Journal ArticleDOI
Optimal control of an HIV immunology model
TLDR
In this paper, a system of ordinary differential equations, which describes the interaction of HIV and T-cells in the immune system is utilized, and optimal controls representing drug treatment strategies of this model are explored.Abstract:
A system of ordinary differential equations, which describes the interaction of HIV and T-cells in the immune system is utilized, and optimal controls representing drug treatment strategies of this model are explored. Two types of treatments are used, and existence and uniqueness results for the optimal control pair are established. The optimality system is derived and then solved numerically using an iterative method with a Runge–Kutta fourth order scheme. Copyright © 2002 John Wiley & Sons, Ltd.read more
Citations
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Journal ArticleDOI
Stability analysis and optimal vaccination of an SIR epidemic model
TL;DR: This paper describes an SIR epidemic model with three components; S, I and R, and describes the study of stability analysis theory to find the equilibria for the model and shows that an optimal control exists for the control problem.
Journal ArticleDOI
Dynamic multidrug therapies for hiv: optimal and sti control approaches.
TL;DR: A dynamic mathematical model is formulated that describes the interaction of the immune system with the human immunodeficiency virus and that permits drug "cocktail" therapies and supports a scenario in which STI therapies can lead to long-term control of HIV by the immune response system after discontinuation of therapy.
Journal ArticleDOI
HIV dynamics: Modeling, data analysis, and optimal treatment protocols
Brian M. Adams,Harvey Thomas Banks,Marie Davidian,Hee-Dae Kwon,Hien T. Tran,Shannon N. Wynne,Eric S. Rosenberg +6 more
TL;DR: In this article, the authors present an overview of some concepts and methodologies useful in modeling HIV pathogenesis, including parameter estimation, data reduction and representation, and optimal control relative to STI.
Journal ArticleDOI
The impact of media coverage on the transmission dynamics of human influenza.
TL;DR: A deterministic transmission and vaccination model is formulated to investigate the effects of media coverage on the transmission dynamics of influenza and shows that the media can trigger a vaccinating panic if the vaccine is imperfect and simplified messages result in the vaccinated mixing with the infectives without regard to disease risk.
Journal ArticleDOI
Global properties of a class of HIV models
TL;DR: In this paper, the authors study the global properties of a class of human immunodeficiency virus (HIV) models and construct Lyapunov functions to establish the global asymptotic stability of the uninfected and infected steady states.
References
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Book
Mathematical Theory of Optimal Processes
TL;DR: The fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems as discussed by the authors, which can be applied in a variety of situations, including linear equations with variable coefficients.
Journal ArticleDOI
The Mathematical Theory of Optimal Processes
Richard Bellman,L. S. Pontryagin,V. G. Boltyanskii,Revaz Valerianovich Gamkrelidze,E. F. Mishchenko,K. N. Trirogoff,Lucien W. Neustadt +6 more
Book
Deterministic and stochastic optimal control
TL;DR: In this paper, the authors considered the problem of optimal control of Markov diffusion processes in the context of calculus of variations, and proposed a solution to the problem by using the Euler Equation Extremals.
Journal ArticleDOI
The Mathematical Theory of Optimal Processes
TL;DR: The Mathematical Theory of Optimal Processes (MTOP) as mentioned in this paper is a mathematical theory of optimal processes that is closely related to our approach to optimal process analysis, but with a different focus.
Journal ArticleDOI
Dynamics of HIV infection of CD4+ T cells
TL;DR: A model for the interaction of HIV with CD4+ T cells that considers four populations, characterized by generating differing numbers of infective virions within infected T cells, can cause different amounts of T-cell depletion and generate depletion at different rates.