Age-structured models and optimal control in mathematical equidemiology: a survey

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this chapter we shall discuss the use of both optimal control theory and age-structured 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 age-structured models have been shown to fit data well and are most commonly applied in practice. This is because vaccination programs are often age-dependent targeting children of a given age and so they need age-structured models. The first section of this chapter discusses age-structured epidemic models including the question of optimal vaccination in them.
2
Then we move on to the optimal control in “stage-structured” (rather than age-structured) 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 age-structured epidemic models. Much of this work concerns the existence and structure of optimal age-dependent 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.
LanguageEnglish
Title of host publicationOptimal Control of Age-Structured Populations in Economy, Demography and the Environment
EditorsRaouf Boucekkine, Natali Hritonenko, Yuri Yatsenko
Pages174-206
Number of pages33
Publication statusPublished - 2010

Publication series

NameRoutledge Explorations in Environmental Economics
PublisherRoutledge

Fingerprint

Age-structured Model
Optimal Control
Optimal Control Theory
Vaccination
Epidemic Model
Stage-structured
Immunization
Dependent
Spatial Model
Epidemiology
Control Policy
Optimal Strategy
Maximum Principle
Dynamic Programming
Control Strategy
Drugs
Cover
Mathematical Model

Keywords

  • models
  • optimal control
  • equidemiology
  • control theory

Cite this

Greenhalgh, D. (2010). Age-structured models and optimal control in mathematical equidemiology: a survey. In R. Boucekkine, N. Hritonenko, & Y. Yatsenko (Eds.), Optimal Control of Age-Structured Populations in Economy, Demography and the Environment (pp. 174-206). (Routledge Explorations in Environmental Economics).
Greenhalgh, David. / Age-structured models and optimal control in mathematical equidemiology: a survey. Optimal Control of Age-Structured Populations in Economy, Demography and the Environment. editor / Raouf Boucekkine ; Natali Hritonenko ; Yuri Yatsenko. 2010. pp. 174-206 (Routledge Explorations in Environmental Economics).
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Greenhalgh, D 2010, Age-structured models and optimal control in mathematical equidemiology: a survey. in R Boucekkine, N Hritonenko & Y Yatsenko (eds), Optimal Control of Age-Structured Populations in Economy, Demography and the Environment. Routledge Explorations in Environmental Economics, pp. 174-206.

Age-structured models and optimal control in mathematical equidemiology: a survey. / Greenhalgh, David.

Optimal Control of Age-Structured Populations in Economy, Demography and the Environment. ed. / Raouf Boucekkine; Natali Hritonenko; Yuri Yatsenko. 2010. p. 174-206 (Routledge Explorations in Environmental Economics).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Greenhalgh D. Age-structured models and optimal control in mathematical equidemiology: a survey. In Boucekkine R, Hritonenko N, Yatsenko Y, editors, Optimal Control of Age-Structured Populations in Economy, Demography and the Environment. 2010. p. 174-206. (Routledge Explorations in Environmental Economics).