  The partner model is an SIS epidemic in a population with random formation
and dissolution of partnerships, and with disease transmission only occuring
within partnerships. Foxall, Edwards, and van den Driessche found the critical
value and studied the subcritical and supercritical regimes. Recently Foxall
has shown that (if there are enough initial infecteds $I_0$) the extinction
time in the critical model is of order $\sqrt{N}$. Here we improve that result
by proving the convergence of $i_N(t)=I(\sqrt{N}t)/\sqrt{N}$ to a limiting
diffusion. We do this by showing that within a short time, this four
dimensional process collapses to two dimensions: the number of $SI$ and $II$
partnerships are constant multiples of the the number of infected singles. The
other variable, the total number of singles, fluctuates around its equilibrium
like an Ornstein-Uhlenbeck process of magnitude $\sqrt{N}$ on the original time
scale and averages out of the limit theorem for $i_N(t)$. As a by-product of
our proof we show that if $\tau_N$ is the extinction time of $i_N(t)$ (on the
$\sqrt{N}$ time scale) then $\tau_N$ has a limit.
