Optimal control of vaccination in an age-structured cholera model

K. Renee Fister; Holly Gaff; Suzanne Lenhart; Eric Shu Numfor; Elsa Schaefer; Jin Wang

doi:10.1007/978-3-319-40413-4_14

Optimal control of vaccination in an age-structured cholera model

K. Renee Fister, Holly Gaff, Suzanne Lenhart, Eric Shu Numfor, Elsa Schaefer, Jin Wang

Mathematics

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

21 Scopus citations

Abstract

A cholera model with continuous age structure is given as a system of hyperbolic (first-order) partial differential equations (PDEs) in combination with ordinary differential equations. Asymptomatic infected and susceptibles with partial immunity are included in this epidemiology model with vaccination rate as a control; minimizing the symptomatic infecteds while minimizing the cost of the vaccinations represents the goal.With themethod of characteristics and a fixed point argument, the existence of a solution to our nonlinear state system is achieved. The representation and existence of a unique optimal control are derived. The steps to justify the optimal control results for such a system with first order PDEs are given. Numerical results illustrate the effect of age structure on optimal vaccination rates.

Original language	English (US)
Title of host publication	Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases
Publisher	Springer International Publishing
Pages	221-248
Number of pages	28
ISBN (Electronic)	9783319404134
ISBN (Print)	9783319404110
DOIs	https://doi.org/10.1007/978-3-319-40413-4_14
State	Published - Jan 1 2016

Keywords

Cholera
Mathematical model
Optimal control
Partial differential equation
Waning immunity

ASJC Scopus subject areas

General Mathematics
General Medicine

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

Access to Document

10.1007/978-3-319-40413-4_14

Cite this

@inbook{8e6810b5279b4e79803dd022abce01bd,

title = "Optimal control of vaccination in an age-structured cholera model",

abstract = "A cholera model with continuous age structure is given as a system of hyperbolic (first-order) partial differential equations (PDEs) in combination with ordinary differential equations. Asymptomatic infected and susceptibles with partial immunity are included in this epidemiology model with vaccination rate as a control; minimizing the symptomatic infecteds while minimizing the cost of the vaccinations represents the goal.With themethod of characteristics and a fixed point argument, the existence of a solution to our nonlinear state system is achieved. The representation and existence of a unique optimal control are derived. The steps to justify the optimal control results for such a system with first order PDEs are given. Numerical results illustrate the effect of age structure on optimal vaccination rates.",

keywords = "Cholera, Mathematical model, Optimal control, Partial differential equation, Waning immunity",

author = "Fister, {K. Renee} and Holly Gaff and Suzanne Lenhart and Numfor, {Eric Shu} and Elsa Schaefer and Jin Wang",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.",

year = "2016",

month = jan,

day = "1",

doi = "10.1007/978-3-319-40413-4_14",

language = "English (US)",

isbn = "9783319404110",

pages = "221--248",

booktitle = "Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases",

publisher = "Springer International Publishing",

}

TY - CHAP

T1 - Optimal control of vaccination in an age-structured cholera model

AU - Fister, K. Renee

AU - Gaff, Holly

AU - Lenhart, Suzanne

AU - Numfor, Eric Shu

AU - Schaefer, Elsa

AU - Wang, Jin

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2016.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - A cholera model with continuous age structure is given as a system of hyperbolic (first-order) partial differential equations (PDEs) in combination with ordinary differential equations. Asymptomatic infected and susceptibles with partial immunity are included in this epidemiology model with vaccination rate as a control; minimizing the symptomatic infecteds while minimizing the cost of the vaccinations represents the goal.With themethod of characteristics and a fixed point argument, the existence of a solution to our nonlinear state system is achieved. The representation and existence of a unique optimal control are derived. The steps to justify the optimal control results for such a system with first order PDEs are given. Numerical results illustrate the effect of age structure on optimal vaccination rates.

AB - A cholera model with continuous age structure is given as a system of hyperbolic (first-order) partial differential equations (PDEs) in combination with ordinary differential equations. Asymptomatic infected and susceptibles with partial immunity are included in this epidemiology model with vaccination rate as a control; minimizing the symptomatic infecteds while minimizing the cost of the vaccinations represents the goal.With themethod of characteristics and a fixed point argument, the existence of a solution to our nonlinear state system is achieved. The representation and existence of a unique optimal control are derived. The steps to justify the optimal control results for such a system with first order PDEs are given. Numerical results illustrate the effect of age structure on optimal vaccination rates.

KW - Cholera

KW - Mathematical model

KW - Optimal control

KW - Partial differential equation

KW - Waning immunity

UR - http://www.scopus.com/inward/record.url?scp=85018233679&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85018233679&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-40413-4_14

DO - 10.1007/978-3-319-40413-4_14

M3 - Chapter

AN - SCOPUS:85018233679

SN - 9783319404110

SP - 221

EP - 248

BT - Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases

PB - Springer International Publishing

ER -

Optimal control of vaccination in an age-structured cholera model

Abstract

Keywords

ASJC Scopus subject areas

UN SDGs

Access to Document

Other files and links

Fingerprint

Cite this