Science Journal of Applied Mathematics and Statistics

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Mathematical Modeling of Cervical Cancer with HPV Transmission and Vaccination

Received: 01 March 2019    Accepted: 24 May 2019    Published: 26 June 2019
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Abstract

Cervical cancer is the most common cancer which affects women next to breast cancer in the worldwide. Most cervical cancers are related to Human Papillomavirus (HPV) infection. We can prevent about 40% of cancer through Primary prevention and considered as the most cost-effective way of battling cancer. In this paper I have constructed a mathematical model of cervical cancer with Human papilloma virus transmission with and without vaccination. Infection with human papillomavirus (HPV) is the main cause of cervical cancer. To construct the mathematical model I consider the population in four compartment (the number of susceptible women, the number of infected women with HPV. Since HPV infected human may or may not infected by cervical cancer, we have two additional compartments, the number of Infectious HPV women population who are uninfected with cervical cancer and number of Infectious HPV women population who are infected with cervical cancer. Ordinary differential equation is used to construct the model and dimension less model is obtained, then the model validity lucidly verified using simulation study and mathematical analysis tools. These models have generally shown that vaccinating females can be technique to reduce and control cervical cancer. Essential observations are made from the simulation study and physical interpretations are drawn and presented strongly in the paper.

DOI 10.11648/j.sjams.20190702.13
Published in Science Journal of Applied Mathematics and Statistics (Volume 7, Issue 2, April 2019)
Page(s) 21-25
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

Cervical Cancer, Mathematical Modeling, Numerical Solution, Human Papillomavirus

References
[1] Aweke YH, Ayanto SY, Ersado TL (2017) Knowledge, attitude and practice for cervical cancer prevention and control among women of childbearing age in Hossana Town, Hadiya, zone, Southern Ethiopia: Community-based cross-sectional study. PLoS ONE 12 (7): e0181415.
[2] Netsanet AA. Cervical Cancer: Ethiopia’s Outlook. J Gynecol women’s Health. 2017; 5 (2): 555660. DOI: 10.19080/JGWH.2017.05.555660.
[3] Abdulsamad Engida Sado, Purnachandra Rao Koya. Application of Brody Growth Function to Describe Dynamics of Breast Cancer Cells. American Journal of Applied Mathematics. Vol. 3, No. 3, 2015, pp. 138-145. doi: 10.11648/j. ajam.20150303.20
[4] Federal ministry of health, Ethiopia, Disease prevention and control directorate, national cancer control plan 2016-2020, October 2015.
[5] Lucy W Kivuti-Bitok, Ganesh P Pokhariyal, Geoff McDonnell, Roudsari Abdul. A Mathematical Model of Cervical Cancer in Kenya. International Journal of Science and Research (IJSR). Volume 4 Issue 2, February 2015, ISSN (Online): 2319-7064.
[6] Erik J. Dasbach, Elamin H. Elbasha, and Ralph P. Insinga. Mathematical Models for Predicting the Epidemiologic and Economic Impact of Vaccination against Human Papillomavirus Infection and Disease, Vol. 28, 2006, DOI: 10.1093/epirev/mxj006, Advance Access publication June 1, 2006.
[7] Mesfin Tafa Segni, Hailu Fekadu Demissie, Dagne Mulu Tadesse, Roza Amdemichael, Yonas Teshome Mamo, Amare Worku. Level of Knowledge and Associated Factor toward Cervical Cancer among Women Age (21-64) Years Visiting Health Facilities in Gulele, Sub-city Addis Ababa Ethiopia, JOP. J Pancreas (Online) 2017 Jan 25; 18 (1): 44-48.
[8] Mathematical analysis for modeling, Joudah Rosenbalt; with collaboration of Stoughton Bell.
[9] D M Parkin, S M Moss. An evaluation of screening policies for cervical cancer in England and Wales using a computer simulation model, Journal of Epidemiology and Community Health, 1986, 40, 143-153.
[10] Sue J. GOLDIE, Daniel GRIMA, Michele Kohthomas c. wright, Milton Weinsteinand Eduardo Franco, A Comprehensive Natural History Model Of HPV Infection And Cervical Cancer to Estimate The Clinical Impact Of A Prophylactic Hpv-16/18 Vaccine.
[11] Barnabas RV, Laukkanen P, Koskela P, Kontula O, Lehtinen M, et al. (2006) Epidemiology of HPV 16 and cervical cancer in Finland and the potential impact of vaccination: Mathematical modelling analyses.
[12] Moscicki A, Hills N, Shiboski S, et al. Risks for incidence human papillomavirus infection and low-grade squamous intraepithelial lesion development in young females. JAMA 2001; 285: 2995–3002.
[13] Manhart LE, Koutsky LA (2002) Do condoms prevent genital HPV infection, external genital warts, or cervical neoplasia? A meta-analysis. Sex Transm Dis 29: 725–735.
[14] What you need to know about Cervical cancer, National Cancer Institute, US. Department of health and human services, National Institute of Health.
[15] Lowy DR, Schiller JT. Papillomaviruses: prophylactic vaccine prospects. Biochimica et Biophysica Acta 1998; 1423: M1–M8. 1998.
Author Information
  • Mathematics Department’s, College of Natural and Computational Sciences, Bule Hora University, Bule Hora, Ethiopia

