The impact of an imperfect vaccine and pap cytology screening on the transmission of human papillomavirus and occurrence of associated cervical dysplasia and cancer

Mathematical Biosciences and Engineering

Volumn 10, Issue 4, 2013, Pages 1173-1205

  Malik, Tufail ^a,b   Reimer, Jody ^c   Gumel, Abba ^b   Elbasha, Elamin ^d   Mahmud, Salaheddin ^b,e  

^a KHALIFA UNIVERSITY   (United Arab Emirates)

^b UNIVERSITY OF MANITOBA   (Canada)

^c UNIVERSITY OF OXFORD   (United Kingdom)

^d MERCK RESEARCH LABORATORIES   (United States)

^e WINNIPEG REGIONAL HEALTH AUTHORITY   (Canada)

Author keywords

Backward bifurcation; Cervical cancer; Endemic equilibrium; Human papillomavirus; Pap cytology screening; Vaccine

Indexed keywords

WART VIRUS VACCINE;

ARTICLE; BASIC REPRODUCTION NUMBER; BIOLOGICAL MODEL; COMPUTER SIMULATION; DISEASE TRANSMISSION; FEMALE; HUMAN; HUMAN PAPILLOMAVIRUS TYPE 16; HUMAN PAPILLOMAVIRUS TYPE 18; IMMUNOLOGY; MALE; PAPANICOLAOU TEST; PAPILLOMAVIRUS INFECTION; UNITED STATES; UTERINE CERVIX TUMOR; VIROLOGY;

BASIC REPRODUCTION NUMBER; COMPUTER SIMULATION; FEMALE; HUMAN PAPILLOMAVIRUS 16; HUMAN PAPILLOMAVIRUS 18; HUMANS; MALE; MODELS, IMMUNOLOGICAL; PAPANICOLAOU TEST; PAPILLOMAVIRUS INFECTIONS; PAPILLOMAVIRUS VACCINES; UNITED STATES; UTERINE CERVICAL NEOPLASMS;

EID: 84884491542     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2013.10.1173     Document Type: Article

References (54)

