Solution
= Solution
The cross-infection terms transfer susceptible individuals into the infected class: $\beta S\widehat I$ is male incidence caused by infected females and $\widehat\beta\widehat S I$ is female incidence caused by infected males. The terms $\nu I$ and $\widehat\nu\widehat I$ are recovery flows back to susceptibility. Adding each susceptible-infected pair shows that $N$ and $\widehat N$ are conserved.