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

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.

DOI	10.11648/j.ajam.20190703.11
Published in	American Journal of Applied Mathematics (Volume 7, Issue 3, June 2019)
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), 2024. Published by Science Publishing Group

Keywords

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

References

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[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.
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[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
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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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