CHARACTERIZING AND MANAGING AN EPIDEMIC: A FIRST PRINCIPLES MODEL AND A CLOSED FORM SOLUTION TO THE KERMACK AND MCKENDRICK EQUATIONS

We derived a closed-form solution to the original epidemic equations formulated by Kermack and McKendrick in 1927 (1). The complete solution is validated using independently measured mobility data and accurate predictions of COVID-19 case dynamics in multiple countries. It replicates the observed phenomenology, quantitates pandemic dynamics, and provides simple analytical tools for policy makers. Of particular note, it projects that increased social containment measures shorten an epidemic and reduce the ultimate number of cases and deaths. In contrast, the widely used Susceptible–Infectious–Recovered (SIR) models, based on an approximation to Kermack and McKendrick’s original equations, project that strong containment measures delay the peak in daily infections, causing a longer epidemic. These projections contradict both the complete solution and the observed phenomenology in COVID-19 pandemic data. The closed-form solution elucidates that the two parameters classically used as constants in approximate SIR models cannot, in fact, be reasonably assumed to be constant in real epidemics. This prima facie failure forces the conclusion that the approximate SIR models should not be used to characterize or manage epidemics. As a replacement to the SIR models, the closed-form solution and the expressions derived from the solution form a complete set of analytical tools that can accurately diagnose the state of an epidemic and provide proper guidance for public health decision makers.