Stochastic processes in epidemic modelling and simulation. (English) Zbl 1017.92030

Greenhalgh, David

Shanbhag, D. N. (ed.) et al., Stochastic processes: Modelling and simulation. Amsterdam: North-Holland. Handb. Stat. 21, 285-335 (2003).

Introduction: This article aims to discuss the uses of stochastic processes in epidemiology, mathematical modelling and the simulation of epidemics. This is a very large area and it will not be possible to cover the entire literature on the topic. Instead, we aim to survey the main areas. We start by looking at some classical applications of stochastic processes in epidemic theory, namely the Chain Binomial, followed by the simple and general stochastic epidemic models. In Section 4 we consider the application of stochastic processes in spatial epidemic modelling, particularly percolation processes, simulation modelling and diffusion processes. One of the major motivations for studying epidemic models is to make predictions about control strategies such as vaccination of susceptible individuals or removal of infected ones, so Section 5 discusses stochastic models for the control of epidemics. Section 6 looks at applications of stochastic modelling for several specific diseases, including HIV/AIDS. This is followed by a description of some uses of stochastic methods in parameter estimation and hypothesis testing. A brief summary concludes our survey.
For the entire collection see [Zbl 1009.00011].

MSC:

92D30	Epidemiology
60G35	Signal detection and filtering (aspects of stochastic processes)
92C60	Medical epidemiology
62P10	Applications of statistics to biology and medical sciences; meta analysis
60J70	Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
60K35	Interacting random processes; statistical mechanics type models; percolation theory

Keywords:

chain binomial models; threshold theorems; spatial models