Jñānābha Special Issue (2018), 22-27
STATISTICAL TIME SERIES ANALYSIS FOR DYNAMICS OF HIV
By
Rashmi Bhardwaj*, Aashima Bangia
USBAS, GGSIPU
Dwarka, Delhi-110078, India.
*Email-id: rashmib22@gmail.com
(Received : November 26, 2017 ; Revised: final from September 06, 2018)
Abstract
HIV has become global disease. These days a lot of people are suffering. Mostly HIV -positive people are not aware that they have been infected. Therefore, a strict check on donor blood and blood products have to be followed. Hence, it becomes important to interpret the chemical mechanism of HIV infection and its spread. It infects a diverse range of immunity cells. It gets carried into the macrophages and CD4+T cells because of the communication among virion wrap glycoproteins with the CD4 molecule on the target cells. These virions then infect a large amount of cellular targets and diffuse into every part of human body. Mathematical modeling for the mechanics of HIV infection has been done to reduce its propagation, find cures for discourse. The model discussed in this paper consists of these states: T, number of cells not infected, I, number of cells infected, V , number of blood virus particles. The non-linear behavior for HIV modelling is studied using time series analysis. Further, statistical tools like Regression, Correlation, Fractal dimension, Hurst Exponent, Predictability Index, Box plot etc. helps to understand the virion behavior in a better way. It is observed that as the state variables changed then the viral dynamics changes behavior from regular to chaotic.
Keywords and phrases: Time series, Statistical Analysis, Regular motion, Chaotic motion, HIV dynamics.
2010 Mathematics Subject Classification: 00A71, 92BXX, 97M60.