Stability analysis of general humoral immunity HIV dynamics models with discrete delays and HAART
Volume 18, Issue 4, pp 430--452
http://dx.doi.org/10.22436/jmcs.018.04.05
Publication Date: December 12, 2018
Submission Date: December 24, 2015
Revision Date: November 19, 2018
Accteptance Date: November 22, 2018
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Authors
A. M. Elaiw
- Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
E. Kh. Elnahary
- Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt.
Abstract
We investigate a general HIV infection model with three types of infected
cells: latently infected cells, long-lived productively infected cells, and
short-lived productively infected cells. We consider two kinds of target
cells: CD4\(^{+}\) T cells and macrophages. We incorporate three discrete time
delays into the model. Moreover, we consider the effect of humoral immunity on
the dynamical behavior of the HIV. The HIV-target incidence rate,
production/proliferation, and removal rates of the cells and HIV are
represented by general nonlinear functions. We show that the solutions of the
proposed model are nonnegative and ultimately bounded. We derive two threshold
parameters which determine the stability of the three steady states of the
model. Using Lyapunov functionals, we established the global stability of the
steady states of the model. The theoretical results are confirmed by numerical simulations.
Share and Cite
ISRP Style
A. M. Elaiw, E. Kh. Elnahary, Stability analysis of general humoral immunity HIV dynamics models with discrete delays and HAART, Journal of Mathematics and Computer Science, 18 (2018), no. 4, 430--452
AMA Style
Elaiw A. M., Elnahary E. Kh., Stability analysis of general humoral immunity HIV dynamics models with discrete delays and HAART. J Math Comput SCI-JM. (2018); 18(4):430--452
Chicago/Turabian Style
Elaiw, A. M., Elnahary, E. Kh.. "Stability analysis of general humoral immunity HIV dynamics models with discrete delays and HAART." Journal of Mathematics and Computer Science, 18, no. 4 (2018): 430--452
Keywords
- HIV infection
- humoral immune response
- latency
- viral reservoirs
MSC
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