# EpiInfer: A Non-Markovian Method and System to Forecast Infection Rates in Epidemics
## 5 Experiments with CoMix/JHU Data on COVID-19  
The experiment in this section used meeting data from CoMix [27] and health status data from the COVID-19 time-series data provided by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University [28]. Figure 3: Using simulated data from sister project EpiPolicy, 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 1 for \(p\)-values and confidence intervals. (**a**) One-day predictions with 10–50 training days. The mean RMSE is 0.042 for EpiInfer and 0.011 for ARIMA. (**b**) Five-day predictions with 10–50 training days. The mean RMSE is 0.165 for EpiInfer and 0.13 for ARIMA. (**c**) Ten-day predictions with 10–50 training days. The mean RMSE is 0.227 for EpiInfer and 0.29 for ARIMA. (**d**) Twenty-day predictions with 10–50 training days. The mean RMSE is 0.28 for EpiInfer and 0.55 for ARIMA. Figure 2: Using simulated data from the simulation engine EpiPolicy, these figures show 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 1 for \(p\)-values and the confidence interval for each forecast length. (**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. The CoMix study collected information on social contact patterns, behaviors, and attitudes during the COVID-19 pandemic across multiple European countries. People were separated into the following groups based on their daily contacts: 0 contacts, 1-5 contacts, 6-10 contacts, 11-15 contacts, 16-20 contacts, 21-50 contacts, 51-100 contacts, and 100+ contacts. The Johns Hopkins data, sourced from the JHU COVID-19 GitHub repository ([[https://github.com/CSSEGISandData/COVID-19](https://github.com/CSSEGISandData/COVID-19)]([https://github.com/CSSEGISandData/COVID-19](https://github.com/CSSEGISandData/COVID-19)), accessed on 25 November 2024), provided daily records of new confirmed cases, new recoveries, and new deaths for each country included in our analysis. To conduct our analysis, we combined the two data sources. That is, we took the meeting distribution from the CoMix contact data and infection/recovered data from the COVID-19 health status data by country and time. Because our model follows a SEIRS framework, where recovered individuals transition back to the susceptible state, we did not explicitly account for deaths in the transmission dynamics. This is justified in the case of COVID-19 because the death rate was in fact quite low. If we did model death, then we would shrink the number who transitioned from R to S by however many died. For this experiment, we used 70 data points, representing the daily number of infected individuals from Austria. Figure 4 shows a visual comparison for CoMix/JHU data predictions for 1-20 days into the future. Figure 5 shows the predictions from the two best methods ARIMA and EpiInfer. Both ARIMA and EpiInfer are more accurate than LSTM or differential equation models for all prediction horizons. Table 2 shows a summary of the results for each forecasting value between 1 and 20 days into the future. Figure 6 shows the relative RMSE for the 1-, 5-, 10-, and 20-day predictions for a given number of training days (10-50). Consistent with Table 2, the figure shows visually that EpiInfer outperforms ARIMA for 10- and 20-day predictions, while ARIMA has a lower RMSE for 1-day predictions and they are about equal for 5-day predictions.