### Assessing the Impact of Prophylactic Vaccines on HPV Prevalence

#### Abstract

A mathematical model considering female and male individuals is proposed to evaluate vaccination strategies applied to control of HPV transmission in human population. The basic reproductive number of the disease, $R_0$, is given by the geometric mean of the basic reproductive number of female and male populations. The model has a globally asymptotically stable disease-free equilibrium whenever $R_0 <1$. Furthermore, it has an unique endemic state when $R_0$ exceeds unity which is globally asymptotically stable. Numerical simulations were done to compare several different vaccination schedules. The results showed that the vaccination strategies that do not include vaccination of men can only control the disease if more than 90\% of women are vaccinated. The sensitivity analysis indicated that the relevant parameters to control HPV transmission, in order of importance, are vaccine efficacy times the fraction of population that is vaccinated, disease recovery-rate, and disease transmission rate. Therefore, health politics that promoting the increase of vaccine coverage, and screening for the disease in both population can improve disease control.

#### Keywords

#### Full Text:

PDF#### References

A. N. Burchell, R. L. Winer, S. de Sanjosé, and E. L. Franco, “Epidemiol-

ogy and transmission dynamics of genital HPV infection,” Vaccine, vol. 24,

p. DOI:10.1016/j.vaccine.2006.05.031, 2006.

P. E. Gravitt and R. L. Winer, “Natural History of HPV Infection across the

Lifespan: Role of Viral Latency,” Viruses, vol. 9, p. DOI:10.3390/v9100267,

B. Y. Hernandez, L. R. Wilkens, X. Zhu, P. Thompson, M. McDuffi, Y. B.

Shvetsov, L. E. Kamemoto, J. Killeen, L. Ning, and M. T. Goodman, “Trans-

mission of Human Papillomavirus in Heterosexual Couples,” Emerging Infectious Diseases, vol. 14, pp. 888–894, 2008.

A. N. Burchell, F. Coutleé, P. Tellier, J. Hanley, and E. L. Franco, “Geni-

tal Transmission of Human Papillomavirus in Recently Formed Heterosexual Couples,” The Journal of Infectious Diseases, vol. 204, pp. 1723–1729, 2011.

M. Lehtinen, C. Lagheden, T. Luostarinen, T. Eriksson, D. Apter, K. Har-

jula, M. Kuortti, K. Natunen, J. Palmroth, T. Petaja, E. Pukkala, M. Siitari-

Mattila, F. Struyf, P. Nieminen, J. Paavonen, G. Dubin, and J. Dil, “Ten-year

follow-up of human papillomavirus vaccine efficacy against the most stringent cervical neoplasia end-point-registry-based follow-up of three cohorts from randomized trials,” BMJ Open, vol. 7, pp. DOI:10.1136/bmjopen–2017–015867, 2017.

D. M. Harpera and L. R. De Mars, “HPV vaccines - A review of the first

decade,” Gynecologic Oncology, vol. 146, pp. 196–204, 2017.

“Center for disease control and prevention https://www.cdc.gov/nchs/products/databriefs/db280.htm.

(cdc).”

R. Donken, T. M. S. Klooster, R. M. Schepp, F. R. M. van der Klis, M. J.

Knol, C. J. L. M. Meijer, and H. E. de Melker, “Immune Responses After 2

Versus 3 Doses of HPV Vaccination up to 4 1/2 Years After Vaccination: An

Observational Study Among Dutch Routinely Vaccinated Girls,” JID, vol. 215, pp. 359–367, 2017.

M. Stanley, “Immune responses to human papillomavirus,” Vaccine, vol. 24,

p. DOI:10.1016/j.vaccine.2005.09.002, 2006.

M. Stanley, “HPV - immune response to infection and vaccination,” Infectious Agents and Cancer, vol. 5, pp. 19–25, 2010.

S. K. Kjaer, M. Nygard, J. Dillner, J. B. Marshall, D. Radley, M. Li, C. Munk,

B. T. Hansen, L. G. Sigurdardottir, M. Hortlund, L. Tryggvadottir, A. Joshi,

R. Das, and A. J. Saah, “A 12-Year Follow-up on the Long-Term Effectivenessof the Quadrivalent Human Papillomavirus Vaccine in 4 Nordic Countries,” Clinical Infectious Diseases, vol. 66, pp. 339–345, 2018.

C. Fraser, J. E. Tomassini, L. Xi, G. Golm, M. Watson, A. R. Giuliano, E. Barr, and K. A. Ault, “Modeling the long-term antibody response of a human papillomavirus (HPV) virus-like particle (VLP) type 16 prophylactic vaccine,”

Vaccine, vol. 25, pp. 4324–4333, 2007.

S. M. Garland, S. K. Kjaer, N. Muñoz, S. L. Block, D. R. Brown, M. J. DiNu-

bile, B. R. Lindsay, B. J. Kuter, G. Perez, G. D. A. J. Saah, R. Drury, D. Das, and C. Velicer, “Impact and Effectiveness of the Quadrivalent Human Papillomavirus Vaccine: A Systematic Review of 10 Years of Real-world Experience,” Clinical Infectious Diseases, vol. 63, pp. 519–527, 2016.

M. Al-arydah and R. J. Smith, “An age-structured model of human papil-

loma virus vaccination,” Mathematics and Computers in Simulation, vol. 82,

pp. 629–652, 2011.

Malik, J. Reimer, A. Gumel, E. H. Elbasha, and S. Mahmud, “The impact of

an imperfect vaccine and pap cytology screening on the transmission of human papillomavirus and occurrence of associated cervical dysplasia and cancer,” Math Biosci Eng., vol. 13, pp. 1173–1205, 2013.

O. Sharomi and T. Malik, “A model to assess the effect of vaccine compliance on Human Papillomavirus infection and cervical cancer,” Applied Mathematical Modelling, vol. 47, pp. 528–550, 2017.

O. Diekmann and J. A. P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. Wiley, 2000.

P. van den Driessche and J. Watmough, “Reproduction numbers and sub-

threshold endemic equilibria for compartmental models of disease transmission,” Math. Biosci., vol. 180, pp. 29–48, 2002.

J. Hale and H. Ko ̧cak, Dynamics and Bifurcations. Springer-Verlag, 1991.

S. Marino, I. B. Hogue, C. J. Ray, and D. E. Kirschner, “A methodology for

performing global uncertainty and sensitivity analysis in systems biology,” J

Theor Biol., vol. 254, pp. 178–196, 2008.

E. Y. Petrosky, G. Liu, S. Hariri, and L. E. Markowitz, “Human Papillomavirus Vaccination and Age at First Sexual Activity, National Health and Nutrition Examination Survey,” Clin Pediatr (Phila), vol. 56, pp. 363–370, 2017.

DOI: https://doi.org/10.5540/tema.2019.020.02.305

#### Article Metrics

_{Metrics powered by PLOS ALM}

### Refbacks

- There are currently no refbacks.

**TEMA - Trends in Applied and Computational Mathematics**

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

ISSN: 1677-1966 (print version), 2179-8451 (online version)

Indexed in: