= Solution
Let $i=I/N$ be the infectious proportion in a closed population. With homogeneous frequency-dependent transmission rate $\beta$ and <recovery rate> $\gamma>0$, the <SIS model> is
$$
\boxed{\dot i=\beta i(1-i)-\gamma i.}
$$
The <basic reproduction number> is the expected number of secondary infections produced by a typical newly infected individual in an otherwise susceptible population under the specified contact conditions. Here the infectious duration has <mean> $1/\gamma$, so $R_0=\beta/\gamma$.
For $R_0>1$ the attracting <endemic equilibrium> has $i_*=1-\gamma/\beta$. The <homogeneous SIS susceptible fraction> is therefore
$$
\boxed{s_* =1-i_* =\frac1{R_0}.}
$$
For $R_0\le1$ the physical <equilibrium> is disease-free, $i_*=0$, $s_*=1$. At equality approach to zero is algebraic. Thus $s_*=1/R_0$ is an endemic relation, not a formula demanding more than one susceptible person per person below the invasion threshold.
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