Agestructured models and optimal control in mathematical equidemiology: a survey
Greenhalgh, David; Boucekkine, Raouf and Hritonenko, Natali and Yatsenko, Yuri, eds. (2010) Agestructured models and optimal control in mathematical equidemiology: a survey. In: Optimal Control of AgeStructured Populations in Economy, Demography and the Environment. Routledge Explorations in Environmental Economics . Routledge Taylor & Francis Group, pp. 174206. ISBN 9780415776516
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Abstract
In this chapter we shall discuss the use of both optimal control theory and agestructured epidemic models in mathematical epidemiology. We use a very broad definition of optimal control, for example mathematical models for control by vaccination, as well as applications of optimal control theory. This is a wide area and we have had to be selective. In terms of applications a lot of the models which we present are applicable to the spread of common childhood diseases as that is an area in which agestructured models have been shown to fit data well and are most commonly applied in practice. This is because vaccination programs are often agedependent targeting children of a given age and so they need agestructured models. The first section of this chapter discusses agestructured epidemic models including the question of optimal vaccination in them. 2 Then we move on to the optimal control in “stagestructured” (rather than agestructured) epidemic models, in which the individuals are grouped into susceptible, infected, and so on, depending on their relation to the epidemic. This gives a survey of how the ideas of optimal control theory, in particular the Maximum Principle and dynamic programming have been applied in the past to determine optimal control strategies for an epidemic, for example by immunization or removal of infected individuals. We finish this section with a few papers which apply optimal control theory to drug epidemics. We next survey some articles which give applications of optimal control to agestructured epidemic models. Much of this work concerns the existence and structure of optimal agedependent vaccination strategies for common childhood diseases but we cover some other applications too. This is followed by a short section on spatial models used to determine optimal epidemic control policies. A brief summary and discussion conclude.


Item type: Book Section ID code: 31251 Dates: DateEvent2010PublishedSubjects: Science > Mathematics > Probabilities. Mathematical statistics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 24 May 2011 10:54 Last modified: 03 Aug 2024 00:33 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/31251