Compute infection density in a cohort of humans, $z_\tau(\alpha, a |h)$

Given a function describing the FoI ($h_\tau(a)$), and a parameter describing the clearance rate of infections ($r$), the density of parasite clones of age $\alpha$ distributed among a cohort of humans of age $a$ is $$z_\tau(\alpha, a) = e^{-r \alpha} h_\tau(a-\alpha)$$