scholarly journals Optimal control in HIV chemotherapy with termination viral load and latent reservoir

2019 ◽  
Vol 16 (2) ◽  
pp. 619-635 ◽  
Author(s):  
Damilola Olabode ◽  
◽  
Libin Rong ◽  
Xueying Wang ◽  
Keyword(s):  
Optimal Control ◽  
Viral Load ◽  
Latent Reservoir

scholarly journals Optimal Control of an HIV Model with Gene Therapy and Latency Reversing Agents

2021 ◽  
Vol 26 (4) ◽  
pp. 77
Author(s):  
Zachary Abernathy ◽  
Kristen Abernathy ◽  
Andrew Grant ◽  
Paul Hazelton
Keyword(s):  
Gene Therapy ◽  
Optimal Control ◽  
Combination Treatment ◽  
Latent Reservoir ◽  
Sweep Method ◽  
Hiv Model ◽  
Future Work ◽  
Disease Free ◽  
Forward Backward Sweep Method ◽  
Reversing Agents

In this paper, we study the dynamics of HIV under gene therapy and latency reversing agents. While previous works modeled either the use of gene therapy or latency reversing agents, we consider the effects of a combination treatment strategy. For constant treatment controls, we establish global stability of the disease-free equilibrium and endemic equilibrium based on the value of R0. We then consider time-dependent controls and formulate an associated optimal control problem that emphasizes reduction of the latent reservoir. Characterizations for the optimal control profiles are found using Pontryagin’s Maximum Principle. We perform numerical simulations of the optimal control model using the fourth-order Runge–Kutta forward-backward sweep method. We find that a combination treatment of gene therapy with latency reversing agents provides better remission times than gene therapy alone. We conclude with a discussion of our findings and future work.

scholarly journals Models of SIV rebound after treatment interruption that involve multiple reactivation events

2020 ◽  
Author(s):  
Christiaan H. van Dorp ◽  
Jessica M. Conway ◽  
James B. Whitney ◽  
Dan H. Barouch ◽  
Alan S. Perelson
Keyword(s):  
Growth Rate ◽  
Viral Load ◽  
Antiretroviral Therapy ◽  
Treatment Interruption ◽  
Latent Reservoir ◽  
Viral Rebound ◽  
Viral Growth ◽  
Art Initiation ◽  
Reactivation Event ◽  
Hiv 1

AbstractIn order to assess the efficacy of novel HIV-1 treatments leading to a functional cure, the time to viral rebound is frequently used as a surrogate endpoint. The longer the time to viral rebound, the more efficacious the therapy. In support of such an approach, mathematical models serve as a connection between the size of the latent reservoir and the time to HIV-1 rebound after treatment interruption. The simplest of such models assumes that a single successful latent cell reactivation event leads to observable viremia after a period of exponential viral growth. Here we consider a generalization developed by Pinkevych et al. and Hill et al. of this simple model in which multiple reactivation events can occur, each contributing to the exponential growth of the viral load. We formalize and improve the previous derivation of the dynamics predicted by this model, and use the model to estimate relevant biological parameters from SIV rebound data. We confirm a previously described effect of very early antiretroviral therapy (ART) initiation on the rate of recrudescence and the viral load growth rate after treatment interruption. We find that every day ART initiation is delayed results in a 39% increase in the recrudescence rate, and a 11% decrease of the viral growth rate. We show that when viral rebound occurs early relative to the viral load doubling time, a model with multiple successful reactivation events fits the data better than a model with only a single successful reactivation event.Author SummaryHIV-1 persists during suppressive antiretroviral therapy (ART) due to a reservoir of latently infected cells. When ART is stopped, HIV generally rebounds within a few weeks. However, there is a small fraction of patients that do not rebound over a period of months or years. A variety of treatments are being tested for their ability to reduce the size of the latent reservoir, to induce effective immune responses against the virus, or to prevent or prolong the time to viral rebound after ART interruption. These novel treatments are typically first tested in SIV infected macaques, and the efficacy of the treatment assessed by interrupting ART and measuring the time to viral rebound. Here, we develop and test a mathematical and statistical model that describes the process of viral rebound. The model can be used for statistical inference of the efficacy of newly developed treatments. Importantly, the model takes into account that multiple recrudescence events can precede rebound. We test the model using data from early treated SIV infected macaques.

scholarly journals Real-time predictions of reservoir size and rebound time during antiretroviral therapy interruption trials for HIV

2016 ◽  
Author(s):  
Alison L Hill ◽  
Daniel Scholes Rosenbloom ◽  
Edward Goldstein ◽  
Emily Hanhauser ◽  
Daniel R Kuritzkes ◽  
...  
Keyword(s):  
Viral Load ◽  
Antiretroviral Therapy ◽  
Real Time ◽  
Latent Infection ◽  
Optimal Schedule ◽  
Simulated Data ◽  
Latent Reservoir ◽  
Modeling Tools ◽  
Hematopoietic Stem ◽  
Relative Contribution

