Optimal control of vaccination in an age-structured cholera model

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

Research output: Chapter in Book/Report/Conference proceedingChapter

5 Citations (Scopus)

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 languageEnglish (US)
Title of host publicationMathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases
PublisherSpringer International Publishing
Pages221-248
Number of pages28
ISBN (Electronic)9783319404134
ISBN (Print)9783319404110
DOIs
StatePublished - Jan 1 2016

Fingerprint

Age-structured Model
Vaccination
Cholera
Age Structure
Optimal Control
First order differential equation
Partial differential equation
Epidemiology
Immunity
Justify
Ordinary differential equation
Fixed point
Partial
Costs and Cost Analysis
Numerical Results
Costs
Model

Keywords

  • Cholera
  • Mathematical model
  • Optimal control
  • Partial differential equation
  • Waning immunity

ASJC Scopus subject areas

  • Mathematics(all)
  • Medicine(all)

Cite this

Fister, K. R., Gaff, H., Lenhart, S., Numfor, E. S., Schaefer, E., & Wang, J. (2016). Optimal control of vaccination in an age-structured cholera model. In Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases (pp. 221-248). Springer International Publishing. https://doi.org/10.1007/978-3-319-40413-4_14

Optimal control of vaccination in an age-structured cholera model. / Fister, K. Renee; Gaff, Holly; Lenhart, Suzanne; Numfor, Eric Shu; Schaefer, Elsa; Wang, Jin.

Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases. Springer International Publishing, 2016. p. 221-248.

Research output: Chapter in Book/Report/Conference proceedingChapter

Fister, KR, Gaff, H, Lenhart, S, Numfor, ES, Schaefer, E & Wang, J 2016, Optimal control of vaccination in an age-structured cholera model. in Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases. Springer International Publishing, pp. 221-248. https://doi.org/10.1007/978-3-319-40413-4_14
Fister KR, Gaff H, Lenhart S, Numfor ES, Schaefer E, Wang J. Optimal control of vaccination in an age-structured cholera model. In Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases. Springer International Publishing. 2016. p. 221-248 https://doi.org/10.1007/978-3-319-40413-4_14
Fister, K. Renee ; Gaff, Holly ; Lenhart, Suzanne ; Numfor, Eric Shu ; Schaefer, Elsa ; Wang, Jin. / Optimal control of vaccination in an age-structured cholera model. Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases. Springer International Publishing, 2016. pp. 221-248
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