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    Abdulsamad Engida Sado. (2019). Mathematical Modeling of Cervical Cancer with HPV Transmission and Vaccination. Science Journal of Applied Mathematics and Statistics, 7(2), 21-25. https://doi.org/10.11648/j.sjams.20190702.13

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    Abdulsamad Engida Sado. Mathematical Modeling of Cervical Cancer with HPV Transmission and Vaccination. Sci. J. Appl. Math. Stat. 2019, 7(2), 21-25. doi: 10.11648/j.sjams.20190702.13

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    AMA Style

    Abdulsamad Engida Sado. Mathematical Modeling of Cervical Cancer with HPV Transmission and Vaccination. Sci J Appl Math Stat. 2019;7(2):21-25. doi: 10.11648/j.sjams.20190702.13

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  • @article{10.11648/j.sjams.20190702.13,
      author = {Abdulsamad Engida Sado},
      title = {Mathematical Modeling of Cervical Cancer with HPV Transmission and Vaccination},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {7},
      number = {2},
      pages = {21-25},
      doi = {10.11648/j.sjams.20190702.13},
      url = {https://doi.org/10.11648/j.sjams.20190702.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.sjams.20190702.13},
      abstract = {Cervical cancer is the most common cancer which affects women next to breast cancer in the worldwide. Most cervical cancers are related to Human Papillomavirus (HPV) infection. We can prevent about 40% of cancer through Primary prevention and considered as the most cost-effective way of battling cancer. In this paper I have constructed a mathematical model of cervical cancer with Human papilloma virus transmission with and without vaccination. Infection with human papillomavirus (HPV) is the main cause of cervical cancer. To construct the mathematical model I consider the population in four compartment (the number of susceptible women, the number of infected women with HPV. Since HPV infected human may or may not infected by cervical cancer, we have two additional compartments, the number of Infectious HPV women population who are uninfected with cervical cancer and number of Infectious HPV women population who are infected with cervical cancer. Ordinary differential equation is used to construct the model and dimension less model is obtained, then the model validity lucidly verified using simulation study and mathematical analysis tools. These models have generally shown that vaccinating females can be technique to reduce and control cervical cancer. Essential observations are made from the simulation study and physical interpretations are drawn and presented strongly in the paper.},
     year = {2019}
    }
    

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    T1  - Mathematical Modeling of Cervical Cancer with HPV Transmission and Vaccination
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    DO  - 10.11648/j.sjams.20190702.13
    T2  - Science Journal of Applied Mathematics and Statistics
    JF  - Science Journal of Applied Mathematics and Statistics
    JO  - Science Journal of Applied Mathematics and Statistics
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    EP  - 25
    PB  - Science Publishing Group
    SN  - 2376-9513
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    AB  - Cervical cancer is the most common cancer which affects women next to breast cancer in the worldwide. Most cervical cancers are related to Human Papillomavirus (HPV) infection. We can prevent about 40% of cancer through Primary prevention and considered as the most cost-effective way of battling cancer. In this paper I have constructed a mathematical model of cervical cancer with Human papilloma virus transmission with and without vaccination. Infection with human papillomavirus (HPV) is the main cause of cervical cancer. To construct the mathematical model I consider the population in four compartment (the number of susceptible women, the number of infected women with HPV. Since HPV infected human may or may not infected by cervical cancer, we have two additional compartments, the number of Infectious HPV women population who are uninfected with cervical cancer and number of Infectious HPV women population who are infected with cervical cancer. Ordinary differential equation is used to construct the model and dimension less model is obtained, then the model validity lucidly verified using simulation study and mathematical analysis tools. These models have generally shown that vaccinating females can be technique to reduce and control cervical cancer. Essential observations are made from the simulation study and physical interpretations are drawn and presented strongly in the paper.
    VL  - 7
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