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

Geomira George Sanga; Oluwole Daniel Makinde; Estomih Shedrack Massawe; Lucy Namkinga

doi:doi:10.11648/j.pamj.20170604.14

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

Geomira George Sanga, Oluwole Daniel Makinde, Estomih Shedrack Massawe, Lucy Namkinga

Published in Pure and Applied Mathematics Journal (Volume 6, Issue 4)

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), 2024. Published by Science Publishing Group

Keywords

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

References

[1]	S. E. Hawes, C. W. Critchlow, M. A. Faye Niang, M. B. Diouf, A. Diop, P. Toure, A. Aziz Kasse, B. Dembele, P. Salif Sow, A. M. Coll-Seck, J. M. Kuypers, N. B. Kiviat, H. S. E., C. C. W., F. N. M. A., D. M. B., D. A., T. P., K. A. A., D. B., S. P. S., C.-S. A. M., K. J. M., and K. N. B., “Increased risk of high-grade cervical squamous intraepithelial lesions and invasive cervical cancer among African women with human immunodeficiency virus type 1 and 2 infections,”J. Infect. Dis., 2003, vol. 188, no. 4, pp. 555–563.
[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.
[4]	B. Maregere, “Analysis of co-infection of human immunodeficiency virus with human papillomavirus,” University of KwaZulu-Natal, 2014.
[5]	K. O. Okosun and O. D. Makinde, “A co-infection model of malaria and cholera diseases with optimal control,” Math. Biosci., 2014, vol. 258, pp. 19–32.
[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.
[11]	“Tanzania-life expectance at birth.” [Online]. Available: http://countryeconomy.com/demography/life-expectancy/tanzania. [Accessed: 09-Oct-2016].
[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.
[14]	“HIV and AIDS in Tanzania,” 2015. [Online]. Available: http://www.avert.org/professionals/hiv-around-world/sub-saharan-africa/tanzania. [Accessed: 09-Oct-2016].
[15]	G. G. Sanga, O. D. Makinde, E. S. Massawe and L. Namkinga, “Modelling co-dynamics of cervical cancer and HIV diseases, Glob. J. Appl. Math., 2017, vol. 13, no. 6, pp. 2057-2078.

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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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TY  - JOUR
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
Y1  - 2017/08/04
PY  - 2017
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

Geomira George Sanga

Department of Mathematics, University of Dar es Salaam, Dar es Salaam, Tanzania
Oluwole Daniel Makinde

Faculty of Military Science, Stellenbosch University, Saldanha, South Africa
Estomih Shedrack Massawe

Department of Mathematics, University of Dar es Salaam, Dar es Salaam, Tanzania
Lucy Namkinga

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

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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
Y1  - 2017/08/04
PY  - 2017
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  -

Copy | Download