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for further information on this code and referencing to this code:

The method is submitted to WHO bulletin and online available (under review):

Forecasting hospitalization and ICU rates of the COVID-19 outbreak: an efficient SEIR model

Jan-Diederik van Wees, Sander Osinga, Martijn van der Kuip, Michael Tanck, Maurice Hanegraaf Maarten Pluymaekers, Olwijn Leeuwenburgh, Lonneke van Bijsterveldt, Logan Brunner, Jaap Zindler, Marceline Tutu van Furth

https://www.who.int/bulletin/online_first/COVID-19/en/

http://dx.doi.org/10.2471/BLT.20.256743

The program has been tested under python 3.7

the figures from the dutch model april 9 and 13 are also explained in the pdf in the root directory of github

To run a calibration and forecast:

  1. Create a .json configuration file. Several example files are provided in this repository in the configs directory china.json korea.json lombardy_mc.json netherlands_april9.json netherlands_april9_narrow.json netherlands_march14.json netherlands_march21.json netherlands_march26.json

  2. run corona_mc.py (for the loglikelyhood mode) or corona_esmda.py (for the ensemble smoother model) from the bin directory as working directory, so the settings (e.g. in pycharm should be as displayed in the figure below). After running esmda you can run confidencecurves.py to generate colored plots displaying expected mean, and confidence intervals for ICU, hospitalized cum, hospitalized and mortalities. For all a zoom close to the actual end of the observation data and a plot over the selected axis range (controlled by XMAX and YMAX)

For corona_mc.py
  script path: {your git corona dir}/bin/corona_mc.py
  parameters: {your git corona dir}../configs/netherlands_march26.json
  working directory {your git corona dir}/bin
For corona_esmda.py
  script path: {your git corona dir}/bin/corona_mc.py
  parameters: {your git corona dir}../configs/netherlands_march26.json
  working directory {your git corona dir}/bin
For confidencecurves.py
  script path: {your git corona dir}/bin/confidencecurves.py
  parameters: {your git corona dir}../configs/netherlands_march26.json
  working directory {your git corona dir}/bin

flow

  1. formats of input and meaning of parameters

China.json :

{
  "worldfile": true,   #  USE John Hopkins  repository for data
  "country": "China",  # name of country in repository or local datafile name e.g. "../res/corona_dataNL_april9.txt",
  "province": "all",  # name of "province": use all, or select no province for others, depending on what is expected
   date, "1/22/2020"  # starting data of data to be used from john hopkins repository, this day corresponds to day 1 da,
   "maxrecords": 60,  # maximum number of days for the data to take into account from the first record onward
  "t_max" : 90,       # maximum range of the model including the time_delay
  "dt" : 0.1,         # dt for ODE solver (days), default=0.1 days
  "time_delay": 17,   # time before first data (in days) where the SEIR model starts
  "population": 16e6,  # population size used to scale the results of the SEIR model
  "nr_prior_samples": 400,   # for corona_mc.py prior number of samples for MC, for ESMDA number of ensembles
  "nr_forecast_samples": 500, # for corona_mc.py only,  number of samples for MC  with alfa variation, based on best fit
  "esmda_iterations": 16,  # corona_esmda.oy  only, number of iterations for multiple data assimilation
  "N" : {                    # initial seed of exposed persons 1/N at start of the model run, here uniform distribution
        "type": "uniform",
      "min":  25000,
      "max":  250000
    },
  "sigma" : 0.2,    # sigma of SEIR model
  "gamma" : 0.5,     # gamma of SEIR model
  "R0" : {              # R0 of SEIR, here uniform distribution
    "type": "uniform",
    "min": 3.3,
    "max": 3.7
  },
  "m": 0.9,     # fraction population susceptible
  "alpha" : [[0.35,0.55], [0.7,1.0],[0.9,0.95]], # 3 alfa phases starting at dayalpha, each with uniform uncertainty range
        # in corona_mc.py these are varied without calibration starting from best fit curve to data
        # in corona_esmda.py these are fit to data
  "dayalpha" : [1, 7, 20], # days at which alfa starts
  "hosfrac" : 0.17,       # relative fraction of infected people hospitalized, default 0.05 but higher for china to
                          # to compare infected with observed

