SOME STATE SPACE MODELS OF AIDS EPIDEMIOLOGY IN HOMOSEXUAL POPULATIONS - Quantitative Medical Data Analysis Using Mathematical Tools and Statistical Techniques - page 43

CHAPTER 3
SOME STATE SPACE MODELS OF AIDS EPIDEMIOLOGY
IN HOMOSEXUAL POPULATIONS
Wai Y. Tan
Department of Mathematical Sciences,
The University of Memphis, Memphis, TN 38152-6429, USA
E-mail: [e-mail]
This article illustrates how to develop state space models for AIDS epi-
demic in homosexual populations. A generalized Bayesian procedure is
proposed to estimate the unknown parameters and the state variables.
As an application, the model and the method are applied to the AIDS
incidence data of homosexual and bisexual men of Switzerland. The anal-
ysis of these data clearly indicates that the model and methods can solve
many dicult problems which are not possible by other currently avail-
able models and approaches.
1. Introduction
As shown by Tan 9 , the AIDS epidemics are very complicated biologically
involving very complex stochastic processes. In these cases, it is very di-
cult to estimate the unknown parameters and to predict the state variables,
especially in cases where not many data are available. To ease the prob-
lems of estimation and prediction and to extract more information from
the system, in this article we propose a state space modelling approach by
combining stochastic models with statistical models. Then one can readily
apply the Gibbs sampling method and the Markov Chain and Monte Carlo
approach (MCMC) to estimate the unknown parameters and to predict
the state variables. By using these estimates, one can validate the model
and extract more information from the system which are not possible by
using stochastic model alone or statistical model alone. We will illustrate
the model and the method by using some data of the AIDS epidemic in
homosexual population of Switzerland.