1. M. Llamazares and R. J. Smith, Evaluating human papillomavirus vaccination programs in Canada: Should provincial healthcare pay for voluntary adult vaccination?, BMC Public Health, 8 (2008), 1-12.
2. M. Al-arydah and R. J. Smith, An age-structured model of human papillomavirus vaccination, Mathematics and Computers in Simulation, 82 (2011), 629-652.
3. F. Brauer, Backward bifurcations in simple vaccination models, J. Math. Anal. Appl., 298 (2004), 418-431. (Pubitemid 39615063)
4. M. Brisson, N. Van de Velde and M. C. Boily, Different population-level vaccination effectiveness for HPV types 16, 18, 6 and 11, Sex. Transm. Infect., 87 (2011), 41-43.
5. V. Brown and K. A. J. White, The HPV vaccination strategy: Could male vaccination have a significant impact?, Comput. Math. Methods. Med., 11 (2010), 223-237.
6. Canadian Cancer Society's Steering Committee, "Cancer Statistics 2009," (2009). Available from: http://www.cancer.ca.
7. J. Carr, "Applications of Centre Manifold Theory," Springer-Verlag, New York, 1981.
8. C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Engrg., 1 (2004), 361-404.
9. B. Crawford and C. M. Kribs Zaleta, The impact of vaccination and coinfection on HPV and cervical cancer, Discrete Contin. Dyn. Syst. Ser. B., 12 (2009), 279-304.
10. L. A. Denny and J. T. C. Wright, Human papillomavirus testing and screening, Best Practice & Research Clinical Obstetrics and Gynaecology, 19 (2005), 501-515. (Pubitemid 41263802)
11. 0 in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.
12. J. Dushoff, H. Wenzhang and C. Castillo-Chavez, Backward bifurcations and catastrophe in simple models of fatal diseases, J. Math. Biol., 36 (1998), 227-248. (Pubitemid 128735143)
13. E. H. Elbasha and A. P. Galvani, Vaccination against multiple HPV types, Math. Biosci., 197 (2005), 88-117. (Pubitemid 41764891)
14. E. H. Elbasha and A. B. Gumel, Theoretical assesment of public health impact of imperfect prophylactic HIV-1 vaccines with therapeutic benefits, Bull. Math. Biol., 68 (2006), 577-614. (Pubitemid 44195562)
15. E. H. Elbasha, E. J.Dasbach and R. P. Insinga, Model for assessing human papillomavirus vaccination strategies, Emerg. Infect. Dis., 13 (2007), 28-41. (Pubitemid 46057835)
16. E. H. Elbasha, Global stability of equilibria in a two-sex HPV vaccination model, Bull. Math. Biol., 70 (2008), 894-909.
17. E. H. Elbasha, E. J. Dasbach and R. P. Insinga, A multi-type HPV transmission model, Bull. Math. Biol., 70 (2008), 2126-2176.
18. J. Ferlay, H. R. Shin, F. Bray, D. Forman, C. Mathers and D. M. Parkin, Estimates of worldwide burden of cancer in 2008: GLOBOCAN 2008, Int. J. Cancer., 127 (2010), 2893-2917.
19. E. L. Franco, S. M. Mahmud, J. Tota, A. Ferenczy and F. Coutle, The expected impact of HPV vaccination on the accuracy of cervical cancer screening: The need for a paradigm change, Arch. Med. Res., 40 (2009), 478-485.
20. E. L. Franco, E. Duarte-Franco and A. Ferenczy, Cervical cancer: Epidemiology, prevention and the role of human papillomavirus infection, CMAJ., 164 (2001), 1017-1025. (Pubitemid 34412231)
21. S. M. Garba, A. B. Gumel and M. R. Abu Bakar, Backward bifurcations in dengue transmission dynamics, Math. Biosci., 215 (2008), 11-25.
22. The Glaxo Smith Kline Vaccine HPV-007 Study Group, Sustained efficacy and immunogenic-ity of the human papillomavirus (HPV)-16/17 ASO4-adjuvanted vaccine: Analysis of a ran-domised placebo-controlled trial up to 6.4 years, Lancet., 374 (2009), 1975-1985.
23. S. J. Goldie et al., Projected clinical benefits and cost-effectiveness of a human papillomavirus 16/18 vaccine, Journal of the National Cancer Institute, 96 (2004), 604-615. (Pubitemid 38584984)
24. O. P. Günther et al., Protecting the next generation: What is the role of the duration of Human Papillomavirus vaccine-related immunity?, J. Infect. Dis., 197 (2008), 1653-1661. (Pubitemid 351919628)
25. B. T. Hansen et al., Factors associated with non-attendance, opportunistic attendance and re-minded attendance to cervical screening in an organized screening program: A cross-sectional study of 12,058 Norwegian women, BMC Public Health, 11 (2011), 1-13.
26. Health Canada, "Cervical Cancer Screening Activities in Canada," (2012). Available from: http://www.phac-aspc.gc.ca.
27. H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000), 599-653.
28. J. Hughes, G. Garnett and L. Koutsky, The theoretical population level impact of a prophy-lactic human papillomavirus vaccine, Epidemiology, 13 (2002), 631-639. (Pubitemid 44698466)
