A Modified Iterative Algorithm for Numerical Investigation of HIV Infection Dynamics
Indranil Ghosh,
Muhammad Mahbubur Rashid,
Shukranul Mawa,
Rupal Roy,
Md Manjurul Ahsan,
Muhammad Ramiz Uddin,
Kishor Datta Gupta,
Pallabi Ghosh
Affiliations
Indranil Ghosh
Department of Science in Engineering, Faculty of Engineering, International Islamic University Malaysia, Jalan Gombak, Kuala Lumpur 53100, Malaysia
Muhammad Mahbubur Rashid
Department of Mechatronics Engineering, Faculty of Engineering, International Islamic University Malaysia, Jalan Gombak, Kuala Lumpur 53100, Malaysia
Shukranul Mawa
Faculty of Pharmacy, Universiti Kebangsaan Malaysia, Jalan Raja Muda Abdul Aziz, Kuala Lumpur 50300, Malaysia
Rupal Roy
Department of Mechatronics Engineering, Faculty of Engineering, International Islamic University Malaysia, Jalan Gombak, Kuala Lumpur 53100, Malaysia
Md Manjurul Ahsan
School of Industrial & Systems Engineering, University of Oklahoma, Norman, OK 73019, USA
Muhammad Ramiz Uddin
Department of Chemistry and Biochemistry, University of Oklahoma, Norman, OK 73019, USA
Kishor Datta Gupta
Department of Computer Science, Clark Atlanta University, Atlanta, GA 30314, USA
Pallabi Ghosh
Department of Teaching English as Second Language, Faculty of Education, International Islamic University Malaysia, Jalan Gombak, Kuala Lumpur 53100, Malaysia
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.
