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 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).
| 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
Qualitative analysis of an age-and sex-structured vaccination model for human papillomavirus. / Malik, Tufail; Gumel, Abba; Elbasha, Elamin.
In: Discrete and Continuous Dynamical Systems - Series B, Vol. 18, No. 8, 10.2013, p. 2151-2174.Research output: Contribution to journal › Article
}
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
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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 -