A Modified Iterative Algorithm for Numerical Investigation of HIV Infection Dynamics

Algorithms

Muhammad Ramiz Uddin¹  Kishor Datta Gupta²  Rupal Roy³  Muhammad Mahbubur Rashid³  Indranil Ghosh⁴  Pallabi Ghosh⁵  Shukranul Mawa⁶  Md Manjurul Ahsan⁷ 

[1] Department of Chemistry and Biochemistry, University of Oklahoma, Norman, OK 73019, USA;Department of Computer Science, Clark Atlanta University, Atlanta, GA 30314, USA;Department of Mechatronics Engineering, Faculty of Engineering, International Islamic University Malaysia, Jalan Gombak, Kuala Lumpur 53100, Malaysia;Department of Science in Engineering, Faculty of Engineering, International Islamic University Malaysia, Jalan Gombak, Kuala Lumpur 53100, Malaysia;Department of Teaching English as Second Language, Faculty of Education, International Islamic University Malaysia, Jalan Gombak, Kuala Lumpur 53100, Malaysia;Faculty of Pharmacy, Universiti Kebangsaan Malaysia, Jalan Raja Muda Abdul Aziz, Kuala Lumpur 50300, Malaysia;School of Industrial & Systems Engineering, University of Oklahoma, Norman, OK 73019, USA;

关键词: new iterative method;    Laplace transform;    HIV infection model;    ordinary differential equation;    modified iterative algorithm;    Runge–Kutta method;   

DOI  :  10.3390/a15050175

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown