```
#' @export
viral_update_cd4_simple_diff_eqn <- function(dat,at)
{
# Description:
# Uses a difference equation to determine CD4 counts
# CD4 counts drop as the square root of log VL
#
# Inputs:
# dat$pop: V
# dat$param: CD4count_end_stage
# Outputs:
# dat$pop: CD4count, CD4, RandomTimeToAIDS, CD4_time_death
#
# ** The following constants have been hard-coded into the function for the moment **
# - Rate at which CD4 declines with log VL (hard-coded to be 0.045)
# - Minimal VL below which CD4 stops declining (hard-coded to be 1.0)
#
# ** This version is NOT designed to work with treatment **
# Define population with VL greater than a pre-specified mininum (1.) for CD4 killing
# Added b/c logV will be negative for VL's < 1 ==> VL-induced increases in CD4's!
# Fortunately, a VL < 1 is so low that we hardly have to worry about time to death anyway
inf_min_vl <- which(dat$pop$V > 1.0 & dat$pop$Status ==1)
# Virological killing of CD4 T-cells (for agents with a VL greater than the minimum for CD4 killing)
# PPP is a multiplier (default = 1) that allows some viral genotypes to kill their hosts faster than expected from the VL.
dat$pop$CD4count[inf_min_vl] <- dat$pop$CD4count[inf_min_vl] - 0.045*dat$pop$PPP[inf_min_vl]*log10(dat$pop$V[inf_min_vl])
# Dissallow zero or negative numbers for CD4count (possible due to roundoff errors)
dat$pop$CD4count[which(dat$pop$CD4count <= 0.0)] = 0.1
# Derive categorical equivalents for compability with other evonet functions
oldCD4 <- dat$pop$CD4
dat$pop$CD4[which(dat$pop$CD4count >= 500)] = 1
dat$pop$CD4[which(dat$pop$CD4count >= 350 & dat$pop$CD4count < 500)] = 2
dat$pop$CD4[which(dat$pop$CD4count >= 200 & dat$pop$CD4count < 350)] = 3
dat$pop$CD4[which(dat$pop$CD4count >= dat$param$CD4count_end_stage & dat$pop$CD4count < 200)] = 4
dat$pop$CD4[which(dat$pop$CD4count < dat$param$CD4count_end_stage)] = 5
# Record times that patients progress to AIDS (for use in other routines)
new_aids_index <- which(dat$pop$CD4==4 & oldCD4 != 4)
dat$pop$RandomTimeToAIDS[new_aids_index] <- at
# Record times that patients progress to end-stage AIDS (for use in other routines)
cd4_dead_final_index <- which(dat$pop$CD4==5 & oldCD4 !=5)
dat$pop$CD4_time_death[cd4_dead_final_index] <- at
if (at == 700) {
cat("Toggling breakpoint here \n")
}
return(dat)
}
```

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