Birth(Death)/Birth-Death Processes and Their Computable Transition Probabilities with Statistical Application

• Activity Number: 73
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: Health Policy Statistics Section
• Author(s): Lam Ho* and Marc A. Suchard
• Companies: UCLA and UCLA
• Keywords: bivariate process ; birth death process ; infectious disease ; SIR model ; transition probabilities

Abstract

Birth-death processes track the size of one population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for evaluating the transition probabilities of bivariate processes has forced researchers to rely on either computational expensive approaches or indirect inference methods like the approximate Bayesian computation. In this paper, we introduce the birth(death)/birth-death process as a bivariate generalization of the birth-death process. The bivariate process finds application in many fields, including epidemiology, genetics and infectious diseases. The susceptible infected recovered model is one prime example. We develop an efficient and robust algorithm to calculate the transition probabilities of birth(death)/birth death processes and then apply these probabilities to draw direct inference about the 17th century Great Plague in Eyam under a stochastic susceptible infected recovered model, ubiquitous in infectious disease ecology.