### Abstract

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.

Language | English |
---|---|

Title of host publication | Optimal Control of Age-Structured Populations in Economy, Demography and the Environment |

Editors | Raouf Boucekkine, Natali Hritonenko, Yuri Yatsenko |

Pages | 174-206 |

Number of pages | 33 |

Publication status | Published - 2010 |

### Publication series

Name | Routledge Explorations in Environmental Economics |
---|---|

Publisher | Routledge |

### Fingerprint

### Keywords

- models
- optimal control
- equidemiology
- control theory

### Cite this

*Optimal Control of Age-Structured Populations in Economy, Demography and the Environment*(pp. 174-206). (Routledge Explorations in Environmental Economics).

}

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Age-structured models and optimal control in mathematical equidemiology: a survey

AU - Greenhalgh, David

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - models

KW - optimal control

KW - equidemiology

KW - control theory

UR - http://www.routledge.com/books/details/9780415776516/

M3 - Chapter

SN - 9780415776516

T3 - Routledge Explorations in Environmental Economics

SP - 174

EP - 206

BT - Optimal Control of Age-Structured Populations in Economy, Demography and the Environment

A2 - Boucekkine, Raouf

A2 - Hritonenko, Natali

A2 - Yatsenko, Yuri

ER -