Extending the SIR epidemic model

We investigate possible extensions of the susceptible–infective-removed (SIR) epidemic model. We show that there exists a large class of functions representing interaction between the susceptible and infective populations for which the model has a realistic behaviour and preserves the essential features of the classical SIR model. We also present a new discretisation of the SIR model which has the advantage of possessing a conserved quantity, thus making possible the estimation of the non-infected population at the end of the epidemic. A cellular automaton SIR is also constructed on the basis of the discrete-time system.