TY - JOUR
T1 - A Computational Approach to a Model for HIV and the Immune System Interaction
AU - Attaullah,
AU - Zeeshan,
AU - Tufail Khan, Muhammad
AU - Alyobi, Sultan
AU - Yassen, Mansour F.
AU - Prathumwan, Din
N1 - Publisher Copyright:
© 2022 by the authors.
PY - 2022/10
Y1 - 2022/10
N2 - This study deals with the numerical solution of the human immunodeficiency virus (HIV) infection model, which is a significant problem for global public health. Acquired immunodeficiency syndrome (AIDS) is a communicable disease, and HIV is the causative agent for AIDS, which damages the ability of the body to fight against disease and easily usual innocuous infections attack the body. On entering the body, HIV infects a large amount of CD4+ T-cells and disturbs the supply rate of these cells from the thymus. Herein, we consider the model with variable source terms in which the production of these cells is a monotonically decreasing function of viral load. Based on the reproduction number, we describe the stability of free equilibrium. The continuous Galerkin–Petrov method, in particular the cGP(2)-method, is implemented to determine the numerical solutions of the model. The influence of different parameters on the population dynamics of healthy/infected CD4+ T-cells and free HIV particles are examined, and the results are presented graphically. On the other hand, the model is solved using the fourth-order Runge–Kutta method, and briefly, the RK4-method, and the results of the proposed schemes are compared with those obtained from other classical schemes such as the Bessel collocation method (BCM), Laplace Adomian decomposition method (LADM), perturbation iteration algorithm (PIA), modified variational iteration method (MVIM), differential transform method (DTM), and exponential Galerkin method (EGM), numerically. Furthermore, absolute errors relative to the RK4 method are computed to describe the accuracy of the proposed scheme. It is presented that the cGP(2)-method gains accurate results at larger time step sizes in comparison with the results of the aforementioned methods. The numerical and graphical comparison reveals that the proposed scheme yields more accurate results relative to other traditional schemes from the literature.
AB - This study deals with the numerical solution of the human immunodeficiency virus (HIV) infection model, which is a significant problem for global public health. Acquired immunodeficiency syndrome (AIDS) is a communicable disease, and HIV is the causative agent for AIDS, which damages the ability of the body to fight against disease and easily usual innocuous infections attack the body. On entering the body, HIV infects a large amount of CD4+ T-cells and disturbs the supply rate of these cells from the thymus. Herein, we consider the model with variable source terms in which the production of these cells is a monotonically decreasing function of viral load. Based on the reproduction number, we describe the stability of free equilibrium. The continuous Galerkin–Petrov method, in particular the cGP(2)-method, is implemented to determine the numerical solutions of the model. The influence of different parameters on the population dynamics of healthy/infected CD4+ T-cells and free HIV particles are examined, and the results are presented graphically. On the other hand, the model is solved using the fourth-order Runge–Kutta method, and briefly, the RK4-method, and the results of the proposed schemes are compared with those obtained from other classical schemes such as the Bessel collocation method (BCM), Laplace Adomian decomposition method (LADM), perturbation iteration algorithm (PIA), modified variational iteration method (MVIM), differential transform method (DTM), and exponential Galerkin method (EGM), numerically. Furthermore, absolute errors relative to the RK4 method are computed to describe the accuracy of the proposed scheme. It is presented that the cGP(2)-method gains accurate results at larger time step sizes in comparison with the results of the aforementioned methods. The numerical and graphical comparison reveals that the proposed scheme yields more accurate results relative to other traditional schemes from the literature.
KW - CD4+ T-cells
KW - computational analysis
KW - immune system
UR - http://www.scopus.com/inward/record.url?scp=85140386090&partnerID=8YFLogxK
U2 - 10.3390/axioms11100578
DO - 10.3390/axioms11100578
M3 - Article
AN - SCOPUS:85140386090
SN - 2075-1680
VL - 11
JO - Axioms
JF - Axioms
IS - 10
M1 - 578
ER -