I employ a simple mathematical model of an epidemic process to evaluate how four basic quantities: the reproduction number (ℛ), the numbers of sensitive (S) and infectious individuals (I), and total community size (N) affect strategies to control COVID-19. Numerical simulations show that strict suppression measures at the beginning of an epidemic can create low infectious numbers, which thereafter can be managed by mitigation measures over longer periods to flatten the epidemic curve. The stronger the suppression measure, the faster it achieves the low numbers of infections that are conducive to subsequent management. Our results on short-term strategies point to a two-step control strategy, following failed mitigation, that begins with suppression of the reproduction number, ℛC, below 1.0, followed by renewed mitigation measures that manage