Viral Infection Model with Diffusion and Distributed Delay: Finite-Dimensional Global Attractor

We study a virus dynamics model with reaction-diffusion, logistic growth terms and a general non-linear infection rate functional response. The model has a distributed delay, including the case of state-selective delay. We construct a dynamical system in a Hilbert space and prove the existence of a finite-dimensional global attractor.

A New Age-Structured Multiscale Model of the Hepatitis C Virus Life-Cycle During Infection and Therapy With Direct-Acting Antiviral Agents

The dynamics of hepatitis C virus (HCV) RNA during translation and replication within infected cells were added to a previous age-structured multiscale mathematical model of HCV infection and treatment. The model allows the study of the dynamics of HCV RNA inside infected cells as well as the release of virus from infected cells and the dynamics of subsequent new cell infections. The model was used to fit in vitro data and estimate parameters characterizing HCV replication. This is the first model to our knowledge to consider both positive and negative strands of HCV RNA with an age-structured multiscale modeling approach. Using this model we also studied the effects of direct-acting antiviral agents (DAAs) in blocking HCV RNA intracellular replication and the release of new virions and fit the model to in vivo data obtained from HCV-infected subjects under therapy.

Multi-scale model for hepatitis C viral load kinetics under treatment with direct acting antivirals

Hepatitis C virus (HCV) infections are a global health problem, and extensive research over the last decades has been targeted at understanding its molecular biology and developing effective antiviral treatments. Recently, a number of potent direct acting antiviral drugs have been developed targeting specific processes in the viral life cycle. Here, we developed a mathematical multi-scale model of the within-host dynamics of HCV infection by integrating a standard model for viral infection with a detailed model of the viral replication cycle inside infected cells. We use this model to study patient time courses of viral load under treatment with daclatasvir, an inhibitor of the viral non-structural protein NS5A. Model analysis predicts that treatment efficacy can be increased by combining daclatasvir with dedicated viral polymerase inhibitors, corresponding to promising current strategies in drug development. Hence, our model presents a predictive tool for in silico simulations, which can be used to study and optimize direct acting antiviral drug treatment.

Modeling population heterogeneity in viral dynamics for chronic hepatitis C infection: Insights from Phase 3 telaprevir clinical studies

Viral dynamic modelling has proven useful for designing clinical studies and predicting treatment outcomes for patients infected with the hepatitis C virus. Generally these models aim to capture and predict the on-treatment viral load dynamics from a small study of individual patients. Here, we explored extending these models (1) to clinical studies with numerous patients and (2) by incorporating additional data types, including sequence data and prior response to interferon. Data from Phase 3 clinical studies of the direct-acting antiviral telaprevir (T; total daily dose of 2250 mg) combined with pegylated-interferon alfa and ribavirin (PR) were used for the analysis. The following data in the treatment-naïve population were reserved to verify the model: (1) a T/PR regimen where T was dosed every 8 h for 8 weeks (T8(q8h)/PR) and (2) a T/PR regimen where T was dosed twice daily for 12 weeks (T12(b.i.d.)/PR). The resulting model accurately predicted (1) sustained virologic response rates for both of these dosing regimens and (2) viral breakthrough characteristics of the T8(q8h)/PR regimen. Since the observed viral variants depend on the T exposure, the second verification suggested that the model was correctly sensitive to the different T regimen even though the model was developed using data from another T regimen. Furthermore, the model predicted that b.i.d. T dosing was comparable to q8h T dosing in the PR-experienced population, a comparison that has not been made in a controlled clinical study. The methods developed in this work to estimate the variability occurring below the limit of detection for the viral load were critical for making accurate predictions.

Modelling hepatitis C therapy--predicting effects of treatment

Mathematically modelling changes in HCV RNA levels measured in patients who receive antiviral therapy has yielded many insights into the pathogenesis and effects of treatment on the virus. By determining how rapidly HCV is cleared when viral replication is interrupted by a therapy, one can deduce how rapidly the virus is produced in patients before treatment. This knowledge, coupled with estimates of the HCV mutation rate, enables one to estimate the frequency with which drug resistant variants arise. Modelling HCV also permits the deduction of the effectiveness of an antiviral agent at blocking HCV replication from the magnitude of the initial viral decline. One can also estimate the lifespan of an HCV-infected cell from the slope of the subsequent viral decline and determine the duration of therapy needed to cure infection. The original understanding of HCV RNA decline under interferon-based therapies obtained by modelling needed to be revised in order to interpret the HCV RNA decline kinetics seen when using direct-acting antiviral agents (DAAs). There also exist unresolved issues involving understanding therapies with combinations of DAAs, such as the presence of detectable HCV RNA at the end of therapy in patients who nonetheless have a sustained virologic response.

Second-phase hepatitis C virus RNA decline during telaprevir-based therapy increases with drug effectiveness: implications for treatment duration

Hepatitis C virus (HCV) RNA decay during antiviral therapy is characterized by a rapid first phase, followed by a slower second phase. The current understanding of viral kinetics attributes the magnitude of the first phase of decay to treatment effectiveness, whereas the second phase of decay is attributed to the progressive loss of infected cells. Here, we analyzed data from 44 patients treated with telaprevir, a potent HCV protease inhibitor. Using a viral kinetic model that accounts for the pharmacokinetics of telaprevir, we found the second-phase slope of viral decline to be strongly correlated with treatment effectiveness and to be roughly four-fold more rapid than has been reported with interferon-based therapies. Because telaprevir is not known to increase the death rate of infected cells, our results suggest that the second-phase slope of viral decline is driven not only by the death of infected cells, but may also involve other mechanisms, such as a treatment-effectiveness-dependent degradation of intracellular viral RNA. As a result of the enhanced viral decay caused by the high antiviral effectiveness of telaprevir, we predict that if drug resistance could be avoided by using an appropriate combination of antiviral agents, treatment duration needed to clear HCV might be dramatically shortened. Indeed, we predict that in 95% of fully compliant patients, the last virus particle should be eliminated by week 7 of therapy. If the remaining infected hepatocytes act as a potential reservoir for the renewal of infection, no more than 10 weeks of treatment should be sufficient to clear the infection in 95% of fully compliant patients. However, if patients miss doses, treatment duration would need to be extended.