Mathematical Model for Co-infection of HPV with Cervical Cancer and HIV with AIDS Diseases

E.D. Gurmu¹ , B.K. Bole² , P.R. Koya³

1. Mathematics, Natural Science, Wollega University, Nekemte, Ethiopia.
2. Mathematics, Natural Science, Wollega University, Nekemte, Ethiopia.
3. Mathematics, Natural Science, Wollega University, Nekemte, Ethiopia.

Correspondence should be addressed to: eshetudadi1@gmail.com, Tel.: +251-912-66-30-87.

Section:Research Paper, Product Type: Journal-Paper
Vol.7 , Issue.2 , pp.107-121, Apr-2020

Online published on Apr 30, 2020

Copyright © E.D. Gurmu, B.K. Bole, P.R. Koya . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

329 Views    222 Downloads    80 Downloads

Abstract :
In this paper a deterministic mathematical model for co-infection of HPV with Cervical Cancer and HIV/AIDS diseases has been formulated and rigorously analyzed. Both local and global stability of the disease free equilibrium and endemic of the model was established using basic reproduction number. The results show that in HPV only model, HIV only model and HPV-HIV co-infection model if the basic reproduction is less than one then the solution converges to the disease free steady state and the disease free equilibrium is locally asymptotically stable. The endemic states are considered to exist when the basic reproduction number for each disease is greater than one. Sensitivity analysis of the model was performed on the key parameters to find out their relative significance and potential impact on the transmission dynamics of HPV and HIV separately. Numerical simulations indicate the effect of varying the contact rate parameters on single disease and the co-infection dynamics. As we increase contact rates, the infections increases.

Key-Words / Index Term :
Co-infection, HPV, HIV/AIDS, Cervical Cancer, Stability Analysis, Sensitivity

References :
[1] Eshetu Dadi Gurmu, Purnachandra Rao Koya, “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, (2019).
[2] A.S. Bergot, A. Kassianos, I.A. Frazer, D Mittal,“New Approaches to immunotherapy for HPV associated cancers”, OPEN ACESS, Cancers, 346-3495, (2011). .
[3] D.R. Lowy and J.T, “Schiller Prophylactic human papillomavirus vaccines”. J C Invest. 116(5), 1167-1173,(2006)..
[4] WHO list of priority medical devices for cancer management Geneva: World Health Organization. Licence: CC BY-NC-SA 3.0 IGO, (2017).
[5] Wodarz, D,”Killer Cell Dynamics”, Mathematical and Computational Approaches to Immunology. Springer Verlag, New York, (2007).
[6] N. Rom, S. B. Markowitz, “Environmental and Occupational Medicine”, (2007).
[7] UNAIDSDATA, (2019).
[8] M. M. Polaczek, J. Zych, K. Oniszh, J. Szopin´ski, J. Grudny, and K. Roszkowski-Sliz, “Pneumocystis´ pneumonia in hiv-infected patients with cytomegalovirus co-infection. Two case reports and a literature review”, Advances in Respiratory Medicine, 82(5):458–466, (2014),.
[9] Kalipeni, S. Craddock, J. R. Oppong, and J. Ghosh, “HIV and AIDS in Africa: beyond epidemiology”, (2004).
[10] R. Aris, “Mathematical modelling techniques,” Courier Corporation, (2012)..
[11] R. V. Culshaw and S. Ruan, “A delay-differential equation model of hiv infection of cd4+ t-cells” Mathematical biosciences. 165(1):27–39, (2000).
[12] Udoy S. Basak, Jannatun Nayeem, Chandra N, “Podder Mathematical study of HIV and HSV-II co-infec tion”. American Journal of Mathematics and Statistics, 5(1), 15-23, (2011).
[13] A. Nwankwo1, D. Okuonghae1, “Mathematical Analysis of the Transmission Dynamics of HIV Syphilis Co-infection in the Presence of Treatment for Syphilis”, Bull Math Biol, (2017)..
[14] O. Okosun and R. Smith, “Optimal control analysis of malaria-schistosomiasis co-infection dynamics”, Mathematical biosciences and engineering: MBE, 14(2):377–405, (2017).
[15] G. G. Sanga, O. D. Makinde, E.S. Massawe and L. Namkinga, “Modelling Co-dynamics of Cervical Cancer and HIV Disease”, Glob.J.Appl.Math. , 13(6), 2057-2078, (2017).
[16] P.V.D.Driessche, J.Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission”, Math. Biosci, 180,29–48, (2002).
[17] C. Castillo-Chavez, B. Song, “Dynamical models of tuberculosis and their applications”, Math. Biosci. Eng, 1 (2), 361–404, (2004).
[18] Eshetu Dadi Gurmu and Purnachandra Rao Koya, “Impact of Chemotherapy treatment of SITR Compartmentalization and Modeling of Human Papilloma Virus (HPV)”, IOSR Journal of Mathematics (IOSR – JM), 15(3), 17 – 29, (2019).
[19] Chitnis, N., Hyman, J.M., and Cusching, J. M., ”Determining important Parameters in the spread of malaria through the sensitivity analysis of a mathematical Model”, Bulletin of Mathematical Biology, 70 (5), 1272–12, (2008).