= Next-generation matrix
{title2=$K=FV^{-1},\quad R_0=\rho(K)$}
The entry $K_{ij}$ is the expected number of newly infected type-$i$ individuals produced by a newly infected type-$j$ individual while the population is disease-free. In a compartmental <linearization>, $F$ describes new-infection production and $V$ transitions and removal. Provided the infection-lifetime subsystem is transient, its integrated occupation <matrix> is $V^{-1}$, yielding $K=FV^{-1}$. The <basic reproduction number> is its <spectral radius>. This construction is described in https://pubmed.ncbi.nlm.nih.gov/19892718/[the original next-generation-matrix derivation].
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