A Mathematical Model for the Transmission of HIV/AIDS with Early Treatment
Journal of Advances in Mathematics and Computer Science,
Page 35-51
DOI:
10.9734/jamcs/2021/v36i530362
Abstract
In this paper, a mathematical model for the transmission of HIV/AIDS with early treatment is developed and analyzed to gain insight into early treatment of HIV/AIDS and other epidemiological features that cause the progression from HIV to full blown AIDS. We established the basic reproduction number which is the average number of new secondary infection generated by a single infected individual during infectious period. The analysis shows that the disease free equilibrium is locally and globally asymptotically stable whenever the threshold quantity is less than unity i.e. Numerical analysis shows that the early treatment of latently infected individuals reduces the dynamical progression to full blown AIDS. The result also showed that immunity boosted substances increase the red blood cells, sensitivity analysis of basic reproduction number with respect to parameters showed that effective contact rate must not exceed 0.3 to avoid endemic stage.
Keywords:
- HIV/AIDS
- treatment; reproduction number
- equilibrium points and stability
How to Cite
References
Karrakchou J, Rachik M, Gourari S. “Optimal control and infectiology: Application to an HIV/AIDS model,” Applied Mathematics and Computation. 2006;177(2):807–818.
Ogunlaran OL, Noutchie SC. “ Mathematical model for an effective management of HIV infection, “ Journal of BioMed research international; 2016. Article ID: 421754
Anderson RM. “The role of mathematical models in the study of HIV transmission and the epidemiology of AIDS,” Journal of Acquired Immune Deficiency Syndromes. 1988;1(3):241-256.
Bajaria SH, Webb G, Cloyd M, Kirschner D. “ Dynamics of naïve and memory CD4+T Lymphocytes in HIV-1 disease progression,” Journal of Acquired Immune Deficiency Syndromes. 2002;30(1):41-58.
“HIV treatment as prevention – it works”, The Lancet. 2011;377(9779):1719.
Huo HF, Chen R, Wang XY. Modelling and stability of HIV/AIDS epidemic model with treatment. Appl. Math. Model. 2016;40:6550-6559.
Chibaya S, Kgosimore M. Mathematical analysis of drug resistance in vertical transmission of HIV/AIDS. Open J. Epidemiol. 2013;3(3):139-148.
De Arazoza H, Lounes R. A non-linear model for a sexually transmitted disease with contact tracing. IMA J. Math. Appl. Med. Biol. 2002;19:221-234.
Naresh, R, Tripathi, A, Omar, S: Modelling the spread of AIDS epidemic with vertical transmission.
Appl. Math. Comput. 2006;178:262-272.
Naresh R, Sharma D. An HIV/AIDS model with vertical transmission and time delay. World J. Model. Simul. 2011;7(3):230-240.
Jorge X, Velasco-Hernandez, Ying-Hen Hsieh: Modelling the effect of treatment and behavioral change in HIV transmission dynamic. Journal of Mathematical Biology. 1994;32:233–249.
Adewale SO, Olopade IA, Ajao SO, Mohammed IT. “Mathematical analysis of sensitive parameters on the dynamical spread of HIV”. International Journal of Innovative Research in Science, Engineering and Technology. India. 2016;5(5):2624-2635. Available:http://www.ijirset.com
Olopade IA, Adesanya AO, Mohammed IT, Afolabi MA, Oladapo AO. Mathematical Analysis of the Global Dynamics of an SVEIR Epidemic Model with Herd Immunity. International Journal of Science and Engineering Investigations. (IJSEI), France. 2017;6(69):141-148. Available:http://www.ijsei.com/ins.htm
Lakshmikantham V, Leela S, Martynyuk AA. Stability analysis of Non-Linear system. Marcel Dekker, Inc; New York and Basel; 1989.
Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola. Global Sensiti-vity Analysis: The Primer. Wiley-Interscience; 2008.
Yue H, Brown M, He F, Jia J, Kell D. Sensitivity ana-lysis and robust experimental design of a signal transduc-tion pathway system. Intern. J. Chem. Kinet. 2008;40:730-741.
Mahdavi A, Davey RE, Bhola P, Yin T, Zandstra PW. Sensitivity analysis of intracellular signaling path- way kinetics predicts targets for stem cell fate control PLoS Comput. Biol. 2007;3:e130.
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