  The basic reproduction number $R_0$ is a fundamental quantity in
epidemiological modeling, reflecting the typical number of secondary infections
that arise from a single infected individual. While $R_0$ is widely known to
scientists, policymakers, and the general public, it has received comparatively
little attention in the controls community. This note provides two novel
characterizations of $R_0$: a stability characterization and a geometric
program characterization. The geometric program characterization allows us to
write $R_0$-constrained and budget-constrained optimal resource allocation
problems as geometric programs, which are easily transformed into convex
optimization problems. We apply these programs to allocating vaccines and
antidotes in numerical examples, finding that targeting $R_0$ instead of the
spectral abscissa of the Jacobian matrix (a common target in the controls
literature) leads to qualitatively different solutions.
