs}\) and \(d_{ijt}\) are the traffic distance and travel time from demand point \(I\) to supply point \(j\), respectively, \(d_{s}\) and \(d_{t}\) are the distance threshold and time threshold. \(d_{s}\) and \(d_{t}\) are closely related and comparable, where \(d_{s}\) is the mileage travelled at the average traffic speed in \(d_{t}\) time. The actual urban road conditions are complex and the average traffic speed tends to be different for each road. However, because the distance threshold for Gaussian decay must be uniform, it can be expressed as the total distance travelled at the average traffic speed of the whole study area in a certain time (see penultimate paragraph of Section 3.2.3).  
On the other hand, long distance often means more uncertainty and more energy consumption. Because uncertainty in transportation is universal, there is no standard answer to time priority or distance priority, it just varies from person to person. In addition, the two options may lead to completely different choices, which is common in the real world. This uncertainty cannot be ignored since the different choices will eventually change the accessibility calculation. Therefore, this study unifies the travel time factor and the distance factor by restricting the sum of the two weights to be equal to 1.0, thus addressing the uncertainty of traffic conditions and residents' perceptions of hospitals in the accessibility calculation to some extent. The new cost decay function \(G_{ij}\) is used for the calculation of the supply-demand ratio and accessibility results.  
Since refined assessment is necessary for refined urban planning and management, explicit accessibility and potential accessibility are equally important. The former reflects the actual perception of residents, while the latter represents the theoretical value of accessibility. By estimating the weights \(W_{t}\) and \(W_{s}\), the actual medical habits can be simulated to a certain extent. Although each person's medical habits are different, once formed, they generally do not change over a long period of time. To quantify such choice habits, this study was analyzed in the form of a questionnaire that included collecting information on residents' residential addresses, frequently visited hospitals, and tolerable time. Then, based on the results of each survey, the distance and time of residents' travel to the hospital were calculated and compared with other hospitals in the neighborhood to determine whether residents prioritize time or distance for medical care. The proportion of the number of residents who chose time priority and the proportion of the number of residents who chose distance priority were used to determine the values of \(W_{t}\) and \(W_{s}\).