A Mathematical Model for Co-infection of HPV and HSV-II with Drug Resistance Compartment

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.34-46, 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, we proposed and analysed a compartmental HPV-HSV-II coinfection model describing the transmission dynamics of HPV and HSV-II using the stability theory of differential equations. The well possedness of the formulated model equations was proved and the equilibrium points of the model have been identified. In addition, the basic reproductive number that governs the disease transmission was obtained from the largest eigenvalue of the next-generation matrix. Both local and global stability of the disease free equilibrium and endemic equilibrium point of the model equation was established using basic reproduction number. Our model revealed that the disease-free equilibrium of the HPV only model, HSV-II only model and HPV-HSV-II co-infection is locally asymptotically stable when the basic reproduction number is less than one. The endemic states are considered to exist when the basic reproduction number for each model is greater than one. We found from the analysis of the impact of HSV-II on HPV that HPV infection increases the risk of HSV-II similarly; HSV-II infection increases the risk for HPV. Sensitivity analysis was carried out on the model parameters in order to determine their impact on the disease dynamics. Numerical simulations of the model equations was carried out using the software DE Discover 2.6.4 and MATLAB R2015b with ODE45 solver and the results are displayed graphically and discussed. We simulate the HPV-HSV-II coinfection model by varying the force of infection to see its effects on infected HPV population, infected HSV-II population, HPV-HSV-II coinfection population and HSV-II- Cervical Cancer coinfected population. The result illustrated that, as force of infection increases or decreases, the infections increases or decreases.

Key-Words / Index Term :
Co-infection, HPV, HSV-II, Cervical Cancer, Stability, Reproduction number.

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