Bayesian estimation of the offspring mean in branching processes: Application to infectious disease data

Authors:
Angel G. Angelov;Maroussia Slavtchova-Bojkova
Affiliations:
Department of Probability, Operational Research and Statistics, Faculty of Mathematics and Informatics, Sofia University, Bulgaria;Department of Probability, Operational Research and Statistics, Faculty of Mathematics and Informatics, Sofia University, Bulgaria and Department of Probability and Statistics, Institute of Mathem ...
Venue:
Computers & Mathematics with Applications
Year:
2012

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Abstract

A single-type Bienayme-Galton-Watson branching process (BGWBP) with a generalized power series offspring distribution is considered as a model of the spread of an infectious disease in a population. Our main goal is to estimate the basic reproduction number R"0, which is represented by the offspring mean of the BGWBP, applying a Bayesian approach. The only data assumed to be available are the initial number of infected individuals and the total number of infected individuals. We are using the Metropolis-Hastings algorithm to simulate the posterior distribution. The usefulness of the described method is demonstrated on some real data on the number of reported cases of mumps in Bulgaria during the period 2005-2008.