Mathematical Modelling of HIV/AIDS Transmission Dynamics with Drug Resistance Compartment
American Journal of Applied Mathematics
Volume 8, Issue 1, February 2020, Pages: 34-45
Received: Nov. 7, 2019; Accepted: Jan. 2, 2020; Published: Feb. 13, 2020
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Authors
Eshetu Dadi Gurmu, Department of Mathematics, Wollega University, Nekemte, Ethiopia
Boka Kumsa Bole, Department of Mathematics, Wollega University, Nekemte, Ethiopia
Purnachandra Rao Koya, Department of Mathematics, Wollega University, Nekemte, Ethiopia
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Abstract
This paper examines a mathematical modelling of HIV/AIDS transmission dynamics with drug resistance compartment. A nonlinear deterministic mathematical model for the problem is proposed using a system of ordinary differential equations. The aim of this study is to investigate the role of passive immunity and drug therapy in reducing the viral replication and transmission of the disease. 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 is obtained from the largest eigenvalue of the next-generation matrix. 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 the disease free equilibrium is locally asymptotically stable if the basic reproduction number is less than unity and unstable if the basic reproduction number is greater than unity. It is observed that if the basic reproduction is less than one then the solution converges to the disease free steady state i.e., disease will wipe out and thus the drug therapy is said to be successful. On the other hand, if the basic reproduction number is greater than one then the solution converges to endemic equilibrium point and thus the infectious cells continue to replicate i.e., disease will persist and thus the drug therapy is said to be unsuccessful. Sensitivity analysis of the model is performed on the key parameters to determine their relative importance and potential impact on the transmission dynamics of HIV/AIDS. Numerical results of the model show that a combination of passive immunity and drug therapy is the best strategy to reduce the disease from the community.
Keywords
HIV, Reproductive Number, Stability Analysis, Drug Therapy
To cite this article
Eshetu Dadi Gurmu, Boka Kumsa Bole, Purnachandra Rao Koya, Mathematical Modelling of HIV/AIDS Transmission Dynamics with Drug Resistance Compartment, American Journal of Applied Mathematics. Vol. 8, No. 1, 2020, pp. 34-45. doi: 10.11648/j.ajam.20200801.16
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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