A male-female mathematical model of human papillomavirus (HPV) in African American population

Najat Ziyadi; Najat Ziyadi

doi:10.3934/mbe.2017022

Mathematical Biosciences and Engineering

2017, Volume 14, Issue 1: 339-358. doi: 10.3934/mbe.2017022

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A male-female mathematical model of human papillomavirus (HPV) in African American population

Najat Ziyadi ^,

Department of Mathematics, Morgan State University, Baltimore, MD 21251, USA

Received: 25 November 2015 Accepted: 22 April 2016 Published: 01 January 2017
MSC : 92B05

We introduce mathematical human papillomavirus (HPV) epidemic models (with and without vaccination) for African American females (AAF) and African American males (AAM) with "fitted" logistic demographics and use these models to study the HPV disease dynamics. The US Census Bureau data of AAF and AAM of 16 years and older from 2000 to 2014 is used to "fit" the logistic demographic models. We compute the basic reproduction number, $\mathcal{R}_0$ , and use it to show that $\mathcal{R}_0$ is less than 1 in the African American (AA) population with or without implementation of HPV vaccination program. Furthermore, we obtain that adopting a HPV vaccination policy in the AAF and AAM populations lower $\mathcal{R}_0$ and the number of HPV infections. Sensitivity analysis is used to illustrate the impact of each model parameter on the basic reproduction number.
- HPV,
- logistic demographics,
- basic reproduction number,
- vaccine
Citation: Najat Ziyadi. A male-female mathematical model of human papillomavirus (HPV) in African American population[J]. Mathematical Biosciences and Engineering, 2017, 14(1): 339-358. doi: 10.3934/mbe.2017022

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Abstract

We introduce mathematical human papillomavirus (HPV) epidemic models (with and without vaccination) for African American females (AAF) and African American males (AAM) with "fitted" logistic demographics and use these models to study the HPV disease dynamics. The US Census Bureau data of AAF and AAM of 16 years and older from 2000 to 2014 is used to "fit" the logistic demographic models. We compute the basic reproduction number, $\mathcal{R}_0$ , and use it to show that $\mathcal{R}_0$ is less than 1 in the African American (AA) population with or without implementation of HPV vaccination program. Furthermore, we obtain that adopting a HPV vaccination policy in the AAF and AAM populations lower $\mathcal{R}_0$ and the number of HPV infections. Sensitivity analysis is used to illustrate the impact of each model parameter on the basic reproduction number.

References

[1]	[ A. Alsaleh,A. B. Gumel, Analysis of risk-structured vaccination model for the dynamics of oncogenic and warts-causing HPV types, Bulletin of Mathematical Biology, 76 (2014): 1670-1726.
[2]	[ Black male statistics, Available from: http://blackdemographics.com/black-male-statistics/. Accessed 4/12/2016.
[3]	[ F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology Texts in Applied Mathematics, Springer, New York, NY, 2001.
[4]	[ J. Cariboni,D. Gatelli,R. Liska,A. Saltelli, The role of sensitivity analysis in ecological modelling, Ecological modelling, 203 (2007): 167-182.
[5]	[ Centers for disease control and prevention, Genital HPV infection: CDC fact sheet Available from: http://www.cdc.gov/std/HPV/STDFact-HPV.htm. Accessed 4/12/2016.
[6]	[ Centers for disease control and prevention, National Vital Statistics Reports, Volume 64, Number 2.
[7]	[ Centers for Disease Control and Prevention, Human Papillomavirus (HPV), What is HPV Available from: http://www.cdc.gov/hpv/whatishpv.html. Accessed 4/12/2016.
[8]	[ Centers for Disease Control and Prevention, Morbidity and mortality weekly report, CDC grand rounds: Reducing the burden of HPV-associated cancer and disease, MMWR, Weekly, 63 (2014), 69-72.
[9]	[ Center for Disease Control and Prevention, Morbidity and Mortality Weekly Report, Weekly / Vol. 64 / No. 29. http://www.cdc.gov/mmwr/pdf/wk/mm6429.pdf. Accessed on 4/8/2016.
[10]	[ N. Chitnis,J. M. Hyman,J. M. Cushing, Determining important parameter in the spread of malaria through the sensitivity analysis of mathematical model, Bulletin of Mathematical Biology, 70 (2008): 1272-1296.
[11]	[ S. Hariri, E. Dunne, M. Saraiya, E. Unger and L. Markowitz, Chapter 5: Human papillomavirus, VPD Surveillance Manual, 5th Edition, 2011. Available from: http://www.cdc.gov/vaccines/pubs/surv-manual/chpt05-hpv.pdf. Accessed 4/12/2016.
[12]	[ http://www.census.gov/popest/data/intercensal/national/tables/US-EST00INT-03-BA.xls. Accessed 4/12/2016.
[13]	[ S. Lee,A. Tameru, A mathematical model of human papillomavirus (HPV) in the United States and its impact on cervical cancer, Journal of Cancer, 3 (2012): 262-268.
[14]	[ L. Ribassin-Majed,R. Lounes,S. Clemencon, Deterministic modelling for transmission of human papillomavirus 6/11: Impact of vaccination, Math Med Biol, 31 (2014): 125-149.
[15]	[ H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems Amer. Math. Soc., Rhode Island, 1995.
[16]	[ US Census Bureau, Available from: http://factfinder.census.gov/faces/tableservices/jsf/pages/productview.xhtml?pid=ACS_11_1YR_B01001B&prodType=table. Accessed 8/28/2016.
[17]	[ P. van den Driessche,J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002): 29-48.
[18]	[ N. Ziyadi, Local and global sensitivity analysis of $\mathcal{R}_0 $ in a male and female human papillomavirus (HPV) epidemic model of Moroccans, Journal of Evolution Equations 9 (2016), Accepted.
[19]	[ N. Ziyadi,A.-A. Yakubu, Local and global sensitivity analysis in a discrete-time seis epidemic model, Advances in Dynamical Systems and Applications, 11 (2016): 15-33.

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