The impact of an imperfect vaccine and pap cytologyscreening on the transmission of human papillomavirus and occurrenceof associated cervical dysplasia and cancer
A mathematical model for the natural history of human papillomavirus(HPV) is designed and used to assess the impact of a hypotheticalanti-HPV vaccine and Pap cytology screening on the transmissiondynamics of HPV in a population. Rigorous qualitative analysis ofthe model reveals that it undergoes the...
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| Format: | Article |
| Language: | English |
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AIMS Press
2013-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1173 |
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| author | Tufail Malik Jody Reimer Abba Gumel Elamin H. Elbasha Salaheddin Mahmud |
| author_facet | Tufail Malik Jody Reimer Abba Gumel Elamin H. Elbasha Salaheddin Mahmud |
| author_sort | Tufail Malik |
| collection | DOAJ |
| description | A mathematical model for the natural history of human papillomavirus(HPV) is designed and used to assess the impact of a hypotheticalanti-HPV vaccine and Pap cytology screening on the transmissiondynamics of HPV in a population. Rigorous qualitative analysis ofthe model reveals that it undergoes the phenomenon of backwardbifurcation. It is shown that the backward bifurcation is caused bythe imperfect nature of the HPV vaccine or the HPV-induced andcancer-induced mortality in females. For the case when thedisease-induced and cancer-induced mortality is negligible, it isshown that the disease-free equilibrium (i.e., equilibrium in theabsence of HPV and associated dysplasia) is globally-asymptoticallystable if the associated reproduction number is less than unity. Themodel has a unique endemic equilibrium when the reproductionthreshold exceeds unity. The unique endemic equilibrium isglobally-asymptotically stable for a special case, where theassociated HPV-induced and cancer-induced mortality is negligible.Numerical simulations of the model, using a reasonable set ofparameter values, support the recent recommendations by some medicalagencies and organizations in the USA to offer Pap screening on a3-year basis (rather than annually). |
| format | Article |
| id | doaj-art-bd2a1ef6beac4afc95d98a048201fd5b |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-bd2a1ef6beac4afc95d98a048201fd5b2025-01-24T02:26:20ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-05-011041173120510.3934/mbe.2013.10.1173The impact of an imperfect vaccine and pap cytologyscreening on the transmission of human papillomavirus and occurrenceof associated cervical dysplasia and cancerTufail Malik0Jody Reimer1Abba Gumel2Elamin H. Elbasha3Salaheddin Mahmud4Department of Applied Mathematics and Sciences, Khalifa University of Science, Technology and Research, PO Box 127788, Abu DhabiDepartment of Applied Mathematics and Sciences, Khalifa University of Science, Technology and Research, PO Box 127788, Abu DhabiDepartment of Applied Mathematics and Sciences, Khalifa University of Science, Technology and Research, PO Box 127788, Abu DhabiDepartment of Applied Mathematics and Sciences, Khalifa University of Science, Technology and Research, PO Box 127788, Abu DhabiDepartment of Applied Mathematics and Sciences, Khalifa University of Science, Technology and Research, PO Box 127788, Abu DhabiA mathematical model for the natural history of human papillomavirus(HPV) is designed and used to assess the impact of a hypotheticalanti-HPV vaccine and Pap cytology screening on the transmissiondynamics of HPV in a population. Rigorous qualitative analysis ofthe model reveals that it undergoes the phenomenon of backwardbifurcation. It is shown that the backward bifurcation is caused bythe imperfect nature of the HPV vaccine or the HPV-induced andcancer-induced mortality in females. For the case when thedisease-induced and cancer-induced mortality is negligible, it isshown that the disease-free equilibrium (i.e., equilibrium in theabsence of HPV and associated dysplasia) is globally-asymptoticallystable if the associated reproduction number is less than unity. Themodel has a unique endemic equilibrium when the reproductionthreshold exceeds unity. The unique endemic equilibrium isglobally-asymptotically stable for a special case, where theassociated HPV-induced and cancer-induced mortality is negligible.Numerical simulations of the model, using a reasonable set ofparameter values, support the recent recommendations by some medicalagencies and organizations in the USA to offer Pap screening on a3-year basis (rather than annually).https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1173cervical cancervaccineendemic equilibrium.backward bifurcationhuman papillomaviruspap cytology screening |
| spellingShingle | Tufail Malik Jody Reimer Abba Gumel Elamin H. Elbasha Salaheddin Mahmud The impact of an imperfect vaccine and pap cytologyscreening on the transmission of human papillomavirus and occurrenceof associated cervical dysplasia and cancer Mathematical Biosciences and Engineering cervical cancer vaccine endemic equilibrium. backward bifurcation human papillomavirus pap cytology screening |
| title | The impact of an imperfect vaccine and pap cytologyscreening on the transmission of human papillomavirus and occurrenceof associated cervical dysplasia and cancer |
| title_full | The impact of an imperfect vaccine and pap cytologyscreening on the transmission of human papillomavirus and occurrenceof associated cervical dysplasia and cancer |
| title_fullStr | The impact of an imperfect vaccine and pap cytologyscreening on the transmission of human papillomavirus and occurrenceof associated cervical dysplasia and cancer |
| title_full_unstemmed | The impact of an imperfect vaccine and pap cytologyscreening on the transmission of human papillomavirus and occurrenceof associated cervical dysplasia and cancer |
| title_short | The impact of an imperfect vaccine and pap cytologyscreening on the transmission of human papillomavirus and occurrenceof associated cervical dysplasia and cancer |
| title_sort | impact of an imperfect vaccine and pap cytologyscreening on the transmission of human papillomavirus and occurrenceof associated cervical dysplasia and cancer |
| topic | cervical cancer vaccine endemic equilibrium. backward bifurcation human papillomavirus pap cytology screening |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1173 |
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