# EpiInfer: A Non-Markovian Method and System to Forecast Infection Rates in Epidemics
## 5 Experiments with CoMix/JHU Data on COVID-19
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Days Predicted** & **DiffEq** & **LSTM** & **ARIMA** & **EpiInfer** & \(p\)**-Value EpiInfer vs. ARIMA** & **Confidence Interval** \\ \hline
1 & 0.76267 & 0.10798 & 0.03950 & 0.0892 & \(<\)10\({}^{-5}\) & (\(-\)0.07\(\ldots\)0.03) \\ \hline
2 & 1.18928 & 0.19909 & 0.07349 & 0.1501 & 0.0001 & (\(-\)0.11\(\ldots\)0.05) \\ \hline
3 & 1.74547 & 0.27690 & 0.11782 & 0.188 & 0.0028 & (\(-\)0.11\(\ldots\)0.03) \\ \hline
4 & 2.46983 & 0.34464 & 0.16704 & 0.2064 & 0.1145 & NA \\ \hline
5 & 3.43477 & 0.40345 & 0.21813 & 0.2233 & 0.4402 & NA \\ \hline
6 & 4.73146 & 0.45760 & 0.26570 & 0.243 & 0.3 & NA \\ \hline
7 & 6.46551 & 0.50773 & 0.31143 & 0.2632 & 0.1364 & NA \\ \hline
8 & 8.80375 & 0.55734 & 0.35559 & 0.2673 & 0.0335 & (0.01\(\ldots\)0.17) \\ \hline
9 & 11.96590 & 0.6056 & 0.40478 & 0.2681 & 0.0048 & (0.05\(\ldots\)0.22) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Root Mean Squared Error (RMSE) results for CoMix/JHU data predictions from 1-20 days into the future. For a prediction value of \(t\) 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 and ARIMA are the best two methods, with ARIMA better for short-term predictions (5 days or fewer) and EpiInfer better afterwards. The \(p\)-values of the difference are under 0.05 for up to 3 days in the case when ARIMA is better and starting at predictions 8 days in the future when EpiInfer is better. Figure 4 shows the RMSE of ARIMA vs. EpiInfer for each forecasting value between 1 and 20. As for the simulated data, we show confidence intervals of the difference in the RMSE only when the \(p\)-value is under 0.05. Figure 4: Visual comparison for CoMix/JHU data predictions for 1–20 days into the future. ARIMA and EpiInfer are better than (lower Root Mean Squared Error than) LSTM and Differential Equation models regardless of the forecast horizon. ARIMA beats EpiInfer for short-term predictions of five days or less. EpiInfer beats all other methods beyond five days. Figure 5: _Cont._  
Figure 5: Using CoMix/JHU data, these are the predictions from the two best methods ARIMA and EpiInfer. EpiInfer has a lower mean relative RMSE than ARIMA for 10- and 20-day predictions, while showing similar performance for 5-day predictions. Please see Table 2 for \(p\)-values and confidence intervals. **(a)** One-day predictions with 10-50 training days. **(b)** Five-day predictions with 10-50 training days. **(c)** Ten-day predictions with 10-50 training days. **(d)** Twenty-day predictions with 10-50 training days. Figure 6: Using CoMix/JHU data, these are the relative RMSE (Root Mean Squared Error) data from the two best methods ARIMA and EpiInfer. EpiInfer has a lower mean relative RMSE than ARIMA for 10- and 20-day predictions, while showing similar performance for 5-day predictions. Please see Table 2 for \(p\)-values. **(a)** One-day predictions with 10-50 training days. The mean RMSE is 0.089 for EpiInfer and 0.04 for ARIMA. **(b)** Five-day predictions with 10-50 training days. The mean RMSE is 0.22 for EpiInfer and 0.22 for ARIMA. **(c)** Ten-day predictions with 10-50 training days. The mean RMSE is 0.266 for EpiInfer and 0.46 for ARIMA. **(d)** Twenty-day predictions with 10-50 training days. The mean RMSE is 0.335 for EpiInfer and 1.29 for ARIMA.