Bayesian Formulation of Time-Dependent Carrier-Borne Epidemic Model with a Single Carrier

Abstract

In this paper, the time dependent carrier-borne epidemic model defined by Weiss in 1965 has been adopted into a Bayesian framework for the estimation of its parameters. A complete methodological structure has been proposed for estimating the relative infection rate and probability of survival of k out of m susceptibles after time t from the start of the epidemic. The methodology has been proposed assuming a single carrier to simplify the study of the behavioral validity of the fitted Bayesian model with respect to time and relative infection rate. Further, the proposed model has been implemented on two real data sets- the typhoid epidemic data from Zermatt in Switzerland and the Covid-19 epidemic data from Kerala in India. Results show that the proposed methodology produces reliable predictions which are consistent with those of the maximum likelihood estimates and with expected epidemiological patterns.