### 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 language | English (US) |
---|---|

Title of host publication | Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases |

Publisher | Springer International Publishing |

Pages | 221-248 |

Number of pages | 28 |

ISBN (Electronic) | 9783319404134 |

ISBN (Print) | 9783319404110 |

DOIs | |

State | Published - Jan 1 2016 |

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### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Medicine(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*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

}

TY - CHAP

T1 - Optimal control of vaccination in an age-structured cholera model

AU - Fister, K. Renee

AU - Gaff, Holly

AU - Lenhart, Suzanne

AU - Numfor, Eric Shu

AU - Schaefer, Elsa

AU - Wang, Jin

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

KW - Cholera

KW - Mathematical model

KW - Optimal control

KW - Partial differential equation

KW - Waning immunity

UR - http://www.scopus.com/inward/record.url?scp=85018233679&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85018233679&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-40413-4_14

DO - 10.1007/978-3-319-40413-4_14

M3 - Chapter

AN - SCOPUS:85018233679

SN - 9783319404110

SP - 221

EP - 248

BT - Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases

PB - Springer International Publishing

ER -