Fig 1.
Overview of our proposed computational framework to perform spatiotemporal prediction of infectious diseases.
(a) Reported case counts are given for location and time period pairs. The proposed framework can be used for three different prediction scenarios: (b) spatial prediction, (c) temporal prediction, and (d) spatiotemporal prediction.
Fig 2.
The total numbers of infected cases reported in 81 provinces of Turkey between years 2004 and 2015.
Note that the northern and northeastern regions had strikingly high numbers of infected cases. The numbers were shown on the province centers. This map was generated using the Turkish administrative map downloaded from https://www.gadm.org and the R package maps version 3.3.0 at https://cran.r-project.org/web/packages/maps.
Fig 3.
The numbers of country-wide infected cases for each month between years 2004 and 2015.
The total numbers of infected cases for each month and each year were also reported as column and row sums, respectively. The columns were annotated by their seasonal group information at the top (yellow: cold; orange: warm; red: hot). Note that there is an annual periodicity of cases and a striking seasonal variation over infected cases.
Fig 4.
(i) temporal scenario to predict case counts of future time points on the training locations, (ii) spatial scenario to predict case counts of unseen locations at the training time points, and (iii) spatiotemporal scenario to predict case counts of unseen locations at future time points.
Table 1.
Pearson’s correlation coefficients of three algorithms on CCHF data set for three prediction scenarios together with ranks in parentheses.
Table 2.
Normalized root mean squared errors of three algorithms on CCHF data set for three prediction scenarios together with ranks in parentheses.
Fig 5.
The total observed and predicted case counts by each algorithm for years 2014 and 2015 over the five provinces with the highest case counts (i.e., endemic region) among 40 common test provinces of all scenarios.
The time periods were annotated by their seasonal group information at the bottom (yellow: cold; orange: warm; red: hot). Note that all three algorithms were able to capture the annual periodicity of CCHF cases in all scenarios, whereas the predicted case counts of GPR algorithm were closer to the observed CCHF cases.
Table 3.
Pearson’s correlation coefficients and normalized root mean squared errors of GPR algorithm on CCHF data set with changing training set size (i.e., 2, 4, 6, 8, and 10 years).
Fig 6.
Pearson’s correlation coefficients and normalized root mean squared errors of three algorithms on CCHF data set for 100 different training and test set splits of 81 provinces for spatial and spatiotemporal modeling scenarios.
GPR was compared against RFR and BRT using a two-sided paired t-test to check whether the predictive performances are significantly different, and p-value for each comparison was also reported. If the p-value is less than 0.05, it is typeset with the color of the winning algorithm.