Modelling imperfect adherence to HIV induction therapy

Abstract Background Induction-maintenance therapy is a treatment regime where patients are prescribed an intense course of treatment for a short period of time (the induction phase), followed by a simplified long-term regimen (maintenance). Since induction therapy has a significantly higher chance of pill fatigue than maintenance therapy, patients might take drug holidays during this period. Without guidance, patients who choose to stop therapy will each be making individual decisions, with no scientific basis. Methods We use mathematical modelling to investigate the effect of imperfect adherence during the inductive phase. We address the following research questions: 1. Can we theoretically determine the maximal length of a possible drug holiday and the minimal number of doses that must subsequently be taken while still avoiding resistance? 2. How many drug holidays can be taken during the induction phase? Results For a 180 day therapeutic program, a patient can take several drug holidays, but then has to follow each drug holiday with a strict, but fairly straightforward, drug-taking regimen. Since the results are dependent upon the drug regimen, we calculated the length and number of drug holidays for all fifteen protease-sparing triple-drug cocktails that have been approved by the US Food and Drug Administration. Conclusions Induction therapy with partial adherence is tolerable, but the outcome depends on the drug cocktail. Our theoretical predictions are in line with recent results from pilot studies of short-cycle treatment interruption strategies and may be useful in guiding the design of future clinical trials

Thresholds for extinction and proliferation in a stochastic tumour-immune model with pulsed comprehensive therapy

Periodical applications of immunotherapy and chemotherapy play significant roles in cancer treatment and studies have shown that the evolution of tumour cells is subject to random events. In order to capture the effects of such noise we developed a stochastic tumour-immune dynamical model with pulsed treatment to describe combinations of immunotherapy with chemotherapy. By using theorems of the impulsive stochastic dynamical equation, the tumour free solution and the global positive solution of the proposed system were investigated. We then show that the expectations of the solutions are bounded. Furthermore, threshold conditions for extinction, non-persistence in the mean, weak persistence and stochastic persistence of tumour cells are provided. The results reveal that comprehensive therapy or noise can dominate the evolution of tumours. Finally, biological implications are addressed and a conclusion is presented

Reconciling conflicting clinical studies of ANTIOXIDANT SUPPLEMENTATION AS HIV THERAPY: A MATHEMATICAL APPROACH

Small highly reactive molecules called reactive oxygen species (ROS) play a crucial role in cell signalling and infection control. However, high levels of ROS can cause significant damage to cell structure and function. Studies have shown that infection with the human immunodeficiency virus (HIV) results in increased ROS concentrations, which can in turn lead to faster progression of HIV infection, and cause CD4+ T-cell apoptosis. To counteract these effects, clinical studies have explored the possibility of raising antioxidant levels, with mixed results. In this thesis, a mathematical model is used to explore this potential therapy, both analytically and numerically. For the numerical work, we use clinical data from both HIV-negative and HIV-positive injection drug users (IDUs) to estimate model parameters; these groups have lower baseline concentrations of antioxidants than non-IDU controls. Our model suggests that increases in CD4+ T cell concentrations can result from moderate levels of daily antioxidant supplementation, while excessive supplementation has the potential to cause periods of immunosuppression. We discuss implications for HIV therapy in IDUs and other populations which may have low baseline concentrations of antioxidants

Optimal control strategies to tailor antivirals for acute infectious diseases in the host

Several mathematical models in SARS-CoV-2 have shown how target-cell model can help to understand the spread of the virus in the host and how potential candidates of antiviral treatments can help to control the virus. Concepts as equilibrium and stability show to be crucial to qualitative determine the best alternatives to schedule drugs, according to effectivity in inhibiting the virus infection and replication rates. Important biological events such as rebounds of the infections (when antivirals are incorrectly interrupted) can also be explained by means of a dynamic study of the target-cell model. In this work a full characterization of the dynamical behavior of the target-cell models under control actions is made and, based on this characterization, the optimal fixeddose antiviral schedule that produces the smallest amount of dead cells (without viral load rebounds) is computed. Several simulation results - performed by considering real patient data - show the potential benefits of both, the model characterization and the control strategy.Fil: Perez, Mara Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Abuin, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Actis, Marcelo Jesús. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; ArgentinaFil: Ferramosca, Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Università Degli Studi Di Bergamo; ItaliaFil: Hernandez Vargas, Esteban Abelardo. Universidad Nacional Autónoma de México; MéxicoFil: González, Alejandro Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentin

