Abstract
Human papillomavirus (HPV) has been a prevalent virus for a long time. The number of cancer cases from benign tumours is constantly increasing and HPV is playing an important role, more aggressively is evolving as cervical cancer in young females. More than 170 types of HPV virus exists and among them some are “High-risk” variety, some are “Low-risk” variety. The control of this virus outbreak remains a challenge till date. The aim of this study is to investigate the role of vaccination as a control strategy in decreasing of the spread of the disease. In this research article, we formulated a model considering high-risk-type HPV, low-risk-type HPV, and low–high risk (infected by both low-risk and high-risk)-type HPV. We derive the basic reproduction ratio and also show that there exists a disease-free equilibrium, which is locally asymptotically stable. Furthermore, an analysis is then performed on crucial parameters in order to determine their importance and potential impact on HPV dynamics. Our analytical and numerical analysis reveals that HPV infection can be reduced by using vaccination as a control strategy.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bergot, A.S., Kassianos, A., Frazer, I.A., Mittal, D.: New Approaches to immunotherapy for HPV associated cancers. Open Access, Cancers 3, 346–3495 (2011). doi:10.3390/cancers3033461
Crow, J.M.: HPV: the global burden. Nature 488, S2–S3 (2012). doi:10.1038/488S2a
Bosch, F.X., Lorincz, A., Munoz, N., Meijer, C.J.L.M., Shah, K.V.: The causal relation between human papillomavirus and cervical cancer. J. Clin. Pathol. 55(4), 244–265 (2002)
Chaturvedi, A.K.: Beyond cervical cancer: burden of other HPV-related cancers among men and women. J. Adolesc. Health 46(4), S20–S26 (2010)
Insinga, R.P., Dasbach, E.J., Elbasha, E.H.: Epidemiologic natural history and clinical management of Human Papillomavirus (HPV) Disease: a critical and systematic review of the literature in the development of an HPV dynamic transmission model. BMC Infect. Dis. 9, article 119 (2009)
Lowy, D.R., Schiller, J.T.: Prophylactic human papillomavirus vaccines. J. Clin. Investigat. 116, 1167–1173 (2006)
Hariri, S., Unger, E.R., Sternberg, M., et al.: Prevalence of genital human papillomavirus among females in the United States, the National Health and Nutrition Examination Survey, 2003–2006. J. Infect. Dis. 204(4), 566–573 (2011)
Dunne, E.F., Unger, E.R., Sternberg, M., McQuillan, G., Swan, D.C., Patel, S.S., Markowitz, L.E.: Prevalence of HPV infection among females in the United States. JAMA 297(8), 813–819 (2007)
Schlipk\(\ddot{0}\)ter, U.: Communicable diseases: achievements and challenges for public health. Public Health Rev. 32(1), 90 (2010)
Burd, E.M.: Human Papillomavirus and Cervical Cancer. Clin. Microbiol. Rev. 16, 1–17 (2003)
Reiter, P.L., Brewer, N.T., Gottlieb, S.L., McRee, A.L., Smith, J.S.: How much will it hurt? HPV vaccine side effects and influence on completion of the three-dose regimen. Vaccine 27(49), 6840–6844 (2009)
Brinth, L., Theibel, A.C., Pors, K., Mehlsen, J.: Suspected side effects to the quadrivalent human papilloma vaccine. Dan. Med. J. 62(4), A5064 (2015)
McLaughlin-Drubin, M.E., Meyers, C.: Evidence for the coexistence of two genital HPV types within the same host cell in vitro. Virology 321, 173–180 (2004)
Smith, R.J., Li, J., Mao, J., Saha, B.: Can. Appl. Math. Q. 21(2) (2015)
Mori, Seiichiro, Kusumoto-Matsuo, Rika, Ishii, Yoshiyuki, Takeuchi, Takamasa, Kukimoto, Iwao: Replication interference between human papillomavirus types 16 and 18 mediated by heterologous E1 helicases. Virol. J. 11, 11 (2014)
Mathematical Models for Therapeutic Approaches to Control HIV Disease Transmission published by Springer in 2016. ISBN: 978-981-287-851-9 (Print) 978-981-287-852-6 (Online)
Roy, P.K., Chatterjee, A.N.: Effect of HAART on CTL mediated immune cells: an optimal control theoretic approach. Electr. Eng. Appl. Comp. Springer 90, 595–607 (2011)
Chatterjee, A.N., Roy, P.K.: Anti-viral drug treatment along with immune activator IL-2: A control based mathematical approach for HIV infection. Int. J. Control 85(2), 220–237 (2012)
Chowdhury, S., Roy, P.K., Smith, R.J.: Mathematical modelling of enfuvirtide and protease inhibitors as combination therapy for HIV. Int. J. Nonlinear Sci. Numer. Simul. 17(6), 259–275 (2016)
Barnabas, R.V., Laukkanen, P., Koskela, P., Kontula, O., Lehtinen, M., Garnett, G.P.: Epidemiology of HPV 16 and cervical cancer in Finland and the potential impact of vaccination: mathematical modelling analyses. PLOS Med 3(0624), 0632 (2006)
Baussano, I., Ronco, G., Segnan, N., French, K., Vineis, P., Garnett, G.P.: HPV-16 infection and cervical cancer: modeling the influence of duration of infection and precancerous lesions. Epidemics 2, 21–28 (2010)
Brown, V., White, K.A.: The HPV vaccination strategy: could male vaccination have an impact? Comput. Math. Methods Med. 11, 223–237 (2010)
Tchuenche, J.M., Dube, N., Bhunu, C.P., Smith, R.J., Bauch, C.T.: The impact of media coverage on the transmission dynamics of human influenza. BMC Public Health 11(1), 1 (2011)
Shaban, N., Mofi, H.: Int. J. Math. Anal. 8(9), 441–454 (2014)
Van den Driessche, P., Watmough, J.: Reproduction numbers and Sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Bio-sci. 180, 29–48 (2002)
Acknowledgements
The research is supported by Government of India, DST PURSE and UGC DRS Programme, Department of Mathematics, Jadavpur University. Sonia Chowdhury is supported by UGC - Dr.D.S. Kothari Post Doctoral Fellowship (No. F.4-2/2006(BSR)/MA/14-15/0038, 5 May 2015).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Chakraborty, S., Pal, J., Chowdhury, S., Roy, P.K. (2017). The Impact of Vaccination to Control Human Papillomavirus Dynamics. In: Manchanda, P., Lozi, R., Siddiqi, A. (eds) Industrial Mathematics and Complex Systems. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-10-3758-0_16
Download citation
DOI: https://doi.org/10.1007/978-981-10-3758-0_16
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-3757-3
Online ISBN: 978-981-10-3758-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)