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.
 

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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

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