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2016 | OriginalPaper | Chapter

Optimal Control of Vaccination in an Age-Structured Cholera Model

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

Published in: Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases

Publisher: Springer International Publishing

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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 the method 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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Metadata
Title
Optimal Control of Vaccination in an Age-Structured Cholera Model
Authors
K. Renee Fister
Holly Gaff
Suzanne Lenhart
Eric Numfor
Elsa Schaefer
Jin Wang
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-40413-4_14