Stability Analysis of Caputo Fractional Model for HIV Infection
DOI:
https://doi.org/10.29304/jqcm.2020.12.4.713Keywords:
Caputo fractional, HIV virus, CD4 T- cells, Local stability.Abstract
This study presents a partial Caputo model of HIV infection. It has been demonstrated that there is a unique non-passive solution identified in this paper. For a fractional Caputo analysis, we proposed a model that represents HIV infection, and suggested that within the body of a seven-dimensional Caputo fractional organism it is a model that represents the dynamics of HIV. The in vivo micro-Caputo model was not only presented in biological terms, but also mathematically. Infection-free new equilibrium points exist and the local stability of these points is checked. In addition, the next generation matrix method is used to measure the baseline reproduction rate for each HIV strain
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References
[1] UNAIDSUNICEF and World Health Organization, in: Global HIV\AIDS Response: Epidemic Update and Health Sector Progress Towards Universal Access: Progress Report, 2011.
[2] P. Ngina, R. W. Mbogo, and L. S. Luboobi, “HIV drug resistance: Insights from mathematical modelling,” Applied Mathematical Modelling, vol. 75, pp. 141–161, nov 2019.
[3] D. A. Lehman, J. M. Baeten, and C. O. M. et al., “Risk of drug resistance among persons acquiring HIV within a randomized clinical trial of single- or dual-agent preexposure prophylaxis,” Journal of Infectious Diseases, jan 2015.
[4] J.W. Darke, J.J. Holland, “Mutation rates among RNA viruses,” Proc. Natl. Acad. Sci. 96 (24) (1999) 13910-13913.
[5] L. Rong, Z. Feng, and A. S. Perelson, “Emergence of HIV-1 drug resistance during antiretroviral treatment,” Bulletin of Mathematical Biology, vol. 69, pp. 2027–2060, apr 2007.
[6] V. D. Lima, V. S. Gill, B. Yip, R. S. Hogg, J. S. G. Montaner, and P. R. Harrigan, “Increased resilience to the development of drug resistance with modern boosted protease inhibitor–based highly active antiretroviral therapy,” The Journal of Infectious Diseases, vol. 198, pp. 51–58, jul 2008.
[7] N. Tarfulea and P. Read, “A mathematical model for the emergence of HIV drug resistance during periodic bang-bang type antiretroviral treatment,” Involve, a Journal of Mathematics, vol. 8, pp. 401–420, jun 2015.
[8] P. Ngina, R. W. Mbogo, and L. S. Luboobi, “Modelling optimal control of in-host HIV dynamics using different control strategies,” Computational and Mathematical Methods in Medicine, vol. 2018, pp. 1–18, jun 2018.
[9] W. Lin, “Global existence theory and chaos control of fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 332, pp. 709–726, aug 2007.
[10] P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, pp. 29–48, nov 2002.
[11] H. Kheiri and M. Jafari, “Optimal control of a fractional-order model for the HIV/AIDS epidemic,” International Journal of Biomathematics, vol. 11, p. 1850086, oct 2018.
[12] C. J. Silva and D. F. Torres, “Stability of a fractional HIV/AIDS model,” Mathematics and Computers in Simulation, vol. 164, pp. 180–190, oct 2019.
[13] E. Ahmed, A. S. Elgazzar. On fractional order differential equations model for nonlocal epidemics. Physica A. 379: 607-614, 2007.
[14] I. Ameen, Dumitru Baleanu, Hegagi Mohamed Ali, “An efficient algorithm for solving the fractional optimal control of SIRV epidemic model with a combination of vaccination and treatment,” Chaos, Solitons and Fractals 137 (2020) 109892.
[15] Odibat, Z.M., Shawagfeh, N.T, “Generalized Taylors formula,” Appl. Math. Comput. 186, 286–293 (2007).
[16] J. Heesterbeek, K. Dietz, “The concept of in epidemic theory,” Stat. Neerl. 50 (1) (1996) 89–110.
[2] P. Ngina, R. W. Mbogo, and L. S. Luboobi, “HIV drug resistance: Insights from mathematical modelling,” Applied Mathematical Modelling, vol. 75, pp. 141–161, nov 2019.
[3] D. A. Lehman, J. M. Baeten, and C. O. M. et al., “Risk of drug resistance among persons acquiring HIV within a randomized clinical trial of single- or dual-agent preexposure prophylaxis,” Journal of Infectious Diseases, jan 2015.
[4] J.W. Darke, J.J. Holland, “Mutation rates among RNA viruses,” Proc. Natl. Acad. Sci. 96 (24) (1999) 13910-13913.
[5] L. Rong, Z. Feng, and A. S. Perelson, “Emergence of HIV-1 drug resistance during antiretroviral treatment,” Bulletin of Mathematical Biology, vol. 69, pp. 2027–2060, apr 2007.
[6] V. D. Lima, V. S. Gill, B. Yip, R. S. Hogg, J. S. G. Montaner, and P. R. Harrigan, “Increased resilience to the development of drug resistance with modern boosted protease inhibitor–based highly active antiretroviral therapy,” The Journal of Infectious Diseases, vol. 198, pp. 51–58, jul 2008.
[7] N. Tarfulea and P. Read, “A mathematical model for the emergence of HIV drug resistance during periodic bang-bang type antiretroviral treatment,” Involve, a Journal of Mathematics, vol. 8, pp. 401–420, jun 2015.
[8] P. Ngina, R. W. Mbogo, and L. S. Luboobi, “Modelling optimal control of in-host HIV dynamics using different control strategies,” Computational and Mathematical Methods in Medicine, vol. 2018, pp. 1–18, jun 2018.
[9] W. Lin, “Global existence theory and chaos control of fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 332, pp. 709–726, aug 2007.
[10] P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, pp. 29–48, nov 2002.
[11] H. Kheiri and M. Jafari, “Optimal control of a fractional-order model for the HIV/AIDS epidemic,” International Journal of Biomathematics, vol. 11, p. 1850086, oct 2018.
[12] C. J. Silva and D. F. Torres, “Stability of a fractional HIV/AIDS model,” Mathematics and Computers in Simulation, vol. 164, pp. 180–190, oct 2019.
[13] E. Ahmed, A. S. Elgazzar. On fractional order differential equations model for nonlocal epidemics. Physica A. 379: 607-614, 2007.
[14] I. Ameen, Dumitru Baleanu, Hegagi Mohamed Ali, “An efficient algorithm for solving the fractional optimal control of SIRV epidemic model with a combination of vaccination and treatment,” Chaos, Solitons and Fractals 137 (2020) 109892.
[15] Odibat, Z.M., Shawagfeh, N.T, “Generalized Taylors formula,” Appl. Math. Comput. 186, 286–293 (2007).
[16] J. Heesterbeek, K. Dietz, “The concept of in epidemic theory,” Stat. Neerl. 50 (1) (1996) 89–110.
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Published
2020-11-22
How to Cite
Khalaf, S. L., & Lazim, Z. A. (2020). Stability Analysis of Caputo Fractional Model for HIV Infection. Journal of Al-Qadisiyah for Computer Science and Mathematics, 12(4), Math Page 1– 16. https://doi.org/10.29304/jqcm.2020.12.4.713
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