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

18 Scopus citations


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
Number of pages28
ISBN (Electronic)9783319404134
ISBN (Print)9783319404110
StatePublished - Jan 1 2016


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

ASJC Scopus subject areas

  • Mathematics(all)
  • Medicine(all)


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