Hist-D

This repository (Reproduce_Results) provides simulation data to reproduce the results shown in Figure3.

0. Set the Reproduce_Results as the working directory.
1. Inference in original simulation data (Fig. 3c ~ 3e).
   a. Run Figure3_cde.R file.
2. Inference in simulation data with measurement errors (Fig. 3f ~ 3h).
   a. Run Figure3_fg.R and Figure3_h.R file.
3. Inference in simulation data when transmission rate changes (Fig. 3i ~ 3k).
   a. Run Figure3_ijk.R file.

Packages to load

• rstan: For constructing credible intervals of the estimates using the MCMC method.
• coda: For convergence diagnostics of the MCMC chains.
• ggplot2: For plotting the results.

Main functions

• HistD_estimation(): Function to estimate the initial condition using the Hist-D method (See detailed options in supporting information). This function returns the estimated initial condition projected for the specified date.
• HistD_stan(): Function to calculate the credible interval of the estimate using the MCMC method (See detailed options in supporting information). These results contain 50%, 75%, 95% credible interval of the initial condition and R hat for convergence diagnostics of the MCMC chains.

Simulation Data

You can construct the simulation SEIR data by delay differential equations (DDE) using the mean_trajectory_SEIR_original() function in the "SEIR_function.R" file.

Column Descriptions

• day: Time point (date format) of the data (corresponding to 'Time (days)' in Fig. 3c–e).
• f_S->E: Number of daily exposed individuals (shown in Fig. 3a).
• f_E->I: Number of daily infectious individuals.
• E: True value of E (as shown in Fig. 3c).