= Susceptible-weighted next-generation matrix
{title2=$\rho(\operatorname{diag}(s_*)K)=1$}
For a heterogeneous <SIS model> with common <recovery rate> and a positive <endemic equilibrium> $I_*$, force balance gives $\operatorname{diag}(s_*)KI_*=I_*$. When the transmission <matrix> is irreducible and nonnegative, the positive <equilibrium> vector and the <Perron–Frobenius theorem> imply the displayed <spectral radius> identity. It replaces the homogeneous scalar relation $s_*=1/R_0$: different recipient types generally have different susceptible fractions.
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