Parameter Variation

This vignette describes how variation in estimated model parameters can be incorporated into model simulations.

Estimating variation in parameters

The malariasimulation transmission model was fit utilizing a Bayesian framework, which produced a posterior distribution of parameter sets. Default parameters for the model were taken as the median across 50 random sets of parameter draws.

## plot parasite prevalence with default model parameters
simparams <- get_parameters(list(
  human_population = 100,
  individual_mosquitoes = FALSE
))

# Default (median) model parameters
sim <- run_simulation(timesteps = 1000, simparams)

# plot the default median parameter
plot(
  sim$timestep,
  sim$n_detect_lm_730_3650 / sim$n_age_730_3650,
  t = "l",
  ylim = c(0, 1),
  ylab = "PfPr",
  xlab = "Time in days",
  xaxs = "i", yaxs = "i",
  lwd = 2, main = 'Parasite prevalence over time with default model parameters',
  cex.main = 0.9)
grid(lty = 2, col = "grey80", lwd = 0.5)

If needed, we can produce stochastic model outputs incorporating variation in model parameters. This is done with the set_parameter_draw function, which pulls parameter draws from this joint posterior of Markov chain Monte Carlo (MCMC) fitting. This function overrides the default model parameters with a sample from one of 1000 draws from the joint posterior.

Keep in mind that set_parameter_draw must be called prior to set_equilibrium, as the baseline transmission intensity must be calibrated to new model parameters.

## run simulation on different samples of the joint posterior distribution
# plot the default median parameter
plot(
  sim$timestep[1:500],
  sim$n_detect_lm_730_3650[1:500] / sim$n_age_730_3650[1:500],
  t = "l",
  ylim = c(0, 1),
  ylab = "PfPr",
  xlab = "Time in days",
  xaxs = "i", yaxs = "i",
  main = 'Parasite prevalence over time for 8 sets of parameter draws',
  cex.main = 0.9
)
grid(lty = 2, col = "grey80", lwd = 0.5)

for (i in 1:7) {
  param_draw <- simparams |>
    set_parameter_draw(sample(1:1000, 1)) |>
    set_equilibrium(init_EIR = 5)
  
  sim <- run_simulation(timesteps = 500, param_draw)
  
  lines(sim$timestep, sim$n_detect_lm_730_3650 / sim$n_age_730_3650, col = cols[i])
}

For more information on uncertainty in parameters, please refer to The US President’s Malaria Initiative, Plasmodium falciparum transmission and mortality: A modelling study, Supplemental material, Section 4.

- Estimating variation in parameters