Optimal control of an HIV immunology model

Joshi, Hem Raj

doi:10.1002/oca.710

Cited by 343 publications

(275 citation statements)

References 9 publications

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“…H.R. Joshi [11] considered two different treatment strategies (controls) in a mathematical model consisting of only two states: uninfected CD4 + T cells and viral loads. His controls represent immune boosting and viral suppressing drugs.…”

Section: Control Formulationmentioning

confidence: 99%

Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches

Adams

Banks²,

Kwon³

et al. 2004

Mathematical Biosciences and Engineering

176

123

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We formulate a dynamic mathematical model that describes the interaction of the immune system with the human immunodeficiency virus (HIV) and that permits drug "cocktail" therapies. We derive HIV therapeutic strategies by formulating and analyzing an optimal control problem using two types of dynamic treatments representing reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs). Continuous optimal therapies are found by solving the corresponding optimality systems. In addition, using ideas from dynamic programming, we formulate and derive suboptimal structured treatment interruptions (STI) in antiviral therapy that include drug-free periods of immune-mediated control of HIV. Our numerical results support a scenario in which STI therapies can lead to long term control of HIV by the immune response system after discontinuation of therapy.

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Section: Control Formulationmentioning

confidence: 99%

Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches

Adams

Banks²,

Kwon³

et al. 2004

Mathematical Biosciences and Engineering

176

123

View full text Add to dashboard Cite

show abstract

“…Proceedings of the 48th ISCIE International Symposium on Stochastic Systems Theory and Its Applications Fukuoka, Nov. [4][5]2016 Infective Recovered…”

Section: Stochastic Sir Model With Discrete Time Delaymentioning

confidence: 99%

“…Because of the difficulty of an experiment on a human body for infectious disease, mathematical models have become important tools in analyzing the spread and control of infectious diseases [2]- [8]. Up until now a variety of infectious models have been proposed, and many studies have been performed using the proposed models [2][3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of the Stochastic SIR Model with Discrete Delay

Ishikawa¹

2017

Stochastic Systems Theory and its Applications (SSS)

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The purpose of this paper is to propose the stochastic infectious model with time delay and to study the stability of the disease-free steady state. In the prevalence of infectious diseases, environmental change and individual difference cause some kinds of random fluctuations in the infection recovery rate, immune effect, etc. Hence, the stochastic infectious model plays an important role in the analysis of the infection disease. Moreover, in the vector-borne diseases such as malaria and dengue fever, there exists time delay caused by an incubation period in the virus development in the vectors (mosquitoes) on the transmission of disease. Taking these facts into consideration, we propose a stochastic SIR(susceptible-infected-recovered) model with time delay. We analyze stability of the disease-free steady state, and study the influence of time delay and the random noise on the stability by numerical simulations.

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“…Over time, HIV is able to deplete the population of CD4 + T cells, preventing that cytotoxic cells from being deployed. CD4 + T cells count in a healthy person is about 1000 mm −3 , when the cell count reaches 200 mm −3 or below in a HIV-patient, and some opportunistic diseases arises, then the person is classified as having AIDS [3,4].…”

Section: Introductionmentioning

confidence: 99%

The Role of Immune Response in Optimal HIV Treatment Interventions

2018

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A mathematical model for the transmission dynamics of human immunodeficiency virus (HIV) within a host is developed. Our model focuses on the roles of immune response cells or cytotoxic lymphocytes (CTLs). The model includes active and inactive cytotoxic immune cells. The basic reproduction number and the global stability of the virus free equilibrium is carried out. The model is modified to include anti-retroviral treatment interventions and the controlled reproduction number is explored. Their effects on the HIV infection dynamics are investigated. Two different disease stage scenarios are assessed: early-stage and advanced-stage of the disease. Furthermore, optimal control theory is employed to enhance healthy CD4 + T cells, active cytotoxic immune cells and minimize the total cost of anti-retroviral treatment interventions. Two different anti-retroviral treatment interventions (RTI and PI) are incorporated. The results highlight the key roles of cytotoxic immune response in the HIV infection dynamics and corresponding optimal treatment strategies. It turns out that the combined control (both RTI and PI) and stronger immune response is the best intervention to maximize healthy CD4 + T cells at a minimal cost of treatments.

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Optimal control of an HIV immunology model

Cited by 343 publications

References 9 publications

Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches

Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches

Stability Analysis of the Stochastic SIR Model with Discrete Delay

The Role of Immune Response in Optimal HIV Treatment Interventions

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