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### SHERP

A Study on Modeling HIV Infection Dynamics.
항레트로바이러스 감염 역학에 관한 모델링연구.

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Authors
김효은
신동우
Major
자연과학대학 협동과정 계산과학전공
Issue Date
2018
Publisher
서울대학교 대학원
Keywords
HIV infection dynamicslatent reservoirreproductive numberparameter estimationfractional derivative
Description
학위논문 (박사)-- 서울대학교 대학원 : 자연과학대학 협동과정 계산과학전공, 2018. 2. 신동우.
Abstract
A focus of this thesis is to develop a mathematical modeling approach to analyze the clinical data of Human immunodeficiency virus(HIV) acute infection. From the several studies, a remarkable stability of the HIV latent reservoir is detected despite the long-term treatment and advances in anti–retroviral therapy, and it has been recognized as a major barrier to HIV cure. We analyze several nonlinear mathematical models including the one that contains latent reservoir effect which provides consecutive viral replication and derive reproductive number (R0) which is a key index on HIV dynamics. For a quantitative analysis, we estimated parameters best describe time-series viral load measurements, obtained from published clinical study. We implement an efficient estimation method for the relevant parameters and numerical algorithm to solve the HIV infection dynamics. By using a nonlinear least square method for parameter estimation, analysis on the sensitivity parameters are performed for each model. In addition, we can obtain the total contribution of the reservoir processes to the productively infected T lymphocyte cells is also examined.
We also propose a new model for HIV infection dynamics. There has been some researches that some influencing fractions on the dynamics of blood flow have been associated with the severity of HIV infection. In order to explain the rheological behavior of HIV infection in T lymphocyte populations we attempt to modify Latent cell model with fractional order differentiation of order α ∈ (0, 1]. The hemorheological parameters and fractional-order derivative in HIV system embody essential features of influencing fractions on the dynamics of blood flow associated with the severity of HIV infection. We show that the modified model has non-negative, bounded solutions and stable equilibrium points. Optimal fractional order and kinetic parameters are estimated by using the nonlinear weighted least-square method, the Levenberg-Marquardt algorithm, and Adams-type predictor-corrector method is employed for the numerical solution. The numerical results confirm that a value of fractional order (α) representing the rheological behavior in plasma is significantly related with a density of lymphocyte population.
Language
English
URI
http://hdl.handle.net/10371/141162
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College of Natural Sciences (자연과학대학)Program in Computational Science and Technology (협동과정-계산과학전공)Theses (Ph.D. / Sc.D._협동과정-계산과학전공)