Bayesian Methods of Estimation of HIV Replication in a 〖CD〗_4^+ T Using Rayleigh Distribution under the Various Loss Function Approach

G. Meenakshi¹ , S. Lakshmi Priya²

Section:Review Paper, Product Type: Isroset-Journal
Vol.5 , Issue.6 , pp.21-37, Dec-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.2137

Online published on Dec 31, 2018

Copyright © G. Meenakshi, S. Lakshmi Priya . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Human Immuno Deficiency Virus (HIV) infection of humans represents a complex biological system and a great challenge to public health. Novel approaches for analysis and prediction of the infection dynamics based on a multi-scale integration of virus ontogeny and immune reactions are needed to deal with the system complexity. It is known from the literature survey that HIV replication models are represented as first order differential equations. It gives only rate of change of HIV replication with respect to time. But, the parameter estimation and analytical solution of the differential equations are very difficult. So, in this paper, the Bayesian Methodology is used to estimate the HIV replication for the future period per infected CD_4^+ T cell. In the Bayesian Methodology, the prior and current sample information simultaneously is used to obtain the posterior estimation of the parameter which gives effective information for future. In the HIV life cycle, there are seven different stages, such as binding, fusion, reverse transcription, integration, replication, assembly and budding. At the stage of binding, the various viral components bind with the CD_4^+ T cell. Such as a-Surface glycoprotein (gp120),b - transmembrane glycoprotein (gp41) CCR5, c - reverse transcriptase (P66 /P51) are considered to estimate the HIV replication. Therefore, in this paper, a new risk function derived to use the components a, b and c. Finally, posterior parameter of HIV replication in a CD_4^+ T cell is estimated. The estimated parameter is compared with some standard parameter using various loss functions.

Key-Words / Index Term :
HIV Replication, New loss function, Bayes estimator, Risk function

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