Mathematical Biosciences and Engineering, 2013, 10(4): 1173-1205. doi: 10.3934/mbe.2013.10.1173.

Primary: 92D30; Secondary: 37N25.

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

The impact of an imperfect vaccine and pap cytologyscreening on the transmission of human papillomavirus and occurrenceof associated cervical dysplasia and cancer

1. Department of Applied Mathematics and Sciences, Khalifa University of Science, Technology and Research, PO Box 127788, Abu Dhabi
2. Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB
3. Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2
4. Merck Research Laboratories, UG1C-60, PO Box 1000, North Wales, PA 19454-1099
5. Community Health Sciences, University of Manitoba, Winnipeg, Manitoba

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).
  Figure/Table
  Supplementary
  Article Metrics

Keywords cervical cancer; vaccine; endemic equilibrium.; backward bifurcation; Human papillomavirus; Pap cytology screening

Citation: 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, 2013, 10(4): 1173-1205. doi: 10.3934/mbe.2013.10.1173

References

  • 1. BMC Public Health, 8 (2008), 1-12.
  • 2. Mathematics and Computers in Simulation, 82 (2011), 629-652.
  • 3. J. Math. Anal. Appl., 298 (2004), 418-431.
  • 4. Sex. Transm. Infect., 87 (2011), 41-43.
  • 5. Comput. Math. Methods. Med., 11 (2010), 223-237.
  • 6. (2009). Available from: http://www.cancer.ca.
  • 7. Springer-Verlag, New York, 1981.
  • 8. Math. Biosci. Engrg., 1 (2004), 361-404.
  • 9. Discrete Contin. Dyn. Syst. Ser. B., 12 (2009), 279-304.
  • 10. Best Practice & Research Clinical Obstetrics and Gynaecology, 19 (2005), 501-515.
  • 11. J. Math. Biol., 28 (1990), 365-382.
  • 12. J. Math. Biol., 36 (1998), 227-248.
  • 13. Math. Biosci., 197 (2005), 88-117.
  • 14. Bull. Math. Biol., 68 (2006), 577-614.
  • 15. Emerg. Infect. Dis., 13 (2007), 28-41.
  • 16. Bull. Math. Biol., 70 (2008), 894-909.
  • 17. Bull. Math. Biol., 70 (2008), 2126-2176.
  • 18. Int. J. Cancer., 127 (2010), 2893-2917.
  • 19. Arch. Med. Res., 40 (2009), 478-485.
  • 20. CMAJ., 164 (2001), 1017-1025.
  • 21. Math. Biosci., 215 (2008), 11-25.
  • 22. Sustained efficacy and immunogenicity of the human papillomavirus (HPV)-16/17 ASO4-adjuvanted vaccine: Analysis of a randomised placebo-controlled trial up to 6.4 years,
  • 23. Journal of the National Cancer Institute, 96 (2004), 604-615.
  • 24. J. Infect. Dis., 197 (2008), 1653-1661.
  • 25. BMC Public Health, 11 (2011), 1-13.
  • 26. (2012). Available from: http://www.phac-aspc.gc.ca.
  • 27. SIAM Rev., 42 (2000), 599-653.
  • 28. Epidemiology, 13 (2002), 631-639.
  • 29. IARC Monographs on the Evaluation of the Carcinogenic Risks to Humans, (1995). Lyon, France.
  • 30. J. Med. Screen, 16 (2009), 91-97.
  • 31. American Journal of Medicine, 102 (1997), 3-8.
  • 32. Math Biosci., 164 (2000), 183-201.
  • 33. Marcel Dekker, Inc., New York and Basel, 1989.
  • 34. Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1976.
  • 35. AHCPR Pub; No 99-E 010 1999.
  • 36. Math. Biosci. Engrg., 6 (2009), 333-362.
  • 37. N. Engl. J. Med., 348 (2003), 518-527.
  • 38. International Journal of Cancer, 111 (2004), 278-285.
  • 39. Am. J. Epidemiol., 151 (2000), 1158-1171.
  • 40. JAMA., 290 (2003), 781-789.
  • 41. Journal of Adolescent Health, 46 (2010), S12-S19.
  • 42. Can. Appl. Math. Quarterly, 17 (2009), 339-386.
  • 43. (2013). Available from: http://www.phac-aspc.gc.ca/publicat/ccsic-dccuac/pdf/chap_3_e.pdf.
  • 44. (2010). Available from: http://www.phac-aspc.gc.ca.
  • 45. Curr. Diagn. Pathol., 12 (2006), 114-126.
  • 46. Am. J. Clin. Pathol., 137 (2012), 516-542.
  • 47. BMJ., 332 (2006), 61-62.
  • 48. Math. Biosci., 210 (2007), 436-463.
  • 49. Math. Biosci. Engrg., 5 (2008), 145-174.
  • 50. Cambridge University Press, 1995.
  • 51. Math. Biosci., 180 (2002), 29-48.
  • 52. Am. J. Epidemiol., 165 (2007), 762-775.
  • 53. British Journal of Cancer, 95 (2006), 1459-1466.
  • 54. J. Pathol., 189 (1999), 12-19.

