Initiation of HIV therapy

In this paper, we numerically show that the dynamics of the HIV system is sensitive to both the initial condition and the system parameters. These phenomena imply that the system is chaotic and exhibits a bifurcation behavior. To control the system, we propose to initiate an HIV therapy based on both the concentration of the HIV-1 viral load and the ratio of the CD4 lymphocyte population to the CD8 lymphocyte population. If the concentration of the HIV-1 viral load is higher than a threshold, then the first type of therapy will be applied. If the concentration of the HIV-1 viral load is lower than or equal to the threshold and the ratio of the CD4 lymphocyte population to the CD8 lymphocyte population is greater than another threshold, then the second type of therapy will be applied. Otherwise, no therapy will be applied. The advantages of the proposed control strategy are that the therapy can be stopped under certain conditions, while the state variables of the overall system is asymptotically stable with fast convergent rate, the concentration of the controlled HIV-1 viral load is monotonic decreasing, as well as the positivity constraint of the system states and that of the dose concentration is guaranteed to be satisfied. Computer numerical simulation results are presented for an illustration

Nonlinear and robust control strategy based on chemotherapy to minimize the HIV concentration in blood plasma

"A nonlinear PI-type control strategy is designed in order to minimize the HIV concentration in blood plasma, via medical drug injection, under the framework of bounded uncertain input disturbances. For control design it is considered a simplified mathematical model of the virus infection as a benchmark. The model is based on mass balances of healthy cells, infected cells, and the virus concentrations. The proposed controller contains a nonlinear feedback PI structure of bounded functions of the regulation error. The closed-loop stability of the system is analyzed via Lyapunov technique, in which robustness against system disturbances is demonstrated. Numerical experiments show a satisfactory performance of the proposed methodology as a HIV therapy, in which the virion particles and the infected CD4+T cells are minimized and, as an interesting result, the drug dosage can be suspended, thus avoiding drug resistance from the virus. Finally, the proposed controller is compared to a standard sliding-mode and hyperbolic tangent controllers showing better performance.

Nonlinear control of HIV-1 infection with a singular perturbation model

Using a singular perturbation approximation, a nonlinear state-space model of HIV-1 infection, having as state variables the number of healthy and infected CD4+T cells and the number of virion particles, is simplified and used to design a control law. The control law comprises an inner block that performs feedback linearizing of the virus dynamics and an outer block implementing an LQ regulator that drives the number of virion particles to a number below the specification. A sensitivity analysis of the resulting law is performed with respect to the model parameter to the infection rate, showing that the controlled system remains stable in the presence of significant changes of this parameter with respect to the nominal value

Nonlinear and Robust Control Strategy Based on Chemotherapy to Minimize the HIV Concentration in Blood Plasma

A nonlinear PI-type control strategy is designed in order to minimize the HIV concentration in blood plasma, via medical drug injection, under the framework of bounded uncertain input disturbances. For control design it is considered a simplified mathematical model of the virus infection as a benchmark. The model is based on mass balances of healthy cells, infected cells, and the virus concentrations. The proposed controller contains a nonlinear feedback PI structure of bounded functions of the regulation error. The closed-loop stability of the system is analyzed via Lyapunov technique, in which robustness against system disturbances is demonstrated. Numerical experiments show a satisfactory performance of the proposed methodology as a HIV therapy, in which the virion particles and the infected CD4+T cells are minimized and, as an interesting result, the drug dosage can be suspended, thus avoiding drug resistance from the virus. Finally, the proposed controller is compared to a standard sliding-mode and hyperbolic tangent controllers showing better performance

Control of infection dynamics, with applications to the HIV disease

The human immunodeficiency virus (HIV) infection, that causes acquired immune deficiency syndrome (AIDS), is a dynamic process that can be modeled via differential equations. The primary goal of this thesis is to show how to drive any initial state into an equilibrium, called the long-term nonprogressor, in which the infected patient does not develop symptoms of AIDS. We first propose three control methods for HIV treatment. These methods are designed for antiretroviral drug therapy and are based on the understanding of the system dynamics. We apply these control strategies to several HIV dynamic models as well as a general disease dynamic model. Then we derive a new output feedback control scheme from one of the proposed methods. To show the feasibility of the output feedback control, the HIV model is studied analytically. This control method guarantees that the immune state is enhanced to a certain level, which is enough for a typical patient to be driven into the long-term nonprogressor. We also investigate methods to estimate approximately the state of the immune system based on the available outputs of the HIV model. The feasibility and effectiveness of the control strategies and estimation ideas are demonstrated by computer simulations. Key Words. HIV dynamic model, AIDS, output feedback control, drug scheduling, biological system analysis

