A Modified Iterative Algorithm for Numerical Investigation of HIV Infection Dynamics

The human immunodeficiency virus (HIV) mainly attacks CD4+ T cells in the host. Chronic HIV infection gradually depletes the CD4+ T cell pool, compromising the host’s immunological reaction to invasive infections and ultimately leading to acquired immunodeficiency syndrome (AIDS). The goal of this s...

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Veröffentlicht in:	Algorithms Jg. 15; H. 5; S. 175
Hauptverfasser:	Ghosh, Indranil, Rashid, Muhammad Mahbubur, Mawa, Shukranul, Roy, Rupal, Ahsan, Md Manjurul, Uddin, Muhammad Ramiz, Gupta, Kishor Datta, Ghosh, Pallabi
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Basel MDPI AG 01.05.2022
Schlagworte:	Acquired immune deficiency syndrome AIDS Algorithms Banach spaces COVID-19 Decomposition Dengue fever Differential equations Dynamic characteristics Exact solutions HIV HIV infection model Human immunodeficiency virus Immune system Immunology Infections Infectious diseases Iterative algorithms Iterative methods Laplace transform Lymphocytes Mathematical models Methods modified iterative algorithm new iterative method Nonlinear dynamics Nonlinear systems ordinary differential equation Quantum field theory Runge-Kutta method Variables
ISSN:	1999-4893, 1999-4893
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Abstract	The human immunodeficiency virus (HIV) mainly attacks CD4+ T cells in the host. Chronic HIV infection gradually depletes the CD4+ T cell pool, compromising the host’s immunological reaction to invasive infections and ultimately leading to acquired immunodeficiency syndrome (AIDS). The goal of this study is not to provide a qualitative description of the rich dynamic characteristics of the HIV infection model of CD4+ T cells, but to produce accurate analytical solutions to the model using the modified iterative approach. In this research, a new efficient method using the new iterative method (NIM), the coupling of the standard NIM and Laplace transform, called the modified new iterative method (MNIM), has been introduced to resolve the HIV infection model as a class of system of ordinary differential equations (ODEs). A nonlinear HIV infection dynamics model is adopted as an instance to elucidate the identification process and the solution process of MNIM, only two iterations lead to ideal results. In addition, the model has also been solved using NIM and the fourth order Runge–Kutta (RK4) method. The results indicate that the solutions by MNIM match with those of RK4 method to a minimum of eight decimal places, whereas NIM solutions are not accurate enough. Numerical comparisons between the MNIM, NIM, the classical RK4 and other methods reveal that the modified technique has potential as a tool for the nonlinear systems of ODEs.
AbstractList	The human immunodeficiency virus (HIV) mainly attacks CD4+ T cells in the host. Chronic HIV infection gradually depletes the CD4+ T cell pool, compromising the host’s immunological reaction to invasive infections and ultimately leading to acquired immunodeficiency syndrome (AIDS). The goal of this study is not to provide a qualitative description of the rich dynamic characteristics of the HIV infection model of CD4+ T cells, but to produce accurate analytical solutions to the model using the modified iterative approach. In this research, a new efficient method using the new iterative method (NIM), the coupling of the standard NIM and Laplace transform, called the modified new iterative method (MNIM), has been introduced to resolve the HIV infection model as a class of system of ordinary differential equations (ODEs). A nonlinear HIV infection dynamics model is adopted as an instance to elucidate the identification process and the solution process of MNIM, only two iterations lead to ideal results. In addition, the model has also been solved using NIM and the fourth order Runge–Kutta (RK4) method. The results indicate that the solutions by MNIM match with those of RK4 method to a minimum of eight decimal places, whereas NIM solutions are not accurate enough. Numerical comparisons between the MNIM, NIM, the classical RK4 and other methods reveal that the modified technique has potential as a tool for the nonlinear systems of ODEs.
Author	Rashid, Muhammad Mahbubur Roy, Rupal Gupta, Kishor Datta Mawa, Shukranul Uddin, Muhammad Ramiz Ghosh, Indranil Ghosh, Pallabi Ahsan, Md Manjurul
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SubjectTerms	Acquired immune deficiency syndrome AIDS Algorithms Banach spaces COVID-19 Decomposition Dengue fever Differential equations Dynamic characteristics Exact solutions HIV HIV infection model Human immunodeficiency virus Immune system Immunology Infections Infectious diseases Iterative algorithms Iterative methods Laplace transform Lymphocytes Mathematical models Methods modified iterative algorithm new iterative method Nonlinear dynamics Nonlinear systems ordinary differential equation Quantum field theory Runge-Kutta method Variables
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Title	A Modified Iterative Algorithm for Numerical Investigation of HIV Infection Dynamics
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