initial(S) <- N - I0
initial(E) <- 0
initial(I) <- I0
initial(R) <- 0
I0 <- 1
Births <- b * N
b <- 1 / 10
N <- 1e7
beta <- 10
sigma <- 1 / 3
delta <- 1 / 21
lat_hum <- 14
## people developing latent infection
new_inf <- beta * S * I / N
## i.e. proportion of humans surviving the latent period
surv <- exp(-b * lat_hum)
## people that become latent 'lath_um' days ago, less those that died
## during that time
lag_inf <- delay(new_inf * surv, lat_hum)
deriv(S) <- Births - b * S - new_inf + delta * R
deriv(E) <- new_inf - lag_inf - b * E
deriv(I) <- lag_inf - (b + sigma) * I
deriv(R) <- sigma * I - b * R - delta * R
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