Sensitivity Analysis and Modeling the Impact of Screening on the Transmission Dynamics of Human Papilloma Virus (HPV)

Eshetu Dadi Gurmu; Purnachandra Rao Koya

doi:doi:10.11648/j.ajam.20190703.11

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Sensitivity Analysis and Modeling the Impact of Screening on the Transmission Dynamics of Human Papilloma Virus (HPV)

Eshetu Dadi Gurmu, Purnachandra Rao Koya

Published in American Journal of Applied Mathematics (Volume 7, Issue 3)

Received: 21 June 2019 Accepted: 22 July 2019 Published: 26 August 2019

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Abstract

In this paper, a mathematical model on the Human Papilloma Virus (HPV) governed by a system of ordinary differential equations is developed. The aim of this study is to investigate the role of screening as a control strategy in reducing the transmission of the disease. It is shown that a solution for the system of model equations exists and is unique. Further, it is shown that the solution is both bounded and positive. Hence, it is claimed that the model developed and presented in this paper is biologically meaningful and mathematically valid. The model is analyzed qualitatively for verifying the existence and stability of disease free and endemic equilibrium points using threshold parameter that governs the disease transmission. Furthermore, sensitivity analysis is performed on the key parameters driving Human Papilloma Virus and to determine their relative importance and potential impact on the dynamics of Human Papilloma Virus. Numerical result shows that Human Papilloma Virus infection is reduced using screening strategies. Due to the presence of interventions, the number of susceptible cells decreases implying that, most of the susceptible cells are screened. Similarly, the number of unaware infected cells decreases. This happens because unaware cells become aware after screening. The screened infected cells initially increase and then start to diminish after the equilibrium point. This is because many people from screened class recovered through treatment. Also, the number of cells with cancer decreases and this may be due to disease induced death. Furthermore, the number of recovered cells increases because there are two ways of recovering, through immune system or treatment. With =0.5677, implies that screening can reduce the transmission of the disease in the population when <1.

Published in	American Journal of Applied Mathematics (Volume 7, Issue 3)
DOI	10.11648/j.ajam.20190703.11
Page(s)	70-79
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

HPV Infection, Sensitivity Analysis, Screening, Basic Reproduction Number, Stability Analysis, Jacobian Matrix, Numerical Simulation

References

[1]	R. V. Barnabas, P. Laukkanen, P. Koskela, O. Kontula, M. Lehtinen, G. P. Garnett, “Epidemiology of HPV 16 and cervical cancer in Finland and the potential impact of vaccination: mathematical modeling analyses”, PLoS Med. 3 (5) (2006) e138.
[2]	A. S. Bergot, A. Kassianos, I. A. Frazer, D. Mittal, “New Approaches to immunotherapy for HPV associated cancers”, OPEN ACESS, Cancers (2011), 346-3495; doi 10.3390/cancers 3033461.
[3]	D. R. Lowy and J. T. Schiller, “Prophylactic human Papilloma virus vaccines”, J C Invest (2006), 116(5): 1167-1173.
[4]	S. L. Lee and A. M. Tameru, “A Mathematical model of Human Papilloma virus in the United States and its impact on cervical cancer”, Ivyspring International Publisher J cancer (2012) 3: 262-266 doi: 10.7150/jca.4161.
[5]	National Cancer Registry of South Africa. Available online: http://www.cansa.org.za/files/2015/10/NCR_Final_2010_tables1.pdf(accessed on 24 April 2018).
[6]	WHO list of priority medical devices for cancer management?Geneva: World Health Organization; 2017. License: CC BY-NC-SA 3.0 IGO.
[7]	Ntekim A.“Cervical Cancer in Sub Sahara Africa, Topics on Cervical Cancer with an Advocacy for Prevention”. Intech, 2012. Google Scholar.
[8]	Jemal A, et al. “Global cancer statistics”. CA Cancer JClin. 2011; 61(2): p 69-90. PubMed\| Google Scholar.
[9]	Addis Ababa Cancer Registry Data (2012-2014).
[10]	M. Llamazares and R. J. Smith, “Evaluating human Papilloma virus vaccination pro-grams in Canada: should provincial healthcare pay for voluntary adult vaccination”. BioMed Central Ltd Ottawa, Canada, (2008).
[11]	L. Ribassin-Majed and R. Lounes, “A SIS Model for Human Papilloma virus transmission”, 2010, hal-00555733, Version 1-14 Jan (2011).
[12]	L. Ribassin-Majed, R. Lounes, S. Clemencos, “Efficacy of vaccination against HPV infections to prevent cervical cancer in France: Present assessment and Pathways to improve vaccination policies (2012)”, PLoS ONE 7(3): e32251. doi: 10.-1371/journal, Pone 0032251.
[13]	Kermack, W. O.; McKendrick, A. G.” A contribution to the mathematical theory of epidemics”. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, London, UK, August 1927; Volume 115, pp. 700–721.
[14]	AkramAshyani, HajimohammadMohammadinejad, Omid RabieiMotlagh, “Stability Analysis of Mathematical Model of Virus Therapy for Cancer”, Vol. 11, No. 2 (2016), pp 97-110.
[15]	EshetuDadiGurmu and Purnachandra Rao Koya. Impact of Chemotherapy treatment of SITR Compartmentalization and Modeling of Human Papilloma Virus (HPV), IOSR Journal of Mathematics (IOSR – JM), Vol. 15, Issue 3, Ser. I, May – June 2019, Pp 17 – 29. DOI: 10.9790/5728-1503011729http://iosrjournals.org/iosr-jm/papers/Vol15-issue3/Series-1/C1503011729.pdf
[16]	TadeleTesfaTegegne, Purnachandra Rao Koya and TemesgenTibebuMekonnen, “Impact of Heterosexuality and Homosexuality on the transmission and dynamics of HIV/AIDS”, IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 12, Issue 6 Ver. V (Nov. - Dec.2016), PP 38-49.
[17]	Chitnis, N., Hyman, J. M., and Cusching, J. M. (2008). Determining important Parameters in the spread of malaria through the sensitivity analysis of a mathematical Model. Bulletin of Mathematical Biology 70 (5): 1272–12.

