Analysis of delayed HIV-1 dynamics model with inflammatory cytokines and cellular infection
Authors
A. A. Raezah
- Department of Mathematics, Faculty of Science, King Khalid University, Abha 62529, Saudi Arabia.
A. M. Elaiw
- Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia.
- Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut, Egypt.
E. Dahy
- Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut, Egypt.
N. H. Alshamrani
- Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia.
H. Z. Zidan
- Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut, Egypt.
A. A. Abdellatif
- Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut, Egypt.
Abstract
The purpose of this research is to develop a mathematical model to study the
dynamics of human immunodeficiency virus type-1 (HIV-1) infection with
inflammatory cytokines. The model incorporates two modes of infection (viral
and cellular), two immune responses (antibody and cytotoxic T lymphocyte
(CTL)) and two types of distributed-time delays. We demonstrate that the
model's solutions are non-negative and eventually bounded, demonstrating the
suggested model's biological viability. We find the equilibrium points of the
model and get the sufficient conditions for their existence and stability. The
Lyapunov approach is utilized to investigate the global stability of the
equilibria. We determine which parameters most affect the basic reproduction
number using sensitivity analysis. We reformulate our model by including the
influence of three classes of antiretroviral drug therapies. We determine a
critical efficacy for each antiretroviral therapy, after which HIV-1 will be
eradicated entirely if treatment effectiveness surpasses this threshold. We
also establish that the estimated treatment efficacy will be lower than what
is necessary to eliminate the virus entirely if the inflammatory cytokines
and/or cellular infection are ignored. Moreover, we show that time delay has
an identical effect on virus elimination as antiretroviral therapy. It is also
shown that, prolonging time delays can successfully reduce the basic
reproduction number and stop HIV-1 replication. According to our findings,
time delay, cellular infection, and inflammatory cytokines are crucial
components of the HIV-1 model and should not be disregarded. The study's
analytical and numerical findings advance our knowledge of HIV-1 dynamics and
may help develop more effective HIV-1 management plans.
Share and Cite
ISRP Style
A. A. Raezah, A. M. Elaiw, E. Dahy, N. H. Alshamrani, H. Z. Zidan, A. A. Abdellatif, Analysis of delayed HIV-1 dynamics model with inflammatory cytokines and cellular infection, Journal of Mathematics and Computer Science, 35 (2024), no. 1, 52--81
AMA Style
Raezah A. A., Elaiw A. M., Dahy E., Alshamrani N. H., Zidan H. Z., Abdellatif A. A., Analysis of delayed HIV-1 dynamics model with inflammatory cytokines and cellular infection. J Math Comput SCI-JM. (2024); 35(1):52--81
Chicago/Turabian Style
Raezah, A. A., Elaiw, A. M., Dahy, E., Alshamrani, N. H., Zidan, H. Z., Abdellatif, A. A.. "Analysis of delayed HIV-1 dynamics model with inflammatory cytokines and cellular infection." Journal of Mathematics and Computer Science, 35, no. 1 (2024): 52--81
Keywords
- HIV-1
- inflammatory cytokines
- viral and cellular infections
- immune response
- time delay
- global stability
- Lyapunov method
MSC
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