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Cervical Cancer and HIV Diseases Co-dynamics with Optimal Control and Cost Effectiveness

Received: 22 June 2017     Accepted: 7 July 2017     Published: 4 August 2017
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Abstract

The deterministic model for co-infection of cervical cancer and HIV (Human Immunodeficiency Virus) diseases is formulated and rigorously analyzed. The optimal control theory is employed to the model to study the level of effort is needed to control the transmission of co-infection of cervical cancer and HIV diseases using three controls; prevention, screening and treatment control strategies. Numerical solutions show a remarkable decrease of infected individuals with HPV (Human Papilloma Virus) infection, cervical cancer, cervical cancer and HIV, cervical cancer and AIDS (Acquire Immunodeficiency Syndrome), HIV infection and AIDS after applying the combination of the optimal prevention, screening and treatment control strategies. However, Incremental Cost-Effective Ratio (ICER) shows that the best control strategy of minimizing cervical cancer among HIV-infected individuals with low cost is to use the combination of prevention and treatment control strategies.

Published in Pure and Applied Mathematics Journal (Volume 6, Issue 4)
DOI 10.11648/j.pamj.20170604.14
Page(s) 124-136
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), 2017. Published by Science Publishing Group

Keywords

HPV Infection, HIV Infection, Cervical Cancer, Optimal Control, Cost-Effectiveness

References
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[2] S. M. Mbulaiteye, E. T. Katabira, H. Wabinga, D. M. Parkin, P. Virgo, R. Ochai, M. Workneh, A. Coutinho, and E. A. Engels, “Spectrum of cancers among HIV-infected persons in Africa: The Uganda AIDS-Cancer registry match study,” Int. J. Cancer, 2006, vol. 118, no. 4, pp. 985–990.
[3] C. Ng’andwe, J. J. Lowe, P. J. Richards, L. Hause, C. Wood, and P. C. Angeletti, “The distribution of sexually-transmitted human papillomaviruses in HIV positive and negative patients in Zambia, Africa.,” BMC Infect. Dis., 2007, vol. 7, pp. 77.
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[6] K. O. Okosun and O. D. Makinde, “Optimal control analysis of malaria in the presence of non-linear incidence rate,” Appl. Comput. Math., 2013, vol. 12, no. 1, pp. 20–32.
[7] K. O. Okosun, O. D. Makinde, and I. Takaidza, “Analysis of recruitment and industrial human resources management for optimal productivity in the presence of the HIV/AIDS epidemic,” J. Biol. Phys., 2013, vol. 39, no. 1, pp. 99–121.
[8] S. Lenhart and J. T. Workman, Optimal control applied to biological models dynamic optimization, 2007.
[9] W. H. Fleming and R. W. Rishel, Deterministic and stochastic optimal control, Springer-Verlag, Berlin Heidelberg New York, 1975.
[10] K. O. Okosun, O. D. Makinde, and I. Takaidza, “Impact of optimal control on the treatment of HIV/AIDS and screening of unaware infectives,” Appl. Math. Model., 2013, vol. 37, no. 6, pp. 3802–3820.
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[12] S. L. Lee and A. M. Tameru, “A mathematical model of human papillomavirus (HPV) in the united states and its impact on cervical cancer,” J. Cancer, 2012, vol. 3, no. 1, pp. 262–268.
[13] R. Federation, S. Africa, and S. Lanka, “Cervical cancer global crisis card,” Cerv. Cancer Free Coalit., 2013.
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  • APA Style

    Geomira George Sanga, Oluwole Daniel Makinde, Estomih Shedrack Massawe, Lucy Namkinga. (2017). Cervical Cancer and HIV Diseases Co-dynamics with Optimal Control and Cost Effectiveness. Pure and Applied Mathematics Journal, 6(4), 124-136. https://doi.org/10.11648/j.pamj.20170604.14

