Application of time series analysis in modeling childhood epidemic diseases

Abstract

In this paper, we aim to discuss the time series-susceptible-infected-recovered (TSIR) model which bridges the gap between the theoretical models in epidemics and the discrete time series data. Using the measles data of London from 1944 to 1960 as a case study, we induce a simple linear relationship between the cumulative births and the cumulative reporting cases, and hence reconstruct the unobserved susceptible class from the births and reporting infected cases. The simulation result traces the observed data remarkably well, and captures both the annual and biennial patterns in the observed cyclicity. In order to improve the accuracy of the estimation, we also discuss the multi-step ahead estimation method, which evaluates the good-of-fitness from the viewpoint of auto-correlation function (ACF). Finally we studied the role of the birth-rate as a bifurcation parameter, which quantitatively explains the episode of annual cyclicity in the observed data corresponding to a high birth rate around 1947.