Control of the HIV infection and drug dosage

Revisiting the observability and identifiability properties of a popular HIV model

This paper revisits the observability and identifiability properties of a popular ODE model commonly adopted to characterize the HIV dynamics in HIV-infected patients with antiretroviral treatment. These properties are determined by using the general analytical solution of the unknown input observability problem, introduced very recently in Martinelli (2022). This solution provides the systematic procedures able to determine the state observability and the parameter identifiability of any ODE model, in particular, even in the presence of time varying parameters. Four variants of the HIV model are investigated. They differ because some of their parameters are considered constant or time varying. Fundamental new properties, which also highlight an error in the scientific literature, are automatically determined and discussed. Additionally, for each variant, the paper provides a quantitative answer to the following practical question: What is the minimal external information (external to the available measurements of the system outputs) required to make observable the state and identifiable all the model parameters? The answer to this fundamental question is obtained by exploiting the concept of continuous symmetry, recently introduced in Martinelli (2019). This concept allows us to determine a first preliminary general result which is then applied to the HIV model. Finally, for each variant, the paper concludes by providing a redefinition of the state and of the parameters in order to obtain a full description of the system only in terms of a state which is observable and a set of parameters which are identifiable (both constant and time varying).

Optimizing antiviral therapy for COVID-19 with learned pathogenic model

COVID-19 together with variants have caused an unprecedented amount of mental and economic turmoil with ever increasing fatality and no proven therapies in sight. The healthcare industry is racing to find a cure with multitude of clinical trials underway to access the efficacy of repurposed antivirals, however the much needed insights into the dynamics of pathogenesis of SARS-CoV-2 and corresponding pharmacology of antivirals are lacking. This paper introduces systematic pathological model learning of COVID-19 dynamics followed by derivative free optimization based multi objective drug rescheduling. The pathological model learnt from clinical data of severe COVID-19 patients treated with remdesivir could additionally predict immune T cells response and resulted in a dramatic reduction in remdesivir dose and schedule leading to lower toxicities, however maintaining a high virological efficacy.

Control strategy design for the anti-HBV mathematical model

Currently, the anti-viral therapy has been extensively utilised to reduce the viral burden and switch off certain infectious sources for hepatitis B virus (HBV) infected patients in clinical treatment. Several pieces of existing evidence have demonstrated that large-scale coverage with anti-viral therapy has obtained a certain great contribution in hygiene and disease control. In this study, an anti-HBV mathematical model is considered and its control strategy of the drug treatment is designed. Based on the Lyapunov theory, this study derives three main theorems to propose three different control strategies, respectively, for drug treatments [inline-formula removed] and [inline-formula removed], such that all states of the anti-HBV model can finally converge to the infection-free equilibrium point [inline-formula removed] asymptotically. Especially, the designed drug treatment [inline-formula removed] or [inline-formula removed] is not a fixed value, but it is time-varying and dependent on states. In Theorem 1, the single drug treatment [inline-formula removed] without [inline-formula removed] is synthesised. Theorem 2 considers the single drug treatment [inline-formula removed] without [inline-formula removed]. In Theorem 3, the combination therapy of [inline-formula removed] and [inline-formula removed] is designed. Finally, there are several simulations to show that the proposed combination therapy is much more effective to cure HBV infected patients than the drug treatment with solely single [inline-formula removed] or single [inline-formula removed].

Robust control of HIV infection by antiretroviral therapy: a super-twisting sliding mode control approach

Acquired immune deficiency syndrome is an epidemic infectious disease which is caused by the human immunodeficiency virus (HIV) and that has proliferated across worldwide. It has been a matter of concern for the scientific community to develop an antiretroviral therapy, which will prompt a rapid decline in viral abundance. With this motivation, this study proposes the design of a robust super twisting sliding mode controller based on output information for an uncertain HIV infection model. The control objective is to decrease the concentration of infected CD4+ T cells to a specified level by drug administration using only the output information of the uncertain HIV infection model which is total CD4+ T cell concentration. The robust output-feedback controller has been developed in combination with a robust exact differentiator, functioning as an observer. The reported analysis demonstrates that the approach proposed here is capable of ensuring robust performance under several operating conditions, measurement and modelling error, parametric uncertainties and external disturbances and the simulation results prove the proficiency of the controller proposed.

PK/PD-based adaptive tailoring of oseltamivir doses to treat within-host influenza viral infections

Influenza A virus (IAV) is a latent global threat to human health. In view of the risk of pandemics, prophylactic and curative treatments are essential. Oseltamivir is a neuraminidase inhibitor efficiently supporting recovery from influenza infections. Current common clinical practice is a constant drug dose (75 or 150 mg) administered at regular time intervals twice a day. We aim to use quantitative systems pharmacology to propose an efficient adaptive drug scheduling. We combined the mathematical model for IAV infections validated by murine data, which captures the viral dynamics and the dynamics of the immune host response, with a pharmacokinetic (PK)/pharmacodynamic (PD) model of oseltamivir. Next, we applied an adaptive impulsive feedback control method to systematically calculate the adaptive dose of oseltamivir in dependence on the viral load and the number of immune effectors at the time of drug administration. Our in silico results revealed that the treatment with adaptive control-based drug scheduling is able to either increase the drug virological efficacy or reduce the drug dose while keeping the same virological efficacy. Thus, adaptive adjustment of the drug dose would reduce not only the potential side effects but also the amount of stored oseltamivir required for the prevention of outbreaks.

Occurrence of HIV eradication for preexposure prophylaxis treatment with a deterministic HIV model

The authors examine the human immunodeficiency virus (HIV) eradication in this study using a mathematical model and analyse the occurrence of virus eradication during the early stage of infection. To this end they use a deterministic HIV-infection model, modify it to describe the pharmacological dynamics of antiretroviral HIV drugs, and consider the clinical experimental results of preexposure prophylaxis HIV treatment. They also use numerical simulation to model the experimental scenario, thereby supporting the clinical results with a model-based explanation. The study results indicate that the protocol employed in the experiment can eradicate HIV in infected patients at the early stage of the infection.

Analysis of the HIV eradication phenomenon at the early stage of infection with an extracellular deterministic model

We investigate the phenomenon of HIV eradication at the early stage of the infection and evaluate the chance of the eradication with a mathematical model. We employ an extracellular deterministic model of the HIV infection dynamics and modify the model to include the pharmacokinetics and pharmacodynamics of antiretroviral HIV drugs. In addition we consider clinical experiments for the prevention of HIV infection using pre-exposure chemoprophylaxis treatment. Exploiting the mathematical model we implement the experiment numerically. The study in this paper is supported by the clinical results and provides a theoretical explanation for the results. The result suggests that the protocol of the experiment eradicates the virus in HIV infected patients.

Mathematical Modeling of HIV Dynamics After Antiretroviral Therapy Initiation: A Review

This review shows the potential ground-breaking impact that mathematical tools may have in the analysis and the understanding of the HIV dynamics. In the first part, early diagnosis of immunological failure is inferred from the estimation of certain parameters of a mathematical model of the HIV infection dynamics. This method is supported by clinical research results from an original clinical trial: data just after 1 month following therapy initiation are used to carry out the model identification. The diagnosis is shown to be consistent with results from monitoring of the patients after 6 months. In the second part of this review, prospective research results are given for the design of individual anti-HIV treatments optimizing the recovery of the immune system and minimizing side effects. In this respect, two methods are discussed. The first one combines HIV population dynamics with pharmacokinetics and pharmacodynamics models to generate drug treatments using impulsive control systems. The second one is based on optimal control theory and uses a recently published differential equation to model the side effects produced by highly active antiretroviral therapy therapies. The main advantage of these revisited methods is that the drug treatment is computed directly in amounts of drugs, which is easier to interpret by physicians and patients.

Nonlinear observer output-feedback MPC treatment scheduling for HIV

BACKGROUND

Mathematical models of the immune response to the Human Immunodeficiency Virus demonstrate the potential for dynamic schedules of Highly Active Anti-Retroviral Therapy to enhance Cytotoxic Lymphocyte-mediated control of HIV infection.

METHODS

In previous work we have developed a model predictive control (MPC) based method for determining optimal treatment interruption schedules for this purpose. In this paper, we introduce a nonlinear observer for the HIV-immune response system and an integrated output-feedback MPC approach for implementing the treatment interruption scheduling algorithm using the easily available viral load measurements. We use Monte-Carlo approaches to test robustness of the algorithm.

RESULTS

The nonlinear observer shows robust state tracking while preserving state positivity both for continuous and discrete measurements. The integrated output-feedback MPC algorithm stabilizes the desired steady-state. Monte-Carlo testing shows significant robustness to modeling error, with 90% success rates in stabilizing the desired steady-state with 15% variance from nominal on all model parameters.

CONCLUSIONS

The possibility of enhancing immune responsiveness to HIV through dynamic scheduling of treatment is exciting. Output-feedback Model Predictive Control is uniquely well-suited to solutions of these types of problems. The unique constraints of state positivity and very slow sampling are addressable by using a special-purpose nonlinear state estimator, as described in this paper. This shows the possibility of using output-feedback MPC-based algorithms for this purpose.

Taking side effects into account for HIV medication

A control-theoretic approach to the problem of designing "low-side-effects" therapies for HIV patients based on highly active drugs is substantiated here. The evolution of side effects during treatment is modeled by an extra differential equation coupled to the dynamics of virions, healthy T-cells, and infected ones. The new equation reflects the dependence of collateral damages on the amount of each dose administered to the patient and on the evolution of the viral load detected by periodical blood analysis. The cost objective accounts for recommended bounds on healthy cells and virions, and also penalizes the appearance of collateral morbidities caused by the medication. The optimization problem is solved by a hybrid dynamic programming scheme that adhere to discrete-time observation and control actions, but by maintaining the continuous-time setup for predicting states and side effects. The resulting optimal strategies employ less drugs than those prescribed by previous optimization studies, but maintaining high doses at the beginning and the end of each period of six months. If an inverse discount rate is applied to favor early actions, and under a mild penalization of the final viral load, then the optimal doses are found to be high at the beginning and decrease afterward, thus causing an apparent stabilization of the main variables. But in this case, the final viral load turns higher than acceptable.