Mating-limited macroparasite transmission ($\mathrm{Pr}(\text{both worm sexes})=(1-e^{-m/2}{)}^2$)

For sexually reproducing worms, an infected host need not contain both sexes. Independent random sexes split a Poisson total burden of mean $m$ into independent male and female Poisson distributions of mean $m/2$, giving the displayed probability of a fertile mixed-sex burden. For an arbitrary burden probability generating function $G$, this probability is $1-2G(1/2)+G(0)$. Its low-burden behaviour can introduce an Allee effect in transmission, so an asexual mean-burden invasion calculation is not automatically valid.