n be reconstructed by a suitable integration over all the resulting frequency components. The frequency bands or subspaces (sub-bands) are scaled versions of a subspace at scale. Therefore, the following conclusions can be drawn from the above wavelet transform:
1) The whole surge of patients admitted was decomposed into one original (or mother) wavelet and 5 small wavelets.
2) Because 5 years is 1826 days, the Haar wavelet time period is derived from 2^n (n = 1, 2, 3, 4, 5) days. The largest wavelet is about 32 days of the time period, which is almost one month.
3) The corresponding Mother wavelet should be the overall trend of hospital admissions, so that as time goes on, admissions increase.
4) The 5th wavelet corresponds to admissions in days, which is almost a normal distribution (Figure 2).
Figure 2. Wavelet transformation of hospitalized patient number. Wavelet analysis was performed on raw data representing the fluctuation.
3.2. Time and Space Distribution and Its Influencing Factors
Using kernel density estimation, As the distance from the patient to the hospital gradually increased, the number of patients decreased exponentially, Using the Matlab®, CF tool toolbox, fit distance of patient from the hospital with the number of patients within these distance, we get the typical fitting formula as follows:
where f(x) is the patients number, and x is the distance to West China Hospital, the correlation coefficient (R^2) is 0.875 (Figure 3). Thus, hospitalized patients will gradually decrease with distance. Using wavelet transform, we obtained the wavelet scale for patients with the distribution fitting, from Haar wavelet from 1 - 5. The smallest scale wavelet (wavelet 5) can be considered as a random white noise, and there is no clear trend for the distribution of patient space in this scale. And with the scale, the third wavelets, second wavelets, it can be viewed as the monthly and seasonal distribution. Therefore, the month and season can be used as a larger distribution cycle to test the source of the patient’s space distribution in Chengdu, in Sichuan, or in China (Figure 2).
3.3. Forecast for Patient Number
The ARIMA the forecast model suggests 3500 - 4700 patients per month, it will be described as follows (Figure 4 and Table 1). And under the short-term modulation of patient’s number, wave 3 represents seasonal patterns of patient surges, so we used seasonal ARIMA models (SAM) to represent patients trend changes  . These data appear in Table 2.
3.4. Effect of Seasonal Rotation to Diseases and the Prediction Model
Classical ARIMA models are typically well-suited for short-term forecasts, but not for longer term forecasts due to the convergence of the autoregressive com-
Figure 3. With the increase in the distance of the patient’s residence, the number of patients gradually reduced.
Figure 4. The fluctuation of patient number from Mar. 2014 to Dec. 2016 and the curve with shadow is on behalf of the forecast of volatility of patient number in future fitted by ARIMA and seasonal ARIMA.
Table 1. The results of the fitting.
Table 2. ARIMA forecast result.
ponent of the model to the mean of the time series. However, as mentioned above, the use of too short a time cycle causes random fluctuations. Therefore, the selection of a reasonable statistical cycle for correct statistical conclusions is essential.
However, according to the multi-scale theory, one random process under the one view can change the organized characteristic in other scales and show corresponding laws. So, tools are needed to observe the time series in different scales. Wavelet analysis is suitable for efficiency in time   , or frequency (as harmonic, Shannon, Meyer)   domain. In the time distribution, and the present random fluctuations inpatient admissions, using wavelet decomposition, patients with fluctuations in different scales have different rules. We calculate the correlation between GDP and the number of patients by at a specific point in time, the formula is:
where Xi represents the number of patients in the i-th period, Yi represents the GDP announced by the Chinese government at the end of the i-th period
From the scale of the mother wave, growth in admissions increased over time in the manner of an accelerating index increase. This increase was closely related to China’s GDP growth (Figure 5). (R = 0.8826). ARIMA model can be used to predict future admissions. From 2nd and 3rd scale, the two scale can reflect the number of patients on the monthly and quarterly changes, which is true for pediatrics. In autumn, patient admissions will decrease because of the school season. Seasonal ARIMA models suggest that outpatients since the end of 2014 declined (Figure 4), suggesting that the classification system of the hospital may contribute to the patient count. However, this cannot be modeled with a classical linear ARIMA fitting. With the ARIMA model the existing classification system of hospital patient decline due to seasonal and monthly differences did not have big fluctuations, and in 2017 the rebound was greater after October. This rebound needs attention (Figure 4).
3.5. The Spatial Distribution of Patients and Its Influencing Factors
Segmentation fitting shows that the number of hospitalized patients will decrease exponentially with distance from the hospital, and these data agree with Wang’s group  . Specific to the urban area of Chengdu, after the implementation of hierarchical treatment in 2015, patients in the urban distribution changed significantly. Patients decreased with increasing distance from the hos-
Figure 5. The patient number will increase with the GDP growth.
pital, and this decrease was exponentially distributed. The relationship with time is clear, too, and it indicates that patients from outer suburbs to the hospital primarily by time constraints. Elective patients will generally avoid peak enrollment in September. Spatial density analysis showed that after the implementation of hierarchical diagnosis and treatment, distribution patient patterns change. In September 2015, hospitalized patient distribution is more concentrated than that from September 2014, indicating that the change in spatial distribution of the diagnosis and treatment system has been identified by the KDE (kernel density estimation) algorithm (Figure 6).
Multi-scale phenomena can be found in numerous natural events that occur over long time periods and within wide spaces. Multi-scale effects can be analysed using multi-scale effects for complex fluctuations caused by complex factors. As can be seen from our study, the number of growing patients presents some seasonal cyclical fluctuations and shows a trend of gradually increase. This spatial and temporal fluctuation poses a double challenge to the allocation of medical resources. In order to cope with this dual challenge, it is advisable to increase the supply of medical care in the surrounding area during the busy season, where most patients with mild symptoms are able to seek medical attention nearby. In the winter and summer school vacation, hospital should increase the supply of elective outpatient clinics.
Multi-scale phenomena can be realized with mathematical microscope-wave- let analysis. Through wavelet analysis and other predictive methods such as ARIMA, we analyse the time and spatial distribution of patients in a Chinese hospital over a five-year period. Data show that even a patient address can be useful information. The idea of data mining based on spectral analysis and spatial distribution can be extended to many aspects of social management such as education resource assessment, medical resources distribution assessment and future social resources planning.
Figure 6. The spatial distribution of patient in downtown of Chengdu in 2014 and 2015.
This project was supported by the funds of Strategic Innovation Funding of Science and Technology of SiChuan University. (No. 20160040321).
Cite this paper
Lei, S.D. (2017) Predict the Future Hospitalized Patients Number Based on Patient’s Temporal and Spatial Fluctuations Using a Hybrid ARIMA and Wavelet Transform Model. Journal of Geographic Information System, 9, 456-465. https://doi.org/10.4236/jgis.2017.94028