Managing HIV treatment in resource-limited and dynamic environments

Containing the HIV epidemic is one of the most pressing global health care issues. Antiretroviral therapy, the only treatment option for chronic HIV, inhibits the progression of the disease. However, there is a severe shortage of treatment in the developing world, particularly in Sub-Saharan Africa, the area hit the hardest by the epidemic. The current guidelines recommend treating HIV patients until death, known as a nonabandonment policy. HIV-infected patients develop resistant mutations and they benefit marginally from treatment. Therefore, there is an opportunity cost for treating patients until they die. We estimate the price of nonabandonment policies in HIV treatment where resources are limited. We develop a mathematical framework to optimize the allocation of scarce HIV treatment for a broad class of admissible policies. Pursuant to this goal, we develop a Markov model of the progression of a population of susceptible and infected individuals. Then, we restrict our attention to two classes of admissible policies: (i) nonabandonment policies, and (ii) abandonment-permitted policies. The price of nonabandonment policies is estimated by the difference between the optimal solution of these two classes of admissible policies. Since the state spaces of the models are unbounded, solving the allocation problems is intractable. Therefore, we approximate the price of nonabandonment policies by the difference between a lower bound on the best performance of allocation policies in abandonment-permitted settings and an upper bound of that in nonabandonment settings. We show that the price of following the nonabandonment policies in HIV treatment is as much as 41%. Moreover, they shed light on the key role allocation policies play in containing the epidemic. In resource-rich environments, when to start HIV treatment is a fundamental question. Current models do not consider the rate of new antiretroviral development in their analysis. We model the arrival of HIV pipeline drugs in resource-rich environments as a split Poisson process and incorporate it in a validated simulation model to measure the effect of HIV pipeline drugs on HIV treatment. The model with the inclusion of pipeline drugs recommends earlier treatment

A Study of the Synergies Between Control Mechanisms in the Immune System and the Variable Structure Control Paradigm

This thesis argues that variable structure control theory finds application in immunology. The immune system maintains a healthy state by using feedback to switch on and off immune responses. Experimental and mathematical work has analysed the dynamics of the immune response of T cells, relatively little attention has been paid to examine the underlying control paradigm. Besides, in modelling and simulation studies, it is necessary to evaluate the impact of uncertainty and perturbations on immunological dynamics. This is important to deliver robust predictions and insights. These facts motivate considering variable structure control techniques to investigate the control strategy and robustness of the immune system in the context of immunity to infection and tolerance. The results indicate that the dynamic response of T cells following foreign or self-antigen stimulation behaves as a naturally occurring switched control law. Further, the reachability analysis from sliding mode control highlights dynamical conditions to assess the performance and robustness of the T cell response dynamics. Additionally, this approach delivers dynamical conditions for the containment of Human Immunodeficiency Virus (HIV) infection by the HIV-specific CD8+ T cell response and antiretroviral therapy by enforcing a sliding mode on a manifold associated with the infection-free steady-state. This condition for immunity reveals particular patterns for early diagnosis of eventual success, marginal and failure cases of antiretroviral therapy. Together, the findings in this thesis evidence that variable structure control theory presents a useful framework to study health and disease dynamics as well as to monitor the performance of treatment regimes

When to Initiate, When to Switch, and How to Sequence HIV Therapies: A Markov Decision Process Approach

HIV and AIDS are major health care problems throughout the world,with 40 million people living with HIV by the end of 2005. Inthat year alone, 5 million people acquired HIV, and 3 millionpeople died of AIDS. For many patients, advances in therapies overthe past ten years have changed HIV from a fatal disease to achronic, yet manageable condition. The purpose of thisdissertation is to address the challenge of effectively managingHIV therapies, with a goal of maximizing a patient's totalexpected lifetime or quality-adjusted lifetime.Perhaps the most important issue in HIV care is when a patientshould initiate therapy. Benefits of delaying therapy includeavoiding the negative side effects and toxicities associated withthe drugs, delaying selective pressures that induce thedevelopment of resistant strains of the virus, and preserving alimited number of treatment options. On the other hand, the risksof delayed therapy include the possibility of irreversible damageto the immune system, development of AIDS-related complications,and death. We develop a Markov decision process (MDP) model thatexamines this question, and we solve it using clinical data.Because of the development of resistance to administered therapiesover time, an extension to the initiation question arises: whenshould a patient switch therapies? Also, inherent in both theinitiation and switching questions is the question of whichtherapy to use each time. We develop MDP models that consider theswitching and sequencing problems, and we discuss the challengesinvolved in solving these models

Modelling the co-infection dynamics of HIV-1 and M. tuberculosis

This dissertation focuses on the modelling, identification and the parameter estimation for the co-infection of HIV-1 and M. tuberculosis. Many research papers in this field focus primarily on HIV, but multiple infections are explored here, as it is common in many individuals infected by HIV. Tuberculosis is also responsible for the highest number of casualties per year in the group of HIV-infected individuals. A model is proposed to indicate the populations of both pathogen as well as key information factors, such as the overall infected cell population and antigen-presenting cells. Simulations are made to indicate the growth and decline in cell-type numbers for a specific individual. Such simulations would provide a means for further, well-founded investigation into appropriate treatment strategies. One previous such model developed by Kirschner is used to obtain a nominal parameter set. Furthermore, the nominal set is then used in conjunction with real-world samples provided by the National Institute for Communicable Diseases in South Africa, to solidify the credibility of the model in the practical case. This is achieved via simulations and employs parameter estimation techniques, namely the Nelder-Mead cost-function method. An identifiability study of the model is also done. Conclusions drawn from this study include the result that the treatment of M. tuberculosis does not affect the course of HIV-1 progression in a notable way, and that the model can indeed be used in the process of better understanding the disease profile over time of infected individuals.Dissertation (MEng)--University of Pretoria, 2008.Electrical, Electronic and Computer EngineeringMEngunrestricte