Optimal Control of Vaccination in an Age-Structured Cholera Model

K. Renee Fister (), Holly Gaff (), Suzanne Lenhart (), Eric Numfor (), Elsa Schaefer () and Jin Wang ()
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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

A chapter in Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases, 2016, pp 221-248 from Springer

Abstract: 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.

Keywords: Cholera; Optimal control; Mathematical model; Partial differential equation; Waning immunity (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-40413-4_14

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