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

18 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

Mathematics(all)
Medicine(all)

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

Cite this

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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.",

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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.

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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

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Optimal control of vaccination in an age-structured cholera model

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Keywords

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