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Eshetu Dadi Gurmu, Purnachandra Rao Koya. (2019). Sensitivity Analysis and Modeling the Impact of Screening on the Transmission Dynamics of Human Papilloma Virus (HPV). American Journal of Applied Mathematics, 7(3), 70-79. https://doi.org/10.11648/j.ajam.20190703.11

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ACS Style

Eshetu Dadi Gurmu; Purnachandra Rao Koya. Sensitivity Analysis and Modeling the Impact of Screening on the Transmission Dynamics of Human Papilloma Virus (HPV). Am. J. Appl. Math. 2019, 7(3), 70-79. doi: 10.11648/j.ajam.20190703.11

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AMA Style

Eshetu Dadi Gurmu, Purnachandra Rao Koya. Sensitivity Analysis and Modeling the Impact of Screening on the Transmission Dynamics of Human Papilloma Virus (HPV). Am J Appl Math. 2019;7(3):70-79. doi: 10.11648/j.ajam.20190703.11

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@article{10.11648/j.ajam.20190703.11,
  author = {Eshetu Dadi Gurmu and Purnachandra Rao Koya},
  title = {Sensitivity Analysis and Modeling the Impact of Screening on the Transmission Dynamics of Human Papilloma Virus (HPV)},
  journal = {American Journal of Applied Mathematics},
  volume = {7},
  number = {3},
  pages = {70-79},
  doi = {10.11648/j.ajam.20190703.11},
  url = {https://doi.org/10.11648/j.ajam.20190703.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20190703.11},
  abstract = {In this paper, a mathematical model on the Human Papilloma Virus (HPV) governed by a system of ordinary differential equations is developed. The aim of this study is to investigate the role of screening as a control strategy in reducing the transmission of the disease. It is shown that a solution for the system of model equations exists and is unique. Further, it is shown that the solution is both bounded and positive. Hence, it is claimed that the model developed and presented in this paper is biologically meaningful and mathematically valid. The model is analyzed qualitatively for verifying the existence and stability of disease free and endemic equilibrium points using threshold parameter that governs the disease transmission. Furthermore, sensitivity analysis is performed on the key parameters driving Human Papilloma Virus and to determine their relative importance and potential impact on the dynamics of Human Papilloma Virus. Numerical result shows that Human Papilloma Virus infection is reduced using screening strategies. Due to the presence of interventions, the number of susceptible cells decreases implying that, most of the susceptible cells are screened. Similarly, the number of unaware infected cells decreases. This happens because unaware cells become aware after screening. The screened infected cells initially increase and then start to diminish after the equilibrium point. This is because many people from screened class recovered through treatment. Also, the number of cells with cancer decreases and this may be due to disease induced death. Furthermore, the number of recovered cells increases because there are two ways of recovering, through immune system or treatment. With  =0.5677, implies that screening can reduce the transmission of the disease in the population when <1.},
 year = {2019}
}

