An Algebraic Solution for the Kermack-McKendrick Model

TL;DR

This paper derives an algebraic, analytical solution for the classic SIR epidemic model, enabling precise computation and comparison with numerical solutions, thus enhancing understanding of disease spread dynamics.

Contribution

It introduces a novel algebraic method to solve the SIR model analytically, improving upon traditional numerical approaches.

Findings

Analytical solution closely matches numerical simulations.

Provides a new algebraic framework for SIR model analysis.

Enhances accuracy and efficiency in epidemic modeling.

Abstract

We present an algebraic solution for the Susceptible-Infective-Removed (SIR) model originally presented by Kermack-McKendrick in 1927. Starting from the differential equation for the removed subjects presented by them in the original paper, we re-write it in a slightly different form in order to derive formally the solution, unless one integration. Then, using algebraic techniques and some well justified numerical assumptions we obtain an analytic solution for the integral. Finally, we compare the numerical solution of the differential equations of the SIR model with the analytically solution here proposed, showing an excellent agreement.