### Abstract

A new model for the transmission dynamics of human pappilomavirus (HPV) is designed and analysed. The model, which stratifies the total population in terms of age and gender, incorporates an imperfect anti-HPV vaccine with some therapeutic benefits. Rigorous qualitative analysis of the resulting age-structured model, which takes the form of a deterministic system of non-linear partial differential equations with separable transmission coefficients, shows that the disease-free equilibrium of the model is locallyasymptotically stable whenever the effective reproduction number (denoted by R_{v}) is less than unity. It is shown to be globally-asymptotically stable if certain additional conditions hold. Furthermore, it is shown that the model has at least one endemic equilibrium when R_{v} exceeds unity. Hence, the effective control of HPV spread in a community, using a vaccine, is governed by the threshold quantity R_{v} (the use of the vaccine will lead to effective disease control or elimination only if it reduces the threshold quantity to a value less than unity; and the use of such vaccine will not lead to effective disease control if it fails to make the threshold quantity to be less than unity).

Original language | English (US) |
---|---|

Pages (from-to) | 2151-2174 |

Number of pages | 24 |

Journal | Discrete and Continuous Dynamical Systems - Series B |

Volume | 18 |

Issue number | 8 |

DOIs | |

State | Published - Oct 2013 |

Externally published | Yes |

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### Keywords

- Age-structure
- Effective reproduction number
- Endemic equilibrium
- Human papillomavirus
- Vaccination

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete and Continuous Dynamical Systems - Series B*,

*18*(8), 2151-2174. https://doi.org/10.3934/dcdsb.2013.18.2151

**Qualitative analysis of an age-and sex-structured vaccination model for human papillomavirus.** / Malik, Tufail; Gumel, Abba; Elbasha, Elamin.

Research output: Contribution to journal › Article

*Discrete and Continuous Dynamical Systems - Series B*, vol. 18, no. 8, pp. 2151-2174. https://doi.org/10.3934/dcdsb.2013.18.2151

}

TY - JOUR

T1 - Qualitative analysis of an age-and sex-structured vaccination model for human papillomavirus

AU - Malik, Tufail

AU - Gumel, Abba

AU - Elbasha, Elamin

PY - 2013/10

Y1 - 2013/10

N2 - A new model for the transmission dynamics of human pappilomavirus (HPV) is designed and analysed. The model, which stratifies the total population in terms of age and gender, incorporates an imperfect anti-HPV vaccine with some therapeutic benefits. Rigorous qualitative analysis of the resulting age-structured model, which takes the form of a deterministic system of non-linear partial differential equations with separable transmission coefficients, shows that the disease-free equilibrium of the model is locallyasymptotically stable whenever the effective reproduction number (denoted by Rv) is less than unity. It is shown to be globally-asymptotically stable if certain additional conditions hold. Furthermore, it is shown that the model has at least one endemic equilibrium when Rv exceeds unity. Hence, the effective control of HPV spread in a community, using a vaccine, is governed by the threshold quantity Rv (the use of the vaccine will lead to effective disease control or elimination only if it reduces the threshold quantity to a value less than unity; and the use of such vaccine will not lead to effective disease control if it fails to make the threshold quantity to be less than unity).

AB - A new model for the transmission dynamics of human pappilomavirus (HPV) is designed and analysed. The model, which stratifies the total population in terms of age and gender, incorporates an imperfect anti-HPV vaccine with some therapeutic benefits. Rigorous qualitative analysis of the resulting age-structured model, which takes the form of a deterministic system of non-linear partial differential equations with separable transmission coefficients, shows that the disease-free equilibrium of the model is locallyasymptotically stable whenever the effective reproduction number (denoted by Rv) is less than unity. It is shown to be globally-asymptotically stable if certain additional conditions hold. Furthermore, it is shown that the model has at least one endemic equilibrium when Rv exceeds unity. Hence, the effective control of HPV spread in a community, using a vaccine, is governed by the threshold quantity Rv (the use of the vaccine will lead to effective disease control or elimination only if it reduces the threshold quantity to a value less than unity; and the use of such vaccine will not lead to effective disease control if it fails to make the threshold quantity to be less than unity).

KW - Age-structure

KW - Effective reproduction number

KW - Endemic equilibrium

KW - Human papillomavirus

KW - Vaccination

UR - http://www.scopus.com/inward/record.url?scp=84886014315&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84886014315&partnerID=8YFLogxK

U2 - 10.3934/dcdsb.2013.18.2151

DO - 10.3934/dcdsb.2013.18.2151

M3 - Article

VL - 18

SP - 2151

EP - 2174

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 8

ER -