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Mike Henderson edited this page May 4, 2020 · 2 revisions

Notes on Model Types

This code computes SIR and SEIR models with different methods and different parameterizations, as described in the following.

Notes on the current approach to uncertainty bound calculations:

  • For each model type, SIR and SEIR, a set of input parameters are iterated across a range to create uncertainty bounds.
  • For SIR models RecoveryDays and SocialDistancing are used
  • For SEIR models RecoveryDays, SocialDistancing, and Sigma are used
  • All combinations of these are used to create a range of scenarios around the inputs:
    • RecoveryDays: from -20% to +20% of the input value in 10% increments
      • used in Gamma calculation which is used in I & R (SIR and SEIR)
    • SocialDistancing: from -.2 to +.2 of the input value in .1 increments and result in the range of 0 to 1
      • used in Beta calculation which is used in S & I (SIR) and S & E (SEIR)
    • Sigma: from -20% to +20% of the input value in 10% increments
      • used in SigmaInv calcualtion which is used in E & I (SEIR)

The output file, MODEL_FINAL, uses the column ModelType to differentiate output from each of the following setups:

  • ModelType = 'SIR with Data Step'
    • Fits a SIR model with Data Step
    • Initial values of &SocialDistancing contribute to BETA and then &ISOChangeDate used to step Beta down using &SocialDistancingChange at the specified date. Similarly, &ISOChangeDateTwo and &SocialDistancingChangeTwo are and additional step down.
    • An internal parameter, &BETA_DECAY, is used to adjust BETA each day. It is currently set to 0.
  • ModelType = 'SEIR with Data Step'
    • Fits an SEIR model with Data Step
    • Initial values of &SocialDistancing contribute to BETA and then &ISOChangeDate used to step Beta down using &SocialDistancingChange at the specified date. Similarly, &ISOChangeDateTwo and &SocialDistancingChangeTwo are and additional step down.
    • An internal parameter, &BETA_DECAY, is used to adjust BETA each day. It is currently set to 0.
  • ModelType = 'SEIR with PROC (T)Model'
    • Fits an SEIR model with PROC (T)MODEL
    • The BETA parameter incorporates different R0 parameters for each phase as defined by: before &ISOChangeDate, starting on &ISOChangeDateTwo, the period between these two
  • ModelType = 'SIR with PROC (T)MODEL'
    • Fits an SEIR model with PROC (T)MODEL
    • The BETA parameter incorporates different R0 parameters for each phase as defined by: before &ISOChangeDate, starting on &ISOChangeDateTwo, the period between these two
  • ModelType = 'SEIR with PROC (T)MODEL-Fit R0'
    • This is a prototype for using a data feed of daily case counts from a geographical region. In this prototype case it is a region of the state of Ohio in the United States.
      • The feed is stored in STORE.FIT_INPUT. You could replace the data in the file with data from your region of analysis.
    • Fits a SEIR model with PROC (T)MODEL
    • Uses input data to fit cumulative cases by day and stores the predictions in STORE.FIT_PRED as well as the parameter estimates in STORE.FIT_PARMS
    • The fitted model is used to solve the specification of the SEIR model.
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