Simulation to illustrate uncertainty and sensitivity analysis

This function performs uncertainty and sensitivity analysis using the simple, continuous-time basic bacteria model.

simulate_usanalysis(
  Bmin = 100,
  Bmax = 200,
  Imin = 1,
  Imax = 2,
  Bmaxmin = 1e+05,
  Bmaxmax = 2e+05,
  dBmin = 0.5,
  dBmax = 1,
  kmin = 1e-04,
  kmax = 2e-04,
  rmin = 1e-04,
  rmax = 2e-04,
  dImin = 1,
  dImax = 2,
  gmean = 2,
  gvar = 0.5,
  samples = 10,
  rngseed = 100,
  tstart = 0,
  tfinal = 300,
  dt = 0.5
)

Arguments

Bmin

: lower bound for initial bacteria numbers : numeric

Bmax

: upper bound for initial bacteria numbers : numeric

Imin

: lower bound for initial immune response : numeric

Imax

: upper bound for initial immune response : numeric

Bmaxmin

: lower bound for maximum bacteria load : numeric

Bmaxmax

: upper bound for maximum bacteria load : numeric

dBmin

: lower bound for bacteria death rate : numeric

dBmax

: upper bound for bacteria death rate : numeric

kmin

: lower bound for immune response kill rate : numeric

kmax

: upper bound for immune response kill rate : numeric

rmin

: lower bound for immune response growth rate : numeric

rmax

: upper bound for immune response growth rate : numeric

dImin

: lower bound for immune response death rate : numeric

dImax

: upper bound for immune response death rate : numeric

gmean

: mean for bacteria growth rate : numeric

gvar

: variance for bacteria growth rate : numeric

samples

: number of LHS samples to run : numeric

rngseed

: seed for random number generator : numeric

tstart

: Start time of simulation : numeric

tfinal

: Final time of simulation : numeric

dt

: times for which result is returned : numeric

Value

The function returns the output as a list. The list element 'dat' contains a data frame. The simulation returns for each parameter sample the peak and final value for B and I. Also returned are all parameter values as individual columns and an indicator stating if steady state was reached. A final variable 'steady' is returned for each simulation. It is TRUE if the simulation did reach steady state, otherwise FALSE.

Details

A simple 2 compartment ODE model (the simple bacteria model introduced in the app of that name) is simulated for different parameter values. The user provides ranges for the initial conditions and parameter values and the number of samples. The function does Latin Hypercube Sampling (LHS) of the parameters and runs the basic bacteria ODE model for each sample. Distribution for all parameters is assumed to be uniform between the min and max values. The only exception is the bacteria growth parameter, which is assumed to be gamma distributed with the specified mean and variance. This code is part of the DSAIRM R package. For additional model details, see the corresponding app in the DSAIRM package.

Warning

This function does not perform any error checking. So if you try to do something nonsensical (e.g. specify negative parameter values or fractions > 1), the code will likely abort with an error message.

See also

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

Author

Andreas Handel

Examples

# To run the simulation with default parameters just call the function:
if (FALSE) result <- simulate_usanalysis()
# To choose parameter values other than the standard one, specify them, like such:
result <- simulate_usanalysis(dImin = 0.1, dImax = 10, samples = 5, tfinal = 50)
# You should then use the simulation result returned from the function, like this:
plot(result$dat[,"dI"],result$dat[,"Bpeak"],xlab='values for d',ylab='Peak Bacteria',type='l')