Matching PfPR2-10 to EIR

library(malariasimulation)
library(mgcv)

Begin by parameterizing the model you wish to run. Be sure to include any seasonality factors and interventions you want to include at baseline.

year <- 365
human_population <- 5000

params <- get_parameters(list(
  human_population = human_population,
  average_age = 8453.323,     # to match flat_demog
  model_seasonality = TRUE,   # assign seasonality
  g0 = 0.284596,                              
  g = c(-0.317878, -0.0017527, 0.116455),     
  h = c(-0.331361, 0.293128, -0.0617547),     
  prevalence_rendering_min_ages = 2 * year,    # set prev age range
  prevalence_rendering_max_ages = 10 * year,
  individual_mosquitoes = FALSE))

  # set species / drugs / treatment parameters
params <- set_species(params, species = list(arab_params, fun_params, gamb_params), 
                      proportions = c(0.25, 0.25, 0.5))
params <- set_drugs(params, list(AL_params))
params <- set_clinical_treatment(params, 1, c(1), c(0.45))

Now run malariasimulation over a range of EIRs. The goal is to run enough points to generate a curve to which you can match PfPR2-10 to EIR effectively.

# loop over malariasimulation runs
init_EIR <- c(0.01, 0.1, 1, 5, 10, 25, 50) # set EIR values

# run model
outputs <- lapply(
  init_EIR,
  function(init) {
    p_i <- set_equilibrium(params, init)
    run_simulation(5 * year, p_i) # sim time = 5 years
  }
)

# output EIR values
EIR <- lapply(
  outputs,
  function(output) {
    mean(
      rowSums(
        output[
          output$timestep %in% seq(4 * 365, 5 * 365), # just use data from the last year
          grepl('EIR_', names(output))
        ] / human_population * year
      )
    )
  }
)

# output prev 2-10 values
prev <- lapply(
  outputs,
  function(output) {
    mean(
      output[
        output$timestep %in% seq(4 * 365, 5 * 365),
        'n_detect_730_3650'
      ] / output[
        output$timestep %in% seq(4 * 365, 5 * 365),
        'n_730_3650'
      ]
    )
  }
)

# create dataframe of initial EIR, output EIR, and prev 2-10 results
EIR_prev <- cbind.data.frame(init_EIR, output_EIR = unlist(EIR), prev = unlist(prev))

Now plot your results! Code is included to compare the results of matching PfPR2-10 to EIR based on malariaEquilibrium (blue line) versus matching based on parameterized malariasimulation runs (red line). Notice that the generated points do not form a smooth curve. We ran malariasimulation using a population of just 5,000. Increasing the population to 10,000 or even 100,000 will generate more accurate estimates, but will take longer to run.

# calculate EIR / prev 2-10 relationship from malariaEquilibrium
eir <- seq(from = 0.1, to = 50, by=.5)
eq_params <- malariaEquilibrium::load_parameter_set("Jamie_parameters.rds")

prev <- vapply( # calculate prevalence between 2:10 for a bunch of EIRs
  eir,
  function(eir) {
    eq <- malariaEquilibrium::human_equilibrium(
      eir,
      ft=0,
      p=eq_params,
      age=0:100
    )
    sum(eq$states[2:10, 'pos_M']) / sum(eq$states[2:10, 'prop'])
  },
  numeric(1)
)

prevmatch <- cbind.data.frame(eir, prev)

# calculate best fit line through malariasimulation data
fit <- predict(gam(prev~s(init_EIR, k=5), data=EIR_prev), 
               newdata = data.frame(init_EIR=c(0,seq(0.1,50,0.1))),  type="response")
fit <- cbind(fit, data.frame(init_EIR=c(0,seq(0.1,50,0.1))))

# plot
plot(x=1, type = "n", 
     frame = F, 
     xlab = "initial EIR", 
     ylab = expression(paste(italic(Pf),"PR"[2-10])),
     xlim = c(0,50), 
     ylim = c(0,.7))

points(x=EIR_prev$init_EIR, 
       y=EIR_prev$prev,
       pch = 19,
       col = 'black')

lines(x=fit$init_EIR, 
      y=fit$fit, 
      col = "red", 
      type = "l", 
      lty = 1)

lines(x=prevmatch$eir, 
      y=prevmatch$prev, 
      col = "blue", 
      type = "l", 
      lty = 1)

legend("bottomright", legend=c("malariasimulation", "malariaEquilibrium"), col=c("red", "blue"), lty = c(1,1), cex=0.8)

Now extract values from the fitted line to generate EIR estimates at your desired PfPR2-10 values.

# Pre-intervention baseline PfPR2-10 starting at values 10, 25, 35, 55 
PfPR <- c(.10, .25, .35, .45)

# match via stat_smooth predictions
match <- function(x){
  
  m <- which.min(abs(fit$fit-x)) # index of closest prev match
  fit[m,2]                       # print match
  
}

eir <- unlist(lapply(PfPR, match))

cbind.data.frame(PfPR, eir)
#>   PfPR  eir
#> 1 0.10  2.3
#> 2 0.25  7.9
#> 3 0.35 18.6
#> 4 0.45 40.5