Numerical simulations of an SIR epidemic model with random initial states

Abstract

When the initial state of an epidemic is uncertain, mathematical descriptions of that epidemic in terms of initial conditions must be modified by regarding these initial conditions as random variables having particular distribution functions. In this paper we assume a beta distribution as the initial proportion of infected in an SIR epidemic model. Numerical simulations are carried out on the various classes of the model as the uncertainties are propagated. The probability density functions of the random solutions of these classes over time are also calculated numerically. Some properties of the random solution and the effect of the parameters of the beta distribution on the behaviour of the epidemic are investigated.