Lie Symmetries Analysis for SIR Model of Epidemiology
A system of nonlinear ordinary differential equations arising from SIR model of epidemiology is transformed into a system of one equation of second order and one of first order.This is a simple model proposed in 1927 by Kermack and Mckendick. The Modified symmetry method is applied and differential invariants are used to obtain some exact solutions of the SIR model.
Kermack, W. McKendick, A contribution to the mathematical theory of epidemics. Pro.R.So. London