Predicting the progress and the peak of an epidemic

The problem is statistical prediction of the number of people that will be infected with a contagious illness in a closed population over time. The prediction is based on the Susceptible-Infectious-Recovered (SIR) model of epidemic dynamics with inhomogeneous population mixing. The paper presents a theoretical analysis of the predictive accuracy based on the Cramer-Rao lower bound (CRLB). The CRLB provides a tool that enables us to quantify the prediction accuracy of a scale of an epidemic as a function of the prior uncertainty of SIR model parameters, measurement accuracy of the number of infected people and the amount of data available for processing. A verification of the theoretical analysis is carried out by Monte Carlo simulations.