An unconditionally convergent finite-difference scheme for the SIR model

A first-order, unconditionally-stable, finite-difference scheme is developed for the numerical solution of the SIR model. It is seen that numerical simulations using the method reflect the long-term behaviour of the continuous-time system accurately. The introduction of seasonal variation into the SIR model leads to periodic and chaotic dynamics of epidemics which are present in the numerical simulations. (C) 2002 Elsevier Inc. All rights reserved.