Monitoring the efficacy of novel reservoir-reducing treatments for HIV is challenging. The limited ability to sample and quantify latent infection means that supervised antiretroviral therapy (ART) interruption studies are generally required. Here we introduce a set of mathematical and statistical modeling tools to aid in the design and interpretation of ART-interruption trials. We show how the likely size of the remaining reservoir can be updated in real-time as patients continue off treatment, by combining the output of laboratory assays with insights from models of reservoir dynamics and rebound. We design an optimal schedule for viral load sampling during interruption, whereby the frequency of follow-up can be decreased as patients continue off ART without rebound. While this scheme can minimize costs when the chance of rebound between visits is low, we find that the reservoir will be almost completely reseeded before rebound is detected unless sampling occurs at least every two weeks and the most sensitive viral load assays are used. We use simulated data to predict the clinical trial size needed to estimate treatment effects in the face of highly variable patient outcomes and imperfect reservoir assays. Our findings suggest that large numbers of patients - between 40 and 150 - will be necessary to reliably estimate the reservoir-reducing potential of a new therapy and to compare this across interventions. As an example, we apply these methods to the two "Boston patients", recipients of allogeneic hematopoietic stem cell transplants who experienced large reductions in latent infection and underwent ART-interruption. We argue that the timing of viral rebound was not particularly surprising given the information available before treatment cessation. Additionally, we show how other clinical data can be used to estimate the relative contribution that remaining HIV+ cells in the recipient versus newly infected cells from the donor made to the residual reservoir that eventually caused rebound. Together, these tools will aid HIV researchers in the evaluating new potentially-curative strategies that target the latent reservoir.

scholarly journals The within-host fitness of HIV-1 increases with age in ART-naïve HIV-1 subtype C infected children

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Pradeep Nagaraja ◽  
Bindu P. Gopalan ◽  
Reena R. D’Souza ◽  
Debolina Sarkar ◽  
Niharika Rajnala ◽  
...  
Keyword(s):  
Viral Load ◽  
Immune System ◽  
Viral Fitness ◽  
Latent Reservoir ◽  
Subtype C ◽  
Viral Control ◽  
Cell Counts ◽  
Data Points ◽  
The Mean ◽  
Hiv 1

AbstractAs the immune system develops with age, children combat infections better. HIV-1, however, targets an activated immune system, potentially rendering children increasingly permissive to HIV-1 infection as they grow. How HIV-1 fitness changes with age in children is unknown. Here, we estimated the within-host basic reproductive ratio, R0, a marker of viral fitness, in HIV-1 subtype C-infected children in India, aged between 84 days and 17 years. We measured serial viral load and CD4 T cell counts in 171 children who initiated first-line ART. For 25 children, regular and frequent measurements provided adequate data points for analysis using a mathematical model of viral dynamics to estimate R0. For the rest, we used CD4 counts for approximate estimation of R0. The viral load decline during therapy was biphasic. The mean lifespans of productively and long-lived infected cells were 1.4 and 27.8 days, respectively. The mean R0 was 1.5 in children aged < 5 years, increased with age, and approached 6.0 at 18 years, close to 5.8 estimated previously for adults. The tolerogenic immune environment thus compromises HIV-1 fitness in young children. Early treatment initiation, when the R0 is small, will likely improve viral control, in addition to suppressing the latent reservoir.

scholarly journals Time Optimal Control Studies on COVID-19 Incorporating Adverse Events of the Antiviral Drugs

2021 ◽  
Vol 9 (1) ◽  
pp. 214-241
Author(s):  
Bishal Chhetri ◽  
Vijay M. Bhagat ◽  
Swapna Muthusamy ◽  
V S Ananth ◽  
D. K. K. Vamsi ◽  
...  
Keyword(s):  
Optimal Control ◽  
Viral Load ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Antiviral Drugs ◽  
Time Optimal Control ◽  
Optimal Controls ◽  
Second Line ◽  
Time Optimal ◽  
Infected Cells

Abstract COVID -19 pandemic has resulted in more than 257 million infections and 5.15 million deaths worldwide. Several drug interventions targeting multiple stages of the pathogenesis of COVID -19 can significantly reduce induced infection and thus mortality. In this study, we first develop SIV model at within-host level by incorporating the intercellular time delay and analyzing the stability of equilibrium points. The model dynamics admits a disease-free equilibrium and an infected equilibrium with their stability based on the value of the basic reproduction number R 0. We then formulate an optimal control problem with antiviral drugs and second-line drugs as control measures and study their roles in reducing the number of infected cells and viral load. The comparative study conducted in the optimal control problem suggests that if the first-line antiviral drugs show adverse effects, considering these drugs in reduced amounts along with the second-line drugs would be very effective in reducing the number of infected cells and viral load in a COVID-19 infected patient. Later, we formulate a time-optimal control problem with the goal of driving the system from any initial state to the desired infection-free equilibrium state in finite minimal time. Using Pontryagin’s Minimum Principle, it is shown that the optimal control strategy is of the bang-bang type, with the possibility of switching between two extreme values of the optimal controls. Numerically, it is shown that the desired infection-free state is achieved in a shorter time when the higher values of the optimal controls. The results of this study may be very helpful to researchers, epidemiologists, clinicians and physicians working in this field.

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