An analytical solution for the Kermack-McKendrick model

We present an analytical solution for the Susceptible-Infective-Removed (SIR) model introduced initially by Kermack-McKendrick in 1927. Starting from the differential equation for the removed subjects presented by them in the original article, we rewrite it in a slightly different form to derive a formal solution, unless one integration. Then, using approximate algebraic techniques, we obtain an analytic solution for the integral. We compare the numerical solution of the differential equations of the SIR model with the analytic solution here proposed, showing an excellent agreement. Finally, the present scheme allows us to represent analytically two fundamental quantities: the time of the infection peak and the fraction of immunized to stop the epidemic. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

The article presents an analytical solution for the SIR model introduced by Kermack-McKendrick in 1927, comparing it with numerical solutions to show excellent agreement. The method also allows for the analytical representation of fundamental quantities such as the time of infection peak and the fraction of immunized individuals needed to stop the epidemic.