A hepatitis C virus infection model with time-varying drug effectiveness: solution and analysis

Incorporating Intracellular Processes in Virus Dynamics Models

In-host models have been essential for understanding the dynamics of virus infection inside an infected individual. When used together with biological data, they provide insight into viral life cycle, intracellular and cellular virus-host interactions, and the role, efficacy, and mode of action of therapeutics. In this review, we present the standard model of virus dynamics and highlight situations where added model complexity accounting for intracellular processes is needed. We present several examples from acute and chronic viral infections where such inclusion in explicit and implicit manner has led to improvement in parameter estimates, unification of conclusions, guidance for targeted therapeutics, and crossover among model systems. We also discuss trade-offs between model realism and predictive power and highlight the need of increased data collection at finer scale of resolution to better validate complex models.

The risk of drug resistance during long-acting antimicrobial therapy

The emergence of drug resistance during antimicrobial therapy is a major global health problem, especially for chronic infections like human immunodeficiency virus, hepatitis B and C, and tuberculosis. Sub-optimal adherence to long-term treatment is an important contributor to resistance risk. New long-acting drugs are being developed for weekly, monthly or less frequent dosing to improve adherence, but may lead to long-term exposure to intermediate drug levels. In this study, we analyse the effect of dosing frequency on the risk of resistance evolving during time-varying drug levels. We find that long-acting therapies can increase, decrease or have little effect on resistance, depending on the source (pre-existing or de novo) and degree of resistance, and rates of drug absorption and clearance. Long-acting therapies with rapid drug absorption, slow clearance and strong wild-type inhibition tend to reduce resistance caused by partially resistant strains in the early stages of treatment even if they do not improve adherence. However, if subpopulations of microbes persist and can reactivate during sub-optimal treatment, longer-acting therapies may substantially increase the resistance risk. Our results show that drug kinetics affect selection for resistance in a complicated manner, and that pathogen-specific models are needed to evaluate the benefits of new long-acting therapies.

What drives the dynamics of HBV RNA during treatment?

Hepatitis B virus RNA (HBV RNA)-containing particles are encapsidated pre-genomic RNA (pgRNA) detectable in chronically infected patients in addition to virions (HBV DNA) that have been suggested as a marker of the treatment efficacy. This makes promising the use of core protein allosteric modulators, such as RG7907, which disrupt the nucleocapsid assembly and profoundly reduce HBV RNA. Here, we developed a multiscale model of HBV extending the standard viral dynamic models to analyse the kinetics of HBV DNA and HBV RNA in 35 patients treated with RG7907 for 28 days. We compare the predictions with those obtained in patients treated with the nucleotide analog tenofovir. RG7907 blocked 99.3% of pgRNA encapsidation (range: 92.1%-99.9%) which led to a decline of both HBV DNA and HBV RNA. As a consequence of its mode of action, the first phase of decline of HBV RNA was rapid, uncovering the clearance of viral particles with half-life of 45 min. In contrast, HBV DNA decline was predicted to be less rapid, due to the continuous secretion of already formed viral capsids (t_1/2  = 17 ± 6 h). After few days, both markers declined at the same rate, which was attributed to the loss of infected cells (t_1/2  ≅ 6 ± 0.8 days). By blocking efficiently RNA reverse transcription but not its encapsidation, nucleotide analog in contrast was predicted to lead to a transient accumulation of HBV RNA both intracellularly and extracellularly. The model brings a conceptual framework for understanding the differences between HBV DNA and HBV RNA dynamics. Integration of HBV RNA in viral dynamic models may be helpful to better quantify the treatment effect, especially in viral-suppressed patients where HBV DNA is no longer detectable.

An approximate solution of the interferon-dependent viral kinetics model of influenza

The analysis of viral kinetics models is mostly achieved by numerical methods. We present an approach via a Magnus expansion that allows us to give an approximate solution to the interferon-dependent viral infection model of influenza which is compared with numerical results. The time of peak viral load is calculated from the approximation and stays within 10% in the studied range of interferon (IFN) efficacy ϵ ∈ [0, 1000]. We utilize our solution to interpret the effect of varying IFN efficacy, suggesting a competition between virions and interferon that can cause an additional peak in the usually exponential increase in the viral load.

A multiscale model of virus pandemic: Heterogeneous interactive entities in a globally connected world

This paper is devoted to the multidisciplinary modelling of a pandemic initiated by an aggressive virus, specifically the so-called SARS-CoV-2 Severe Acute Respiratory Syndrome, corona virus n.2. The study is developed within a multiscale framework accounting for the interaction of different spatial scales, from the small scale of the virus itself and cells, to the large scale of individuals and further up to the collective behaviour of populations. An interdisciplinary vision is developed thanks to the contributions of epidemiologists, immunologists and economists as well as those of mathematical modellers. The first part of the contents is devoted to understanding the complex features of the system and to the design of a modelling rationale. The modelling approach is treated in the second part of the paper by showing both how the virus propagates into infected individuals, successfully and not successfully recovered, and also the spatial patterns, which are subsequently studied by kinetic and lattice models. The third part reports the contribution of research in the fields of virology, epidemiology, immune competition, and economy focussed also on social behaviours. Finally, a critical analysis is proposed looking ahead to research perspectives.

Cancer-induced immunosuppression can enable effectiveness of immunotherapy through bistability generation: A mathematical and computational examination

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The presence of an immunological barrier in cancer- immune system interaction (CISI) is consistent with the bistability patterns in that system.

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In CISI models, bistability patterns are consistent with immunosuppressive effects dominating immunoproliferative effects.

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Bistability could be harnessed to devise effective combination immunotherapy approaches.

