• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.475-489
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• 2014

In this paper, a mathematical model for HIV infection with saturating infection rate and time delay is established. By some analytical skills, we study the global asymptotical stability of the viral free equilibrium of the model, and obtain the sufficient conditions for the local asymptotical stability of the other two infection equilibria. Finally, some related numerical simulations are also presented to verify our results.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.12
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• pp.597-603
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• 2001

In the mathematical model for the transmission dynamics of HIV infection described in previous papers, the population under consideration is assumed to be homogeneous community of homosexual males for which the parameter x represents the constant rate at which individual members of the population acquire new sexual partners. This is a gross oversimplification since it is well known that individuals vary widely in their levels of sexual activity and in this papers the heterogeneous model is modified to allow for this variation. The pattern on the epidemic character of HIV, the causative agent of AIDS, was analysed by heterogeneous-mixing model. The computer simulation was performed using real date.

• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.815-822
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• 2001

The aim of this study is to estimate the seroconversion date of the human immunodeficiency virus(HIV) infection for the HIV infected patients in Korea. Data are collected from two cohorts. The first cohort is a group of "seroprevalent" patients who were seropositive and AIDS-free at entry. The other is a group of "seroincident" patients who were initially seronegative but later converted to HIV antibody-positive. The seroconversion dates of the seroincident cohort are available while those of the seroprevalent cohort are not. Estimation of seroconversion date is important because it can be used to calculate the incubation period of AIDS which is defined as the elapsed time between the HIV infection and the development of AIDS. In this paper, a Weibull regression model Is fitted for the seroincident cohort using information about the elapsed time since seroconversion and the CD4$^{+}$ cell count.The seroconversion dates for the seroprevalent cohort are imputed on the basis of the marker of maturity of HIV infection percent of CD4$^{+}$cell count.unt.

• 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.

• International Journal of Control, Automation, and Systems
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• v.1 no.3
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• pp.282-288
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• 2003

It is known that HIV (Human Immunodeficiency Virus) infection, which causes AIDS after some latent period, is a dynamic process that can be modeled mathematically. Effects of available anti-viral drugs, which prevent HIV from infecting healthy cells, can also be included in the model. In this paper we illustrate control theory can be applied to a model of HIV infection. In particular, the drug dose is regarded as control input and the goal is to excite an immune response so that the symptom of infected patient should not be developed into AIDS. Finite horizon optimal control is employed to obtain the optimal schedule of drug dose since the model is highly nonlinear and we want maximum performance for enhancing the immune response. From the simulation studies, we found that gradual reduction of drug dose is important for the optimality. We also demonstrate the obtained open-loop optimal control is vulnerable to parameter variation of the model and measurement noise. To overcome this difficulty, we finally present nonlinear receding horizon control to incorporate feedback in the drug treatment.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1951-1956
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• 2003

It is known that HIV (Human Immunodeficiency Virus) infection, which causes AIDS after some latent period, is a dynamic process that can be modeled mathematically. Effects of available anti-viral drugs, which prevent HIV from infecting healthy cells, can also be included in the model. In this paper we illustrate control theory can be applied to a model of HIV infection. In particular, the drug dose is regarded as control input and the goal is to excite an immune response so that the symptom of infected patient should not be developed into AIDS. Finite horizon optimal control is employed to obtain the optimal schedule of drug dose since the model is highly nonlinear and we want maximum performance for enhancing the immune response. From the simulation studies, we find that gradual reduction of drug dose is important for the optimality. We also demonstrate the obtained open-loop optimal control is vulnerable to parameter variation of the model and measurement noise. To overcome this difficulty, we finally present nonlinear receding horizon control to incorporate feedback in the drug treatment.

• 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.

• Asian Pacific Journal of Cancer Prevention
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• v.16 no.18
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• pp.8085-8091
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• 2016

Human papillomavirus is a virus that is distributed worldwide, and persistent infection with high-risk genotypes (HR-HPV) is considered the most important factor for the development of squamous cell cervical carcinoma (SCC). However, by itself, it is not sufficient, and other factors may contribute to the onset and progression of lesions. For example, infection with other sexually transmitted diseases such as human immunodeficiency virus (HIV) may be a factor. Previous studies have shown the relationship between HPV infection and SCC development among HIV-infected women in many regions of the world, with great emphasis on low- and middle-income countries (LMICs). Brazil is considered a LMIC and has great disparities across different regions. The purpose of this review was to highlight the current knowledge about HPV infection and cervical abnormalities in HIV+ women in Brazil because this country is an ideal setting to evaluate HIV impact on SCC development and serves as model of LMICs and low-resource settings.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.8
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• pp.753-759
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• 2011

The HIV (Human Immunodeficiency Virus) causes AIDS (Acquired Immune Deficiency Syndrome). The process of infection and mutation by HIV can be described by a 3rd order state equation. For this HIV model that includes the dynamics of the mutant virus, we present a parameter estimation scheme using two state variables sporadically measured, out of the three, by employing a genetic algorithm. It is assumed that these non-uniformly sampled measurements are subject to random noises. The effectiveness of the proposed parameter estimation is demonstrated by simulations. In addition, the estimated parameters are used to analyze the equilibrium points of the HIV model, and the results are shown to be consistent with those previously obtained.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.1
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• pp.29-62
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• 2018

We investigate a class of HIV infection models with two kinds of target cells: $CD4^+$ T cells and macrophages. We incorporate three distributed time delays into the models. Moreover, we consider the effect of humoral immunity on the dynamical behavior of the HIV. The viruses are produced from four types of infected cells: short-lived infected $CD4^+$T cells, long-lived chronically infected $CD4^+$T cells, short-lived infected macrophages and long-lived chronically infected macrophages. The drug efficacy is assumed to be different for the two types of target cells. The HIV-target incidence rate is given by bilinear and saturation functional response while, for the third model, both HIV-target incidence rate and neutralization rate of viruses are given by nonlinear general functions. We show that the solutions of the proposed models are nonnegative and ultimately bounded. We derive two threshold parameters which fully determine the positivity and stability of the three steady states of the models. Using Lyapunov functionals, we established the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.