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TY - JOUR
T1 - Sensitivity Analysis and Modeling the Impact of Screening on the Transmission Dynamics of Human Papilloma Virus (HPV)
AU - Eshetu Dadi Gurmu
AU - Purnachandra Rao Koya
Y1 - 2019/08/26
PY - 2019
N1 - https://doi.org/10.11648/j.ajam.20190703.11
DO - 10.11648/j.ajam.20190703.11
T2 - American Journal of Applied Mathematics
JF - American Journal of Applied Mathematics
JO - American Journal of Applied Mathematics
SP - 70
EP - 79
PB - Science Publishing Group
SN - 2330-006X
UR - https://doi.org/10.11648/j.ajam.20190703.11
AB - In this paper, a mathematical model on the Human Papilloma Virus (HPV) governed by a system of ordinary differential equations is developed. The aim of this study is to investigate the role of screening as a control strategy in reducing the transmission of the disease. It is shown that a solution for the system of model equations exists and is unique. Further, it is shown that the solution is both bounded and positive. Hence, it is claimed that the model developed and presented in this paper is biologically meaningful and mathematically valid. The model is analyzed qualitatively for verifying the existence and stability of disease free and endemic equilibrium points using threshold parameter that governs the disease transmission. Furthermore, sensitivity analysis is performed on the key parameters driving Human Papilloma Virus and to determine their relative importance and potential impact on the dynamics of Human Papilloma Virus. Numerical result shows that Human Papilloma Virus infection is reduced using screening strategies. Due to the presence of interventions, the number of susceptible cells decreases implying that, most of the susceptible cells are screened. Similarly, the number of unaware infected cells decreases. This happens because unaware cells become aware after screening. The screened infected cells initially increase and then start to diminish after the equilibrium point. This is because many people from screened class recovered through treatment. Also, the number of cells with cancer decreases and this may be due to disease induced death. Furthermore, the number of recovered cells increases because there are two ways of recovering, through immune system or treatment. With =0.5677, implies that screening can reduce the transmission of the disease in the population when <1.
VL - 7
IS - 3
ER -

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Author Information

Eshetu Dadi Gurmu

Department of Mathematics, Wollega University, Nekemte, Ethiopia
Purnachandra Rao Koya

Department of Mathematics, Wollega University, Nekemte, Ethiopia

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APA Style

Eshetu Dadi Gurmu, Purnachandra Rao Koya. (2019). Sensitivity Analysis and Modeling the Impact of Screening on the Transmission Dynamics of Human Papilloma Virus (HPV). American Journal of Applied Mathematics, 7(3), 70-79. https://doi.org/10.11648/j.ajam.20190703.11

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ACS Style

Eshetu Dadi Gurmu; Purnachandra Rao Koya. Sensitivity Analysis and Modeling the Impact of Screening on the Transmission Dynamics of Human Papilloma Virus (HPV). Am. J. Appl. Math. 2019, 7(3), 70-79. doi: 10.11648/j.ajam.20190703.11

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AMA Style

Eshetu Dadi Gurmu, Purnachandra Rao Koya. Sensitivity Analysis and Modeling the Impact of Screening on the Transmission Dynamics of Human Papilloma Virus (HPV). Am J Appl Math. 2019;7(3):70-79. doi: 10.11648/j.ajam.20190703.11

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@article{10.11648/j.ajam.20190703.11,
  author = {Eshetu Dadi Gurmu and Purnachandra Rao Koya},
  title = {Sensitivity Analysis and Modeling the Impact of Screening on the Transmission Dynamics of Human Papilloma Virus (HPV)},
  journal = {American Journal of Applied Mathematics},
  volume = {7},
  number = {3},
  pages = {70-79},
  doi = {10.11648/j.ajam.20190703.11},
  url = {https://doi.org/10.11648/j.ajam.20190703.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20190703.11},
  abstract = {In this paper, a mathematical model on the Human Papilloma Virus (HPV) governed by a system of ordinary differential equations is developed. The aim of this study is to investigate the role of screening as a control strategy in reducing the transmission of the disease. It is shown that a solution for the system of model equations exists and is unique. Further, it is shown that the solution is both bounded and positive. Hence, it is claimed that the model developed and presented in this paper is biologically meaningful and mathematically valid. The model is analyzed qualitatively for verifying the existence and stability of disease free and endemic equilibrium points using threshold parameter that governs the disease transmission. Furthermore, sensitivity analysis is performed on the key parameters driving Human Papilloma Virus and to determine their relative importance and potential impact on the dynamics of Human Papilloma Virus. Numerical result shows that Human Papilloma Virus infection is reduced using screening strategies. Due to the presence of interventions, the number of susceptible cells decreases implying that, most of the susceptible cells are screened. Similarly, the number of unaware infected cells decreases. This happens because unaware cells become aware after screening. The screened infected cells initially increase and then start to diminish after the equilibrium point. This is because many people from screened class recovered through treatment. Also, the number of cells with cancer decreases and this may be due to disease induced death. Furthermore, the number of recovered cells increases because there are two ways of recovering, through immune system or treatment. With  =0.5677, implies that screening can reduce the transmission of the disease in the population when <1.},
 year = {2019}
}

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