Homogeneous SIS susceptible fraction
= Homogeneous SIS susceptible fraction
{title2=$s_*=1/R_0$}
For $\dot i=\beta i(1-i)-\gamma i$, a positive <endemic equilibrium> requires $R_0=\beta/\gamma>1$ and gives susceptible fraction $s_*=\gamma/\beta$. Below threshold the disease-free susceptible fraction is one. The reciprocal relation is a property of this homogeneous scalar <SIS model>, not a universal identity for heterogeneous populations.