For the times to move from Removed in the SEIR model to recover or die, we used in the WHO paper very simple settings for the hospital flow, resulting in an average stay of ICU patients of 14 days. In the mean time we improved the flow parameters as depicted below. In order to be in agreement with the WHO paper, below we show settings in accordance with the average stay. The ICUdfrac has been set artificilly to 0.0 to obtain results which are very similar to the WHO paper results. Evidently the flow diagram allows realistic settings in accordance with country specific or time dependent measures

flow

  "delayHOS" : 5,          # delay between recovered and hospitalization (days)
  "delayHOSREC" : 14,      # average time for recovery of hopsitalized patients not in need for ICU
  "delayHOSD" : 3,        # average time for death of hopsitalized patients not in need for ICU
  "delayREC" : 12,         # average time for recovery of non hopsitalized patients
  "delayICUCAND": 0,     # average time for hopsitalized patients to move to ICU
  "delayICUD": 3,        # average time for ICU patients to die
  "delayICUREC": 14,       # average time for ICU patients to recover
  "dfrac" : 0.22,         # hospitalization case fatality rate
  "icudfrac" : 0.5,         # fraction of ICU patients dying
  "calibration_mode": "dead",  # calibration on "dead"
  "observation_error": 200,    # standard error for esmda in corona_esmda.py
  "YMAX": 1e6,              # y axis plotting range (population, scaled for ICU and hospitalization plots)
  "XMAX": 60,               # x axis plottting range (days)
  "ICufrac": 0.0,           # fraction of hospitalized patients in need for ICU
   "p_values": [0.05, 0.3, 0.5, 0.7, 0.95],  # P ranges for confidence data (for csv files)
  "plot" : {                       # plot settings
    "legendloc" : "best",
    "legendfont" : "x-small",
    "y_axis_log": true,
    "hindcast_plume": false        # show all prior monte carlo samples in the hindcast plot of corona_mc.py
    "xmaxalpha": 31,               # for confidencecurves.py  output
     "casename": "China"     # for confidencecurves.py  output in esdma 
  },
  "hist_time_steps": [30,35,40,50,60] # histogram days

}

In the flow of hospitalized for each delay parameter you can add a distribution. In the monte carlo samples these will be varied indvidually based on the sampled delay time. THis should be interpreted as the sample expected delay time. On top of this mean delay time varied for each sample you can add a gaussian distribution with defining a standard deviation smooth_sd (in days). The netherlands cases netherlands_april9_narrow and netherlands_april9 shoWs this. The figure below also shows how the gaussian smoothing works

flow

4 . Netherlands cases

We used the SEIR program for the Netherlands. The cases netherlands_april9.jon and cases_april9_narrow.jon reproduce the models which are described in the presentations which are also on the github. The prediction below was made april 5 suggesting the near reach of the peak of ICU use. The model was marked by relatively low uncertainty regarding future strength of social distancing
and did not incorporate yet the gaussian smoothing effects

flow

The model has been updated 4 days later, after the reaching of the peak (or plateau) has indeed been confirmed by the data. The model has been updated for new information on flow of patients and case fatality ratios. The enhanced flow scheme for hospitalized patients look according to the figure below:

flow

The updated model results is given below. This is the result from netherlands_april9, fitted to hospitalized cumulative

flow

flow

flow

5 . own input files:

In the Netherlands input file, custom data is loaded including information on hospitalization, The files should be txt file as corona_dataNL26.txt with  6 columns
    #  column 0 -  day (number starting from 1)
    #  column 1 - cumulative registered infected (postive test cases)
    #  column 2  - cum  dead
    #  column 3 - cum recovered
    #  column 4 - cumulative hospitalized
    #  column 5 - actual IC units used (may be estimated or 0)
    #  column 6 - actual hospilatized (put all to 0 to overwrite from estimates calculated from the hospital flow model)

6 . output files

corona_mc/esmda will create several plots and a datafile in csv format in the output directory.

Output file names start with the json name. corona_mc.py generates hindcast and forecast (shown in paper appendix, fig. 3) as well as ensemble plots.data corona_esmda generates prior and posterior ensembles of dead, hospitalized, etc

The csv file can be used for further post_processing, containing confidence intervals, which can be plotted with running confidencecurves.py

6 . errors If a config keyword is misspelled or missing this easily results in an error, please provide all keywords. if output writing gives an error make sure your you working directory is located at bin

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