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    ACS Style

    Geomira George Sanga; Oluwole Daniel Makinde; Estomih Shedrack Massawe; Lucy Namkinga. Cervical Cancer and HIV Diseases Co-dynamics with Optimal Control and Cost Effectiveness. Pure Appl. Math. J. 2017, 6(4), 124-136. doi: 10.11648/j.pamj.20170604.14

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    AMA Style

    Geomira George Sanga, Oluwole Daniel Makinde, Estomih Shedrack Massawe, Lucy Namkinga. Cervical Cancer and HIV Diseases Co-dynamics with Optimal Control and Cost Effectiveness. Pure Appl Math J. 2017;6(4):124-136. doi: 10.11648/j.pamj.20170604.14

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  • @article{10.11648/j.pamj.20170604.14,
      author = {Geomira George Sanga and Oluwole Daniel Makinde and Estomih Shedrack Massawe and Lucy Namkinga},
      title = {Cervical Cancer and HIV Diseases Co-dynamics with Optimal Control and Cost Effectiveness},
      journal = {Pure and Applied Mathematics Journal},
      volume = {6},
      number = {4},
      pages = {124-136},
      doi = {10.11648/j.pamj.20170604.14},
      url = {https://doi.org/10.11648/j.pamj.20170604.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20170604.14},
      abstract = {The deterministic model for co-infection of cervical cancer and HIV (Human Immunodeficiency Virus) diseases is formulated and rigorously analyzed. The optimal control theory is employed to the model to study the level of effort is needed to control the transmission of co-infection of cervical cancer and HIV diseases using three controls; prevention, screening and treatment control strategies. Numerical solutions show a remarkable decrease of infected individuals with HPV (Human Papilloma Virus) infection, cervical cancer, cervical cancer and HIV, cervical cancer and AIDS (Acquire Immunodeficiency Syndrome), HIV infection and AIDS after applying the combination of the optimal prevention, screening and treatment control strategies. However, Incremental Cost-Effective Ratio (ICER) shows that the best control strategy of minimizing cervical cancer among HIV-infected individuals with low cost is to use the combination of prevention and treatment control strategies.},
     year = {2017}
    }
    

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    T1  - Cervical Cancer and HIV Diseases Co-dynamics with Optimal Control and Cost Effectiveness
    AU  - Geomira George Sanga
    AU  - Oluwole Daniel Makinde
    AU  - Estomih Shedrack Massawe
    AU  - Lucy Namkinga
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    N1  - https://doi.org/10.11648/j.pamj.20170604.14
    DO  - 10.11648/j.pamj.20170604.14
    T2  - Pure and Applied Mathematics Journal
    JF  - Pure and Applied Mathematics Journal
    JO  - Pure and Applied Mathematics Journal
    SP  - 124
    EP  - 136
    PB  - Science Publishing Group
    SN  - 2326-9812
    UR  - https://doi.org/10.11648/j.pamj.20170604.14
    AB  - The deterministic model for co-infection of cervical cancer and HIV (Human Immunodeficiency Virus) diseases is formulated and rigorously analyzed. The optimal control theory is employed to the model to study the level of effort is needed to control the transmission of co-infection of cervical cancer and HIV diseases using three controls; prevention, screening and treatment control strategies. Numerical solutions show a remarkable decrease of infected individuals with HPV (Human Papilloma Virus) infection, cervical cancer, cervical cancer and HIV, cervical cancer and AIDS (Acquire Immunodeficiency Syndrome), HIV infection and AIDS after applying the combination of the optimal prevention, screening and treatment control strategies. However, Incremental Cost-Effective Ratio (ICER) shows that the best control strategy of minimizing cervical cancer among HIV-infected individuals with low cost is to use the combination of prevention and treatment control strategies.
    VL  - 6
    IS  - 4
    ER  - 

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Author Information
  • Department of Mathematics, University of Dar es Salaam, Dar es Salaam, Tanzania

  • Faculty of Military Science, Stellenbosch University, Saldanha, South Africa

  • Department of Mathematics, University of Dar es Salaam, Dar es Salaam, Tanzania

  • Department of Molecular Biology and Biotechnology, University of Dar es Salaam, Dar es Salaam, Tanzania

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