A multistate model using Gompertz mortality but that produces a non-monotonic prevalence pattern

non-monotonic-prevalence.R

gompmx <- function(a,b,x){
  a * exp(b*x)
}

a1 <- .0002
a2 <- .0001
b1 <- .06
b2 <- .1
x  <- 0:110

# convert to qx
hd <- DemoTools::lt_id_ma_q(gompmx(a1,b1,x),rep(.5,111),AgeInt = rep(1,111))
ud <- DemoTools::lt_id_ma_q(gompmx(a2,b2,x),rep(.5,111),AgeInt = rep(1,111))
# make a linear
hu <- seq(.1,.3,length=111) * (1-hd)

hh <- 1 - hd - hu
uu <- 1 - ud
uh <- rep(0,111)

lu <- rep(0,112)
lh <- rep(0,112)
lh[1] <- 1
n  <- 111
for (i in 1:n) {
  lu[i + 1] <- lu[i] * uu[i] + lh[i] * hu[i]
  lh[i + 1] <- lh[i] * hh[i] + lu[i] * uh[i]
}
lx  <- lu+lh
pix <- lh / lx

plot(pix, main = paste("LE =",round(sum(lx),2),"\nHLE =", round(sum(lh),2)))