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Optimal Control of Vaccination in an Age-Structured Cholera Model

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

Author

Listed:
  • K. Renee Fister

    (Murray State University, Department of Mathematics and Statistics)

  • Holly Gaff

    (Old Dominion University, Department of Biological Sciences)

  • Suzanne Lenhart

    (University of Tennessee, Department of Mathematics)

  • Eric Numfor

    (Augusta University, Department of Mathematics)

  • Elsa Schaefer

    (Marymount University, Department of Mathematics)

  • Jin Wang

    (University of Tennessee at Chattanooga, Department of Mathematics)

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.

Suggested Citation

  • K. Renee Fister & Holly Gaff & Suzanne Lenhart & Eric Numfor & Elsa Schaefer & Jin Wang, 2016. "Optimal Control of Vaccination in an Age-Structured Cholera Model," Springer Books, in: Gerardo Chowell & James M. Hyman (ed.), Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases, pages 221-248, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-40413-4_14
    DOI: 10.1007/978-3-319-40413-4_14
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