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World J Virology. Nov 12, 2015; 4(4): 356-364
Published online Nov 12, 2015. doi: 10.5501/wjv.v4.i4.356
Human immunodeficiency virus/acquired immune deficiency syndrome: Using drug from mathematical perceptive
Amar Nath Chatterjee, Shubhankar Saha, Priti Kumar Roy
Amar Nath Chatterjee, Shubhankar Saha, Priti Kumar Roy, Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
Author contributions: All authors had equally contributed to this work.
Conflict-of-interest statement: The authors state that there are no conflicts of interest regarding the publication of this work.
Open-Access: This article is an open-access article which was selected by an in-house editor and fully peer-reviewed by external reviewers. It is distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 4.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited and the use is non-commercial. See: http://creativecommons.org/licenses/by-nc/4.0/
Correspondence to: Dr. Priti Kumar Roy, MSc, MPhil, PhD, Associate Professor, Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, 188, Raja Subodh Chandra Mullick Road, Kolkata 700032, India. pritiju@gmail.com
Telephone: +91-94-32095603
Received: November 2, 2014
Peer-review started: November 2, 2014
First decision: April 22, 2015
Revised: May 19, 2015
Accepted: June 1, 2015
Article in press: June 2, 2015
Published online: November 12, 2015
Abstract

Entry of acquired immune deficiency syndrome virus into the host immune cell involves the participation of various components of host and viral cell unit. These components may be categorized as attachment of the viral surface envelope protein subunit, gp120, to the CD4+ receptor and chemokine coreceptors, CCR5 and CXCR4, present on T cell surface. The viral fusion protein, gp41, the second cleaved subunit of Env undergoes reconfiguration and the membrane fusion reaction itself. Since the CD4+ T cell population is actively involved; the ultimate outcome of human immunodeficiency virus infection is total collapse of the host immune system. Mathematical modeling of the stages in viral membrane protein-host cell receptor-coreceptor interaction and the effect of antibody vaccine on the viral entry into the susceptible host cell has been carried out using as impulsive differential equations. We have studied the effect of antibody vaccination and determined analytically the threshold value of drug dosage and dosing interval for optimum levels of infection. We have also investigated the effect of perfect adherence of drug dose on the immune cell count in extreme cases and observed that systematic drug dosage of the immune cells leads to longer and improved lives.

Keywords: Human immunodeficiency virus, Acquired immune deficiency syndrome, Antibody vaccine, Perfect drug adherence, Impulsive differential equation

Core tip: Use of single-cell antibody-cloning techniques uncover naturally arising, broad and potent human immunodeficiency virus (HIV) neutralizing antibodies. These antibodies can protect against infection and suppress new HIV infection. This antibody vaccination gives new ideas about the fight against the HIV infection. From the analytical study of the effect of antibody vaccination we found the threshold value of drug dosage and dosing interval for optimum levels of infection. We have also investigated the effect of perfect adherence of drug dose on the immune cell count in extreme cases and observed that systematic drug dosage of the immune cells leads to longer and improved lives.