### Abstract

In this paper we study a single serotype transmission model of dengue to determine the optimal vaccination age for Dengvaxia. The transmission dynamics are modelled with an age-dependent force of infection. The force of infection for each serotype is derived from the serological profile of dengue in Brazil without serotype distinction and from serotype-specic reported cases. The risk due to an infection is measured by the probability of requiring hospitalisation based on Brazilian Ministry of Health data.

The optimal vaccination age is determined for any number and combination of the four distinct dengue virus serotypes DENv1-4. The lifetime expected risk is adapted to include antibody dependent enhancement (ADE) and permanent cross-immunity after two heterologous infections. The risk is assumed to be serostatus-dependent. The optimal vaccination age is computed for constant, serostatus-specic vaccine efficacies. Additionally, the vaccination age is restricted to conform to the licence of Dengvaxia in Brazil and the achievable and minimal lifetime expected risks are compared.

The optimal vaccination age obtained for the risk of hospitalisation varies significantly with the assumptions relating to ADE and cross-immunity. Risk-free primary infections leads to higher optimal vaccination ages, as do asymptomatic third and fourth infections. Sometimes vaccination is not recommended at all, for example for any endemic area with a single serotype if primary infections are risk-free. Restricting the vaccination age to Dengvaxia licensed ages mostly leads to only a slightly higher lifetime expected risk and the vaccine should be administered as close as possible to the optimal vaccination age.

The optimal vaccination age is determined for any number and combination of the four distinct dengue virus serotypes DENv1-4. The lifetime expected risk is adapted to include antibody dependent enhancement (ADE) and permanent cross-immunity after two heterologous infections. The risk is assumed to be serostatus-dependent. The optimal vaccination age is computed for constant, serostatus-specic vaccine efficacies. Additionally, the vaccination age is restricted to conform to the licence of Dengvaxia in Brazil and the achievable and minimal lifetime expected risks are compared.

The optimal vaccination age obtained for the risk of hospitalisation varies significantly with the assumptions relating to ADE and cross-immunity. Risk-free primary infections leads to higher optimal vaccination ages, as do asymptomatic third and fourth infections. Sometimes vaccination is not recommended at all, for example for any endemic area with a single serotype if primary infections are risk-free. Restricting the vaccination age to Dengvaxia licensed ages mostly leads to only a slightly higher lifetime expected risk and the vaccine should be administered as close as possible to the optimal vaccination age.

Original language | English |
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Journal | Mathematical Medicine and Biology |

Publication status | Accepted/In press - 19 May 2020 |

### Keywords

- dengue
- vaccination
- optimal vaccination age
- age-structured mathematical model
- serological data
- hospitalisation risk

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## Cite this

Maier, S. B., Massad, E., Amaku, M., Burattini, M. N., & Greenhalgh, D. (Accepted/In press). The optimal age of vaccination against dengue in Brazil based on serotype-specific forces of infection derived from serological data.

*Mathematical Medicine and Biology*.