Cervical Cancer and HIV Diseases Co-dynamics with Optimal Control and Cost Effectiveness
Pure and Applied Mathematics Journal
Volume 6, Issue 4, August 2017, Pages: 124-136
Received: Jun. 22, 2017;
Accepted: Jul. 7, 2017;
Published: Aug. 4, 2017
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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
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.
Geomira George Sanga,
Oluwole Daniel Makinde,
Estomih Shedrack Massawe,
Cervical Cancer and HIV Diseases Co-dynamics with Optimal Control and Cost Effectiveness, Pure and Applied Mathematics Journal.
Vol. 6, No. 4,
2017, pp. 124-136.
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.
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.
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.
B. Maregere, “Analysis of co-infection of human immunodeficiency virus with human papillomavirus,” University of KwaZulu-Natal, 2014.
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.
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.
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.
S. Lenhart and J. T. Workman, Optimal control applied to biological models dynamic optimization, 2007.
W. H. Fleming and R. W. Rishel, Deterministic and stochastic optimal control, Springer-Verlag, Berlin Heidelberg New York, 1975.
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.
“Tanzania-life expectance at birth.” [Online]. Available: http://countryeconomy.com/demography/life-expectancy/tanzania. [Accessed: 09-Oct-2016].
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.
R. Federation, S. Africa, and S. Lanka, “Cervical cancer global crisis card,” Cerv. Cancer Free Coalit., 2013.
“HIV and AIDS in Tanzania,” 2015. [Online]. Available: http://www.avert.org/professionals/hiv-around-world/sub-saharan-africa/tanzania. [Accessed: 09-Oct-2016].
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.