29. "International Agency for Research on Cancer" Working Group. Human papillomaviruses, IARC Monographs on the Evaluation of the Carcinogenic Risks to Humans, (1995). Lyon, France.
30. O. Klungsøyr, M. Nygård, G. Skare, T. Eriksen and J. F Nygård, Validity of self-reported Pap smear history in Norwegian women, J. Med. Screen, 16 (2009), 91-97.
31. L. Koutsky, Epidemiology of genital human papillomavirus infection, American Journal of Medicine, 102 (1997), 3-8. (Pubitemid 127695953)
32. C. Kribs-Zaleta and J. Velasco-Hernandez, A simple vaccination model with multiple endemic states, Math Biosci., 164 (2000), 183-201. (Pubitemid 30211016)
33. V. Lakshmikantham, S. Leela and A. A. Martynyuk, "Stability Analysis of Nonlinear Systems," Marcel Dekker, Inc., New York and Basel, 1989.
34. J. P. LaSalle, "The Stability of Dynamical Systems," Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1976.
35. D. C. McCrory and D. B. Matchar, Evaluation of Cervical Cytology. Evidence Re-port/Technology Assessment No. 5;, AHCPR Pub; No 99-E 010 1999.
36. Z. Mukandavire, A. B. Gumel, W. Garira and J. M. Tchuenche, Mathematical analysis of a model for HIV-malaria co-infection, Math. Biosci. Engrg., 6 (2009), 333-362.
37. N. Munoz, F. X. Bosch, S. de Sanjose et al., Epidemiologic Classification of human papillo-mavirus types associated with cervical cancer, N. Engl. J. Med., 348 (2003), 518-527. (Pubitemid 36159887)
38. N. Munoz et al., Against which human papillomavirus types shall we vaccinate and screen? The international perspective, International Journal of Cancer, 111 (2004), 278-285. (Pubitemid 38924707)
39. E. R. Myers et al., Mathematical model for the natural history of human papillomavirus infection and cervical carcinogenesis, Am. J. Epidemiol., 151 (2000), 1158-1171. (Pubitemid 30451948)
40. S. L. Kulasingam and E. R. Myers, Potential health and economic impact of adding a human papillomavirus vaccine to screening programs, JAMA., 290 (2003), 781-789. (Pubitemid 37432955)
41. J. M. Palefsky, Human papillomavirus-related disease in men: Not just a women's issue, Journal of Adolescent Health, 46 (2010), S12-S19.
42. C. N. Podder and A. B. Gumel, Transmission dynamics of a two-sex model for Herpes Simplex Virus type 2, Can. Appl. Math. Quarterly, 17 (2009), 339-386.
43. Public Health Agency of Canada, "Cervical Cancer Screening in Canada," (2013). Available from: http://www.phac-aspc.gc.ca/publicat/ccsic- dccuac/pdf/chap-3-e.pdf.
44. Public Health Agency of Canada, "Human Papillomavirus. HPV Purple Paper (bds)," (2010). Available from: http://www.phac-aspc.gc.ca.
45. P. Sasieni and A. Castanon, Call and recall cervical screening programme: Screening interval and age limits, Curr. Diagn. Pathol., 12 (2006), 114-126. (Pubitemid 43208849)
46. D. Saslow et al., American cancer society, American society for colposcopy and cervical pathology, and American society for clinical pathology screening guidelines for the prevention and early detection of cervical cancer, Am. J. Clin. Pathol., 137 (2012), 516-542.
47. M. Schiffman and P. E. Castle, When to test women for human papillomavirus, BMJ., 332 (2006), 61-62. (Pubitemid 43099240)
48. O. Sharomi, C. N. Podder, A. B. Gumel, E. H. Elbasha and J. Watmough, Role of incidence function in vaccine-induced backward bifurcation in some HIV models, Math. Biosci., 210 (2007), 436-463. (Pubitemid 350116899)
49. O. Sharomi, C. N. Podder, A. B. Gumel and B. Song, Mathematical analysis of the transmission dynamics of HIV/TB co-infection in the presence of treatment, Math. Biosci. Engrg., 5 (2008), 145-174. (Pubitemid 351888843)
50. H. L. Smith and P. Waltman, "The Theory of the Chemostat," Cambridge University Press, 1995.
51. P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48. (Pubitemid 35304346)
52. N. Van de Velde, M. Brisson and M. C. Boily, Modeling human papillomavirus vaccine effectiveness: Quantifying the impact of parameter uncertainty, Am. J. Epidemiol., 165 (2007), 762-775. (Pubitemid 46434599)
53. L. L. Villa et al., High sustained efficacy of a prophylactic quadrivalent human Papillomavirus types 6/11/16/18 virus-like particle vaccine through 5 years of follow-up, British Journal of Cancer, 95 (2006), 1459-1466. (Pubitemid 44863348)
54. J. M. M. Walboomers, Human papillomavirus is a necessary cause of invasive cervical cancer worldwide, J. Pathol., 189 (1999), 12-19. (Pubitemid 29406813)