The Mathematical Methods for the H1N1 Transmission Statistics
Bayes’ Theorem: Image by Mike DeHaan
The team used Bayesian, Markov Chain, Monte Carlo methods with a Gamma distribution to model the transmissibility within households.
The mathematics of “Bayesian analysis“ is a methodology in statistics that can “estimate parameters of an underlying distribution based on the observed distribution.” Collecting and analyzing more data improves the accuracy of parameters such as the probability and variance. Starting with a more accurate “prior” distribution will lead to a more accurate “posterior” result for a given set of observations. Page 2 of my previous Population Prediction of More Retirees, Fewer Workers by 2100 discusses Bayes Theorem in a bit more detail.
A “Markov chain“ is a series of events for which the current event is “conditionally independent of the past“. This applies to the transmission of infectious disease within a household, given that at least one person is already infected.
A “Monte Carlo method” simulates a situation by “generating suitable random numbers” to test a mathematical model. In this case, the Monte Carlo method would help determine the probability of transmission and also the statistical variation. Typically, a computer would generate many parameter values to determine which gave the best “fit” for the observations in the H1N1 pandemic study in Birmingham.
A typical “Gamma distribution” is an “n-shaped” probability distribution that is skewed to the left and has a long tail to the right. (The familiar “bell curve” is n-shaped with the bulge in the centre). It is often used in Bayesian inference as the “prior”. One example is to model the risk that a person will become ill in a given period of time under specific circumstances. Dr. House took a different approach to the statistical distribution.
Dr. House explained to Decoded Science: “The standard statistical distributions are typically n-shaped. The one used is a class of u-shaped distributions derived in 1986 (reference 9 in the paper: [Ball F: A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models. Adv Appl Probab 1986, 18:289–310]), which don’t have a standard name but I would call the ‘household final size distributions‘.”
The Team of Authors who Estimated the Transmissibility of H1N1 Swine Flu
Dr. Thomas House: Image courtesy of Dr. Thomas House
Dr. Thomas House, PhD, is the lead author of this study. He teaches at the Warwick Mathematics Institute in Coventry, England.
Matt J Keeling is also from the University of Warwick, straddling the Mathematics and Life Sciences departments.
Nadia Inglis, Shakeel Suleman, Obaghe Edeghere, Gillian Smith, and Babatunde Olowokure all work with the Health Protection Agency, West Midlands. Inglis and House performed the literature search. Suleman was the database designer. Edeghere, Smith and Olowokure gathered the data.
Joshua Ross, of the University of Adelaide, Australia, contributed to the mathematical model, along with House and Keeling.
Reference:
House, Thomas, et. al. Estimation of outbreak severity and transmissibility: Influenza A(H1N1)pdm09 in households. (2012). BMC Medicine. Accessed Oct. 8, 2012.
