تجزیه و تحلیل سیستم های کنترل مدل پیشگیری HIV با استفاده از ورودی ضربه ای

We investigate a control systems analysis on HIV infection dynamics with regard to enhancement of the immune response. The HIV dynamic model is modified to include the pharmacokinetics and pharmacodynamics of antiretroviral HIV drugs, and the intake of drug is considered as impulsive control input. As it is administrated at discrete time instants, we assume that this yields an impulsive control problem for a nonlinear continuous-time system. Based on this new model, we study clinical experiments about antirretoviral treatments via numerical simulation and analyse the experimental results. It is noted that this modeling approach can help to provide a theoretical explanation of the clinical results. The analysis result in the paper could imply that the protocol of the experiment might enhance the immune response against HIV.

Acquired immune deficiency syndrome (AIDS) is caused by the human immunodeficiency virus (HIV). After HIV infection, CD4 T-cells are infected by the virus. An infected CD4 T-cell does not perform its role in the human immune system and makes multiple HIV copies. With a low level of CD4 T-cell count, the human immune system cannot work properly. HIV/AIDS is still a prevalent and lethal infectious disease world-wide. In 2009 the estimated number of HIV-infected people was 33.3 million and 1.8 million people died of AIDS [1]. Several studies have reported model-based approaches to understand the HIV/AIDS infection process. Some examples of HIV dynamic models are found in [2] and [3] and control theoretic studies of the authors, based on the HIV models in [3], are reported in [4] and [5]. In this paper we research a control scheme using a model-based approach to enhance the human immune response in HIV infection dynamics.1 The control method is applied to the HIV model in [3], together with the pharmacological dynamics in [7] and [8], on the basis of the immune boosting process analysed by the authors in [5]. The research in this paper is supported by the experimental data recently published in [9] and [10]. Although our research can be applicable to analyse the data of [10], we focus on the experimental result of [9]. Note that we do not analyse the properties of the controlled system formally, which will be done elsewhere, but focus on the conceptual method of the controller design, as well as on the application to the HIV infection dynamics. This paper contains two major contributions. First, it presents a model modification based on an existing HIV model, considering pharmacological dynamics. The modification introduces dynamic equations describing the pharmacokinetics and pharmacodynamics of antiretroviral drugs. In addition we assume that the controlled drug intake can be considered as impulsive control input for the mathematical model, although in general the drugs are taken orally as extended-release formulation (see [11] for more details). Impulsive control gives a sudden change of the state variable at discrete instants (see [12] for rigorous definition of impulsive control). The modified model is able to accurately describe the effect on HIV patients of a drug regimen. This model helps to study HIV infection dynamics with a realistic regimen of HIV therapy. Second, the experimental results in [9] can be explained by the immune system analysis on the modified HIV model in the paper. The clinical work of [9] leads to the application of a mathematical approach to the HIV dynamics. Based on the modified HIV model we obtain an insight into the result of [9], providing an interpretation of the experiment. By analysing the simulation study it is implied that the protocol of the experiment might enhance the immune response against HIV. The paper is organised as follows. The proposed modeling method is presented in Section 2. Particularly Section 2.1 gives a brief description of the experiments in [9]. Then in Section 2.2 we recall some of the analysis of [5] for the HIV dynamic model of [3] and we modify the model to study numerical realisation of the experiments in [9]. Then Section 3 reports the numerical results with the modified HIV infection model. Finally we discuss the results and conclude the paper in Section 4.

In this paper we have investigated a control scheme for HIV dynamics to enhance the immune response using a model-based approach. The dynamics were analysed. It was shown that this HIV model is accessible but cannot be linearized by a state feedback. This suggests that the model is truly nonlinear. We have proposed the idea of using impulsive input as control mechanism. The control idea has been applied to the HIV model in [3] on the basis of the immune boosting mechanism reported in [5]. To implement the impulsive input we have modified an HIV dynamic model considering the pharmacokinetics and pharmacodynamics of antiretroviral drug and studied numerical realisation of the recently reported clinical experiments in [9]. Through computer simulations of the modified model we have simulated the experiment and analysed the experimental results. By analysing the simulations we have provided some insights into the implications of the experiments. The analysis has shown that the protocol of the experiment might enhance the immune response against HIV. We can list just a few future works following this paper: Note that the HIV drugs are usually delivered as extended-release formulation [11] although we simply assume that the drug intake is impulsive control input of the HIV model in Section 2.2. Thus further analysis on the modeling of the intestinal absorption of an extended-release oral administration could be one of the future works. In addition, although we simply employ a time-invariant phamacodynamic model (11), we could consider time-varying phamacodynamic model to sophisticate our analysis in the future. Over the past few years there have been considerable advances in the issues of the suppression of HIV transmission by using antiretroviral drug [17] with new scientific findings including the result in [9]. The new use of Truvada has been approved as a medication to reduce the risk of HIV infection for the first time by the U.S. Food and Drug Administration in July 2012 [43].