• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.559-578
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• 2015

Human Immune Deficiency Virus (or simply HIV) induces a persistent infection that leads to AIDS causing death in almost every infected individual. As HIV affects the immune system directly by attacking the CD4+ T cells, to exterminate the infection, the natural immune system produces virus-specific cytotoxic T lymphocytes(CTLs) that kills the infected CD4+ T cells. The reduced CD4+ T cell count produce reduced amount of cytokines to stimulate the production of CTLs to fight the invaders that weakens the body immunity succeeding to AIDS. In this paper, we introduce a mathematical model with discrete time-delay to represent this cell dynamics between CD4+ T cells and the CTLs under HIV infection. A modified functional form has been considered to describe the infection mechanism. Characteristics of the system are studied through mathematical analysis. Numerical simulations are carried out to illustrate the analytical findings.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.555-574
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• 2011

It is well known that the mathematical models provide very important information for the research of human immunodeciency virus type. However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T-cells and the viral particles. In this paper, a differential equation model of HIV infection of $CD4^+$ T-cells with Crowley-Martin function response is studied. We prove that if the basic reproduction number $R_0$ < 1, the HIV infection is cleared from the T-cell population and the disease dies out; if $R_0$ > 1, the HIV infection persists in the host. We find that the chronic disease steady state is globally asymptotically stable if $R_0$ > 1. Numerical simulations are presented to illustrate the results.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.779-794
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• 2012

In this paper, we study the global stability of two mathematical models for human immunodeficiency virus (HIV) infection with intra-cellular delays. The first model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, $CD4^+$ T cells and macrophages taking into account the saturation infection rate. The second model generalizes the first one by assuming that the infection rate is given by Beddington-DeAngelis functional response. Two time delays are used to describe the time periods between viral entry the two classes of target cells and the production of new virus particles. Lyapunov functionals are constructed and LaSalle-type theorem for delay differential equation is used to establish the global asymptotic stability of the uninfected and infected steady states of the HIV infection models. We have proven that if the basic reproduction number $R_0$ is less than unity, then the uninfected steady state is globally asymptotically stable, and if the infected steady state exists, then it is globally asymptotically stable for all time delays.

• Journal of Microbiology and Biotechnology
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• v.32 no.12
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• pp.1515-1526
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• 2022

Eukaryotic chromatin is highly organized in the 3D nuclear space and dynamically regulated in response to environmental stimuli. This genomic organization is arranged in a hierarchical fashion to support various cellular functions, including transcriptional regulation of gene expression. Like other host cellular mechanisms, viral pathogens utilize and modulate host chromatin architecture and its regulatory machinery to control features of their life cycle, such as lytic versus latent status. Combined with previous research focusing on individual loci, recent global genomic studies employing conformational assays coupled with high-throughput sequencing technology have informed models for host and, in some cases, viral 3D chromosomal structure re-organization during infection and the contribution of these alterations to virus-mediated diseases. Here, we review recent discoveries and progress in host and viral chromatin structural dynamics during infection, focusing on a subset of DNA (human herpesviruses and HPV) as well as RNA (HIV, influenza virus and SARS-CoV-2) viruses. An understanding of how host and viral genomic structure affect gene expression in both contexts and ultimately viral pathogenesis can facilitate the development of novel therapeutic strategies.

• Tuberculosis and Respiratory Diseases
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• v.74 no.3
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• pp.104-110
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• 2013

Background: Notified tuberculosis (TB) cases in Korea have not decreased over the last decade (2001-2010). Methods: To clarify the reasons, we analyzed an annual report on notified tuberculosis patients and age-specific population drift in Korea. Results: Compared to the age-specific notified TB cases between 2001 and 2010, distinctive features in notified TB cases and new cases increased markedly in people aged 45-54 years and in patients over 65 years old, whereas those between 15-34 years in 2010 decreased drastically. In particular, notified TB individuals over 65 years old occupied 29.6% of the cases in 2010, which was 1.5 times higher than that in 2001. The main reason not to decrease in notified TB patients for the last decade (2001-2010) was due to the increasing elderly population as well as the aging of baby boomers, which have a higher risk of TB development. Conclusion: Korea needs to pay attention to the older population in order to successfully decrease the burden of TB in the future.

• Computers and Concrete
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• v.34 no.1
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• pp.63-77
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• 2024

In this research, we considered fractional order optimal control models for cancer, HIV treatment and glucose.These models are based on fractional order differential equations that describe the dynamics underlying the disease.It is formulated in term of left and right Caputo fractional derivative. Pontryagin's Maximum Principle is used as a necessary condition to find the optimal curve for the respective controls over fixed time period. The formulated problems are numerically solved using forward backward sweep method with generalized Euler scheme.