# EpiInfer: A Non-Markovian Method and System to Forecast Infection Rates in Epidemics
## 9 Multiple Locales
### Multilocale Experiment with EpiPolicy Data  
This experiment tests whether making use of data from multiple locales can lead to better results than using data from just a single locale. Figure 11 shows the comparison of three approaches--single locale, similar locales (having similar meeting distributions), and locales having different meeting distributions--for 1- to 20-day predictions. Because using locales having different meeting distributions leads to worse results on average thanusing similar locales, all our subsequent comparisons will be between using similar locales (which we will call EpiInfer-multi) and EpiInfer on a single locale. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Days Predicted** & **DiffEq** & **LSTM** & **ARIMA** & **EpiInfer** & **EpiInfer Multi-Locale** & \
\begin{tabular}{c} \(p\)**-Value EpiInfer-Multi** \\ **vs. ARIMA** \\ \end{tabular} &
\begin{tabular}{c} \(p\)**-Value EpiInfer-Multi** \\ **vs. EpInfer** \\ \end{tabular} \\ \hline
1 & 0.33277 & 0.09573 & 0.01070 & 0.04196 & 0.0273 & 0.0018 (-0.03.—0.01) & 0.029 (0..0.3) \\ \hline
2 & 0.63757 & 0.18064 & 0.03437 & 0.06985 & 0.0373 & 0.3675 & 0.0011 (0.01..0.05) \\ \hline
3 & 1.09561 & 0.24920 & 0.06351 & 0.10496 & 0.0463 & 0.1057 & \(<\)10\({}^{-5}\) (0.03..0.08) \\ \hline
4 & 1.66645 & 0.30655 & 0.09570 & 0.13063 & 0.0555 & 0.0062 (0.01..0.07) & 0.0004 (0.04.01.11) \\ \hline
5 & 2.20159 & 0.35327 & 0.12914 & 0.16496 & 0.0639 & 0.0006 (0.03..0.10) & \(<\)10\({}^{-5}\) (0.06..0.14) \\ \hline
6 & 2.50284 & 0.39124 & 0.16296 & 0.19230 & 0.0766 & \(<\)10\({}^{-5}\) (0.05..0.13) & \(<\)10\({}^{-5}\) (0.07..0.16) \\ \hline
7 & 2.50845 & 0.42264 & 0.19636 & 0.21148 & 0.0912 & \(<\)10\({}^{-5}\) (0.06..0.15) & \(<\)10\({}^{-5}\) (0.07..0.17) \\ \hline
8 & 2.34101 & 0.44845 & 0.22872 & 0.21356 & 0.1026 & 0.0001 (0.08..0.17) & 0.0003 (0.06..0.16) \\ \hline
9 & 2.12217 & 0.46871 & 0.26021 & 0.21829 & 0.1143 & \(<\)10\({}^{-5}\) (0.09..0.2) & 0.0008 (0.05..0.16) \\ \hline
10 & 1.91056 & 0.48642 & 0.29065 & 0.22700 & 0.1261 & \(<\)10\({}^{-5}\) (0.11..0.22) & 0.0038 (0.05..0.16) \\ \hline
11 & 1.73462 & 0.50015 & 0.31965 & 0.23986 & 0.1383 & \(<\)10\({}^{-5}\) (0.12..0.24) & 0.0033 (0.04..0.16) \\ \hline
12 & 1.57637 & 0.51113 & 0.34811 & 0.25326 & 0.1509 & \(<\)10\({}^{-5}\) (0.14..0.26) & 0.004 (0.04..0.17) \\ \hline
13 & 1.43706 & 0.52018 & 0.37555 & 0.26602 & 0.1651 & \(<\)10\({}^{-5}\) (0.15..0.28) & 0.0055 (0.04..0.17) \\ \hline
14 & 1.31618 & 0.52729 & 0.40174 & 0.26977 & 0.1761 & \(<\)10\({}^{-5}\) (0.16..0.29) & 0.0159 (0.03..0.16) \\ \hline
15 & 1.21238 & 0.53306 & 0.42775 & 0.28016 & 0.1839 & \(<\)10\({}^{-5}\) (0.17..0.31) & 0.0159 (0.03..0.17) \\ \hline
16 & 1.12391 & 0.53706 & 0.45325 & 0.28652 & 0.1978 & \(<\)10\({}^{-5}\) (0.18..0.33) & 0.0219 (0.02..0.16) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: \(p\)**-Value of comparison of EpiInfer-multi vs single locale EpiInfer**. Root Mean Squared Error (RMSE) results for EpiPolicy data predictions from 1–20 days into the future. For a prediction value of \(f\) days in the future, the methods use the data from day \(d\) and possibly previous days to predict day \(d+f\). The results show that EpiInfer-multi (over multiple locales having a similar meeting distribution) and ARIMA are the best two methods, with ARIMA better for 1-day predictions and EpiInfer-multi is about equal to ARIMA for two days and then better for all longer forecasting horizons. The \(p\)-values of the difference are under 0.05 for up to 1 day in the case when ARIMA is better and starting at predictions 4 days in the future when EpiInfer-multi has a lower RMSE. Figure 11: Using simulated data from EpiPolicy, these are the relative Root Mean Squared Error (see definition in the text) data from EpiInfer when using one, similar (in meeting distribution) and different locales. EpiInfer using similar locales (EpiInfer-multi) shows the best overall performance. Please see Table 4 for \(p\)-values of the comparison between one and similar locales.