Reconciling conflicting clinical studies of antioxidant supplementation as HIV therapy: a mathematical approach

<p>Abstract</p> <p>Background</p> <p>Small, highly reactive molecules called reactive oxygen species (ROS) play a crucial role in cell signalling and infection control. However, high levels of ROS can cause significant damage to cell structure and function. Studies have shown that infection with the human immunodeficiency virus (HIV) results in increased ROS concentrations, which can in turn lead to faster progression of HIV infection, and cause CD4⁺T-cell apoptosis. To counteract these effects, clinical studies have explored the possibility of raising antioxidant levels, with mixed results.</p> <p>Methods</p> <p>In this paper, a mathematical model is used to explore this potential therapy, both analytically and numerically. For the numerical work, we use clinical data from both HIV-negative and HIV-positive injection drug users (IDUs) to estimate model parameters; these groups have lower baseline concentrations of antioxidants than non-IDU controls.</p> <p>Results</p> <p>Our model suggests that increases in CD4⁺T cell concentrations can result from moderate levels of daily antioxidant supplementation, while excessive supplementation has the potential to cause periods of immunosuppression.</p> <p>Conclusion</p> <p>We discuss implications for HIV therapy in IDUs and other populations which may have low baseline concentrations of antioxidants.</p

Global dynamics of a state-dependent feedback control system

The main purpose is to develop novel analytical techniques and provide a comprehensive qualitative analysis of global dynamics for a state-dependent feedback control system arising from biological applications including integrated pest management. The model considered consists of a planar system of differential equations with state-dependent impulsive control. We characterize the impulsive and phase sets, using the phase portraits of the planar system and the Lambert W function to define the Poincaré map for impulsive point series defined in the phase set. The existence, local and global stability of an order-1 limit cycle and sharp sufficient conditions for the global stability of the boundary order-1 limit cycle have been provided. We further examine the flip bifurcation related to the existence of an order-2 limit cycle. We show that the existence of an order-2 limit cycle implies the existence of an order-1 limit cycle. We derive sufficient conditions under which any trajectory initiating from a phase set will be free from impulsive effects after finite state-dependent feedback control actions, and we also prove that order-k (k ≥ 3) limit cycles do not exist, providing a solution to an open problem in the integrated pest management community. We then investigate multiple attractors and their basins of attraction, as well as the interior structure of a horseshoe-like attractor. We also discuss implications of the global dynamics for integrated pest management strategy. The analytical techniques and qualitative methods developed in the present paper could be widely used in many fields concerning state-dependent feedback control

Study of Infectious Diseases by Mathematical Models: Predictions and Controls

The aim of this thesis is to understand the spread, persistence and prevention mechanisms of infectious diseases by mathematical models. Microorganisms that rapidly evolve pose a constant threat to public health. Proper understanding of the transmission machinery of these existing and new pathogens may facilitate devising prevention tools. Prevention tools against transmissions, including vaccines and drugs, are evolving at a similar pace. Efficient implementation of these new tools is a fundamental issue of public health. We primarily focus on this issue and explore some theoretical frameworks. Pre-exposure prophylaxis (PrEP) is considered one of the promising interventions against HIV infection as experiments on various groups and sites have reported its significant effectiveness. This study evaluates the effectiveness of Tenofovir gel, one of the widely used PrEPs for women, through a mathematical model. Our model has excellent agreement with the experimental data on the use of Tenofovir gel as a PrEP in South African women. Using our model, we estimate both male-to-female and female-to-male transmission rates with and without Tenofovir gel protection. Through these estimates, we demonstrate that the use of Tenofovir gel as a PrEP can significantly reduce the reproduction numbers, new infections, and HIV prevalence in South Africa. Our results further show that the effectiveness of Tenofovir gel largely depends on the level of adherence to the gel and the proportion of women under gel coverage. Even though Tenofovir gel alone may not be able to eradicate the disease, as indicated by our estimates of the reproduction numbers, together with other interventions, such as condom use, it can serve as a strong weapon to fight against HIV epidemics. Another promising drug-oriented intervention against HIV infection is antiretroviral treatment (ART). We study some crucial aspects of this intervention on the HIV epidemic. ART has the potential to reduce mortality and disease progression among HIV infected individuals. It can reduce the viral load of the infected individual to an undetectable level and help prevent new infections. Whether the treatment should begin early or be delayed is still under debate. This study considers the impact of early versus delayed ART on the HIV epidemic and demonstrates the optimum timing of ART initiation. Our results highlight the long-term consequences of early treatment. Finally, we investigate the consequences of vaccine implementation strategies for infectious diseases. Vaccines are said to be the intervention with the most potential against many infectious diseases. However, their success relies on proper and strategic management and distribution. In an infectious disease, the degree of infection may vary widely among those individuals. Reports show that individuals belonging to certain groups possess considerably higher risk for infection. Integrating this phenomenon into vaccination strategies, the host is categorized into different groups to measure the outcome of the vaccination. A mathematical model is proposed and analyzed to evaluate this measure. Our results suggest that vaccinating a group with a certain priority may lead to effective elimination of the disease