 

This article has been cited by

  • 1. Oluwaseun Sharomi, Tufail Malik, A model to assess the effect of vaccine compliance on Human Papillomavirus infection and cervical cancer, Applied Mathematical Modelling, 2017, 47, 528, 10.1016/j.apm.2017.03.025
  • 2. Aliya A. Alsaleh, Abba B. Gumel, Analysis of Risk-Structured Vaccination Model for the Dynamics of Oncogenic and Warts-Causing HPV Types, Bulletin of Mathematical Biology, 2014, 76, 7, 1670, 10.1007/s11538-014-9972-4
  • 3. Fei Xu, Ross Cressman, Voluntary vaccination strategy and the spread of sexually transmitted diseases, Mathematical Biosciences, 2016, 274, 94, 10.1016/j.mbs.2016.02.004
  • 4. Raúl Peralta, Cruz Vargas-De-León, Augusto Cabrera, Pedro Miramontes, Dynamics of High-Risk Nonvaccine Human Papillomavirus Types after Actual Vaccination Scheme, Computational and Mathematical Methods in Medicine, 2014, 2014, 1, 10.1155/2014/542923
  • 5. ALIYA A. ALSALEH, ABBA B. GUMEL, DYNAMICS ANALYSIS OF A VACCINATION MODEL FOR HPV TRANSMISSION, Journal of Biological Systems, 2014, 22, 04, 555, 10.1142/S0218339014500211
  • 6. Tufail Malik, Mudassar Imran, Raja Jayaraman, Optimal control with multiple human papillomavirus vaccines, Journal of Theoretical Biology, 2016, 393, 179, 10.1016/j.jtbi.2016.01.004
  • 7. Ana Gradíssimo, Robert D. Burk, Molecular tests potentially improving HPV screening and genotyping for cervical cancer prevention, Expert Review of Molecular Diagnostics, 2017, 17, 4, 379, 10.1080/14737159.2017.1293525
  • 8. Abba B. Gumel, Jean M.-S. Lubuma, Oluwaseun Sharomi, Yibeltal Adane Terefe, Mathematics of a sex-structured model for syphilis transmission dynamics, Mathematical Methods in the Applied Sciences, 2018, 10.1002/mma.4734
  • 9. A. Omame, R. A. Umana, D. Okuonghae, S. C. Inyama, Mathematical analysis of a two-sex Human Papillomavirus (HPV) model, International Journal of Biomathematics, 2018, 1850092, 10.1142/S1793524518500924
  • 10. Fernando Saldaña, Andrei Korobeinikov, Ignacio Barradas, Optimal Control against the Human Papillomavirus: Protection versus Eradication of the Infection, Abstract and Applied Analysis, 2019, 2019, 1, 10.1155/2019/4567825
  • 11. A. Omame, D. Okuonghae, R.A. Umana, S.C. Inyama, Analysis of a co-infection model for HPV-TB, Applied Mathematical Modelling, 2019, 10.1016/j.apm.2019.08.012

Reader Comments

your name: *   your email: *  

Copyright Info: 2013, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved