Fitting a SIR-type model to flu data

Fitting fitting mortality data from the 1918 influenza pandemic to an SIR-type model to estimate R0. For the data, see 'flu1918data'.

simulate_flu_fit(
  S = 5e+06,
  I = 1,
  D = 0,
  b = 1e-06,
  blow = 1e-08,
  bhigh = 1e-04,
  g = 1,
  glow = 0.01,
  ghigh = 100,
  f = 0.01,
  flow = 1e-04,
  fhigh = 1,
  usesimdata = 0,
  bsim = 1e-06,
  gsim = 1,
  fsim = 0.01,
  noise = 0,
  iter = 1,
  solvertype = 1,
  logfit = 0,
  rngseed = 100
)

Arguments

S

: starting value for Susceptible : numeric

I

: starting value for Infected : numeric

D

: starting value for Dead : numeric

b

: infection rate : numeric

blow

: lower bound for infection rate : numeric

bhigh

: upper bound for infection rate : numeric

g

: recovery rate : numeric

glow

: lower bound for g : numeric

ghigh

: upper bound for g : numeric

f

: fraction dying : numeric

flow

: lower bound for f : numeric

fhigh

: upper bound for f : numeric

usesimdata

: set to 1 if simulated data should be fitted, 0 otherwise : numeric

bsim

: infection rate for simulated data : numeric

gsim

: recovery rate for simulated data : numeric

fsim

: fraction dying for simulated data : numeric

noise

: noise to be added to simulated data : numeric

iter

: max number of steps to be taken by optimizer : numeric

solvertype

: the type of solver/optimizer to use (1-3) : numeric

logfit

: set to 1 if the log of the data should be fitted, 0 otherwise : numeric

rngseed

: random number seed for reproducibility : numeric

Value

The function returns a list containing as elements the best fit time series data frame, the best fit parameters, the data and the final SSR

Details

A simple compartmental ODE model is fitted to data. The model includes susceptible, infected, and dead compartments. The two processes that are modeled are infection and recovery. A fraction of recovered can die. Data can either be real or created by running the model with known parameters and using the simulated data to determine if the model parameters can be identified. The fitting is done using solvers/optimizers from the nloptr package (which is a wrapper for the nlopt library). The package provides access to a large number of solvers. Here, we only implement 3 solvers, namely 1 = NLOPT_LN_COBYLA, 2 = NLOPT_LN_NELDERMEAD, 3 = NLOPT_LN_SBPLX For details on what those optimizers are and how they work, see the nlopt/nloptr documentation.

Warning

This function does not perform any error checking. So if you try to do something nonsensical (e.g. specify negative parameter or starting values, the code will likely abort with an error message.

See also

See the Shiny app documentation corresponding to this function for more details on this model.

Author

Andreas Handel

Examples

# To run the code with default parameters just call the function:
if (FALSE) result <- simulate_flu_fit()
# To apply different settings, provide them to the simulator function, like such:
result <- simulate_flu_fit(iter = 5, logfit = 1, solvertype = 2, usesimdata = 1)