Alcohol as a catalyst for hiv-associated neuroinflammation and tbi-induced iron toxicity

Alcohol has long been considered an exacerbator of diseases, disorders, and injuries as well as many of the accompanying symptoms. As an alternative approach, this dissertation explores alcohol as a catalyst for two different human disease conditions, human immunodeficiency virus (HIV)-associated neuroinflammation and traumatic brain injury (TBI)-induced iron toxicity. In HIV-1 infection, this dissertation presents a novel anti-viral drug, called Drug-S, for a possible inhibition and treatment of HIV-1 disease progression. The first aim explores the influence of alcohol with HIV-associated neuroinflammation on macrophage migration across an in vitro model of the blood brain barrier. There is a gap in knowledge on the effects of low dose alcohol under HIV-associated injury in people living with HIV-1 who have achieved viral suppression. The model, consisting of a quad-cultivation of neuroimmune cells including endothelial, astrocyte, macrophage, and neuron cells, is challenged with low dose (10 mM) alcohol and the viral protein trans-activator of transcription (TAT). It was then observed for changes to barrier integrity and neuronal injury upon macrophage migration. Results show that combined alcohol and viral injuries significantly increases migration even under the clinically lowest concentrations of alcohol. The cause of enhanced macrophage migration and related neurotoxicity is implicated to alcohol-induced nitric oxide production by endothelial cells and TAT\u27s chemoattractant properties. The second aim analyzes a compound called Drug-S as a possible therapeutic for inhibiting HIV-1 replication and HIV-1 disease progression. Although the combination of highly active antiretroviral therapy can remarkably control HIV-1, it is not a cure. Current therapy is unable to eliminate persistent HIV-1 contained in latent reservoirs in the central nervous system and to prevent rebound viral replication and resurgence when treatment is withdrawn. Treating HIV-1 infected macrophage with Drug-S shows inhibition of infection and persistence at a low concentration without causing any toxicity to neuroimmune cells. Results suggest that Drug-S may have a direct effect on viral structure, prevent rebounding of HIV-1 infection, and arrest progression into acquired immunodeficiency syndrome. The third aim explores the role of low level of alcohol use in TBI-induced hemolytic iron management. As hemorrhage is a major component of TBI, the accumulated red blood cells in the tissue layers undergo hemolysis and release free iron into the central nervous system. As a secondary stressor, prior alcohol consumption can increase iron aggregation and alter its management. The effects of alcohol on TBI- induced iron toxicity is explored in an in vivo model of chronic alcohol exposure subjected to fluid percussion injury. Results show that alcohol increases the iron overload and alters iron management following injury by changing the expression profile of the iron regulatory proteins lipocalin 2, heme oxygenase 1, ferritin light chain, and hemosiderin. Accompanying these results, it was also found that microglia can similarly play a significant role in iron management by phagocytosing red blood cells and retaining iron. Overall, the results of this dissertation demonstrate the pervasive impact of alcohol use in neuropathophysiology arising from HIV protein TAT toxicity or TBI-induced iron toxicity. In addition, the newly discovered DrugS can be an effective antiviral drug for a possible HIV/AIDS disease prevention and progression

