### Abstract

In this paper we study a mathematical model to analyse the optimal vaccination age against Dengue in Brazil. Data from Brazil are used to estimate the basic reproduction numbers for each of the four Dengue serotypes and then the optimal vaccination age is calculated using a method due to Hethcote [1]. The vaccine has different efficacies against each serotype. Vaccination that is too early is inffective as individuals are protected by maternal antibodies but leaving vaccination until later may allow the disease to spread.

First of all the optimal vaccination ages are calculated where there is just one serotype in circulation and then when there are multiple serotypes. The calculations are done using data both assuming constant vaccine efficacy and age-dependent vaccine efficacy against a given serotype. The multiple serotype calculations are repeated assuming that the rst infection is a risky infection and that it is not (to model Dengue Antibody Enhancement). The calculations are then repeated when any third or fourth Dengue infections are asymptomatic, so that two Dengue infections with different serotypes provide effective permanent immunity. The calculations are also repeated when the age-dependent risk function (fitted to Brazilian data) is hospitalisation from Dengue and when it is mortality due to Dengue. We find a wide variety of optimal vaccination ages depending on both the serotypes in circulation and the assumptions of the model.

First of all the optimal vaccination ages are calculated where there is just one serotype in circulation and then when there are multiple serotypes. The calculations are done using data both assuming constant vaccine efficacy and age-dependent vaccine efficacy against a given serotype. The multiple serotype calculations are repeated assuming that the rst infection is a risky infection and that it is not (to model Dengue Antibody Enhancement). The calculations are then repeated when any third or fourth Dengue infections are asymptomatic, so that two Dengue infections with different serotypes provide effective permanent immunity. The calculations are also repeated when the age-dependent risk function (fitted to Brazilian data) is hospitalisation from Dengue and when it is mortality due to Dengue. We find a wide variety of optimal vaccination ages depending on both the serotypes in circulation and the assumptions of the model.

Original language | English |
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Pages (from-to) | 15-32 |

Number of pages | 18 |

Journal | Mathematical Biosciences |

Volume | 294 |

Early online date | 19 Sep 2017 |

DOIs | |

Publication status | Published - 31 Dec 2017 |

### Keywords

- Dengue
- vaccination
- optimal vaccination age
- age-structured models
- serotype
- risk function
- mortality
- hospitalisation
- mathematical model

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## Cite this

Maier, S. B., Huang, X., Massad, E., Amaku, M., Burattini, M. N., & Greenhalgh, D. (2017). Analysis of the optimal vaccination age for Dengue in Brazil with a tetravalent Dengue vaccine.

*Mathematical Biosciences*,*294*, 15-32. https://doi.org/10.1016/j.mbs.2017.09.004