Cancer immunotherapies rely on how interactions between cancer and immune system cells are constituted. The more essential to the emergence of the dynamical behavior of cancer growth these interactions are, the more effectively they may be used as mechanisms for interventions. Mathematical modeling can help unearth such connections, and help explain how they shape the dynamics of cancer growth. Here, we explored whether there exist simple, consistent properties of cancer-immune system interaction (CISI) models that might be harnessed to devise effective immunotherapy approaches. We did this for a family of three related models of increasing complexity. To this end, we developed a base model of CISI, which captures some essential features of the more complex models built on it. We find that the base model and its derivates can plausibly reproduce biological behavior that is consistent with the notion of an immunological barrier. This behavior is also in accord with situations in which the suppressive effects exerted by cancer cells on immune cells dominate their proliferative effects. Under these circumstances, the model family may display a pattern of bistability, where two distinct, stable states (a cancer-free, and a full-grown cancer state) are possible. Increasing the effectiveness of immune-caused cancer cell killing may remove the basis for bistability, and abruptly tip the dynamics of the system into a cancer-free state. Additionally, in combination with the administration of immune effector cells, modifications in cancer cell killing may be harnessed for immunotherapy without the need for resolving the bistability. We use these ideas to test immunotherapeutic interventions in silico in a stochastic version of the base model. This bistability-reliant approach to cancer interventions might offer advantages over those that comprise gradual declines in cancer cell numbers.

Interferon at the cellular, individual, and population level in hepatitis C virus infection: Its role in the interferon-free treatment era

The advent of powerful direct-acting antiviral agents (DAAs) has revolutionized the treatment of hepatitis C. DAAs cure nearly all patients with short duration, oral treatments. Significant efforts are now underway to optimize DAA-based treatments. We discuss the potential role of interferon in this optimization. Clinical studies present compelling evidence that DAAs perform better in treatment-naive individuals than in individuals who previously failed treatment with interferon, a surprising correlation because interferon and DAAs are thought to act independently. Recent mathematical models explore a mechanistic hypothesis underlying this correlation. The hypothesis invokes the action of interferon at the cellular, individual, and population levels. Strong interferon responses prevent the productive infection of cells, reduce viral replication, and impede the development of resistance to DAAs in infected individuals and improve cure rates elicited by DAAs in treated populations. The models develop descriptions of these processes, integrate them into a comprehensive framework, and capture clinical data quantitatively, providing a successful test of the hypothesis. Individuals with strong endogenous interferon responses thus present a promising subpopulation for reducing DAA treatment durations. This review discusses the conceptual advances made by the models, highlights the new insights they unravel, and examines their applicability to optimize DAA-based treatments.

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.

HCV Kinetic Models and Their Implications in Drug Development

Chronic infection with hepatitis C virus (HCV) affects about 170 million people worldwide and is a major cause of liver complications. Mathematical modeling of viral kinetics under treatment has provided insight into the viral life cycle, treatment effectiveness, and drugs' mechanisms of action. Here we review the implications of viral kinetic models at the different stages of development of anti-HCV agents.

A pharmacokinetic/viral kinetic model to evaluate the treatment effectiveness of danoprevir against chronic HCV

BACKGROUND

Viral kinetic models have proven useful to characterize treatment effectiveness during HCV therapy with interferon (IFN) or with direct-acting antivirals.

METHODS

We use a pharmacokinetic/viral kinetic (PK/VK) model to describe HCV RNA kinetics during treatment with danoprevir, a protease inhibitor. In a Phase I study, danoprevir monotherapy was administered for 14 days in ascending doses ranging from 200 to 600 mg per day to 40 patients of whom 32 were treatment-naive and 8 were non-responders to prior pegylated IFN-α/ribavirin treatment.

RESULTS

In all patients, a biphasic decline of HCV RNA during therapy was observed. A two-compartment PK model and a VK model that considered treatment effectiveness to vary with the predicted danoprevir concentration inside the second compartment provided a good fit to the viral load data. A time-varying effectiveness model was also used to fit the viral load data. The antiviral effectiveness increased in a dose-dependent manner, with a 14-day time-averaged effectiveness of 0.95 at the lowest dose (100 mg twice daily) and 0.99 at the highest dose (200 mg three times daily). Prior IFN non-responders exhibited a 14-day time-averaged effectiveness of 0.98 (300 mg twice daily). The second phase decline showed two different behaviours, with 30% of patients exhibiting a rapid decline of HCV RNA, comparable to that seen with other protease inhibitors (>0.3 day(-1)), whereas the viral decline was slower in the other patients.

CONCLUSIONS

Our results are consistent with the modest SVR rates from the INFORM-SVR study where patients were treated with a combination of mericitabine and ritonavir-boosted danoprevir.

Viral kinetic modeling: state of the art

Viral kinetic (VK) modeling has led to increased understanding of the within host dynamics of viral infections and the effects of therapy. Here we review recent developments in the modeling of viral infection kinetics with emphasis on two infectious diseases: hepatitis C and influenza. We review how VK modeling has evolved from simple models of viral infections treated with a drug or drug cocktail with an assumed constant effectiveness to models that incorporate drug pharmacokinetics and pharmacodynamics, as well as phenomenological models that simply assume drugs have time varying-effectiveness. We also discuss multiscale models that include intracellular events in viral replication, models of drug-resistance, models that include innate and adaptive immune responses and models that incorporate cell-to-cell spread of infection. Overall, VK modeling has provided new insights into the understanding of the disease progression and the modes of action of several drugs. We expect that VK modeling will be increasingly used in the coming years to optimize drug regimens in order to improve therapeutic outcomes and treatment tolerability for infectious diseases.