Quantifying the treatment efficacy of reverse transcriptase inhibitors: new analyses of clinical data based on within-host modeling

Abstract Background Current measures of the clinical efficacy of antiretroviral therapy (ART) in the treatment of HIV include the change in HIV RNA in the plasma and the gain in CD4 cells. Methods We propose new measures for evaluating the efficacy of treatment that is based upon combinations of non-nucleoside and nucleoside reverse transcriptase inhibitors. Our efficacy measures are: the CD4 gain per virion eliminated , the potential of CD4 count restoration and the viral reproduction number (R0) . These efficacy measures are based upon a theoretical understanding of the impact of treatment on both viral dynamics and the immune reconstitution. Patient data were obtained from longitudinal HIV clinical cohorts. Results We found that the CD4 cell gain per virion eliminated ranged from 10-2 to 600 CD4 cells/virion, the potential of CD4 count restoration ranged from 60 to 1520 CD4 cells/μl, and the basic reproduction number was reduced from an average of 5.1 before therapy to an average of 1.2 after one year of therapy. There was substantial heterogeneity in these efficacy measures among patients with detectable viral replication. We found that many patients who achieved viral suppression did not have high CD4 cell recovery profiles. Our efficacy measures also enabled us to identify a subgroup of patients who were not virally suppressed but had the potential to reach a high CD4 count and/or achieve viral suppression if they had been switched to a more potent regimen. Conclusion We show that our new efficacy measures are useful for analyzing the long-term treatment efficacy of combination reverse transcriptase inhibitors and argue that achieving a low R0 does not imply achieving viral suppression

Drug Resistance in Infectious Diseases : Modeling, Analysis and Simulation

Resistenzen bei Infektionskrankheiten stellen ein großes gesundheitliches Problem in der ganzen Welt dar. Das Ziel dieser Arbeit ist eine quantitative Untersuchung von Resistenzen bei Infektionskrankheiten durch mathematische Modellierung, Analyse und Simulation. Im Rahmen unserer Arbeit präsentieren wir zwei neue Modelle von Resistenzen bei Infektionskrankheiten. Diese Arbeit enthält mehrere Beiträge: 1. Der Hintergrund: Wir geben einen Überblick über den Stand der mathematischen Modellierung von Resistenzen. 2. Die Modellierung: Durch zwei neue Modelle für nicht-strukturierte und strukturierte Populationen tragen wir zur Entwicklung der mathematischen Modelle bei, die die Dynamik von vektorübertragenen Krankheiten beschreiben. 3. Die Theorie: Wir tragen zur mathematischen Theorie der Integro-Differential-gleichungen bei, durch Erweiterung der Methode der Charakteristiken, um ein System mit unterschiedlichen Charakteristiken in multi-dimensionalem Raum zu behandeln. Dies bietet eine solide Grundlage für numerische Untersuchungen. 4. Die Numerik: Wir empfehlen geeignete Methoden und Algorithmen, um die Modelle zu untersuchen. Für das nicht-strukturierte Modell präsentieren wir eine Parameterschätzung und Simulation mit einem Datensatz aus Burkina Faso, Afrika. Für das strukturierte Modell schlagen wir einen konstruktiven Algorithmus vor und diskutieren über mögliche Daten, um das Modell numerisch zu untersuchen. 5. Die Anwendung: Wir betrachten verschiedene quantitative Situationen und Richtlinien. Mit einem guten Datensatz können die Simulationen wichtige Ergebnisse liefern, die die Behandlung von Resistenz, vor allem bei vektorübertragenen Krankheiten, verbessern. Die Modelle verweisen auch auf die Notwendigkeit weiterer experimenteller Arbeiten, um ein genaueres Verständnis zu erreichen. Mit all diesen Beiträgen bauen wir eine wichtige Brücke von der Theorie zur Praxis, um geeignete Strategien zur Verminderung von Resistenz und zur Kontrolle von Infektionskrankheiten herauszufinden