Virus Dynamics Model Research Articles

Hepatitis C Viral Entry Inhibitors Prolong Viral Suppression by Replication Inhibitors in Persistently-Infected Huh7 Cultures

Efforts to treat HCV patients are focused on developing antiviral combinations that lead to the eradication of infection. Thus, it is important to identify optimal combinations from the various viral inhibitor classes. Based on viral dynamic models, HCV entry inhibitors are predicted to reduce viral load in a monophasic manner reflecting the slow death rate of infected hepatocytes (t1/2 = 2–70 days) and the protection of naïve, un-infected cells from HCV infection. In contrast, replication inhibitors are predicted to reduce viral load in a biphasic manner. The initial rapid reduction phase is due to the inhibition of virus production and elimination of plasma virus (t1/2∼3 hours). The second, slower reduction phase results from the elimination of infected hepatocytes. Here we sought to compare the ability of HCV entry and replication inhibitors as well as combinations thereof to reduce HCV infection in persistently-infected Huh7 cells. Treatment with 5×EC50 of entry inhibitors anti-CD81 Ab or EI-1 resulted in modest (≤1 log10 RNA copies/ml), monophasic declines in viral levels during 3 weeks of treatment. In contrast, treatment with 5×EC50 of the replication inhibitors BILN-2016 or BMS-790052 reduced extracellular virus levels more potently (∼2 log10 RNA copies/ml) over time in a biphasic manner. However, this was followed by a slow rise to steady-state virus levels due to the emergence of resistance mutations. Combining an entry inhibitor with a replication inhibitor did not substantially enhance the rate of virus reduction. However, entry/replication inhibitor and replication/replication inhibitor combinations reduced viral levels further than monotherapies (up to 3 log10 RNA copies/ml) and prolonged this reduction relative to monotherapies. Our results demonstrated that HCV entry inhibitors combined with replication inhibitors can prolong antiviral suppression, likely due to the delay of viral resistance emergence.

A Delay Virus Dynamics Model with General Incidence Rate

In this paper, the dynamical behavior of a virus dynamics model with general incidence rate and intracellular delay is studied. Lyapunov functionals are constructed and LaSalle invariance principle for delay differential equation is used to establish the global asymptotic stability of the disease-free equilibrium and the chronic infection equilibrium. The results obtained show that the global dynamics are completely determined by the value of a certain threshold parameter called the basic reproduction number $$R_0$$ and under some assumptions on the general incidence function. Our results extend the known results on delay virus dynamics considered in other papers and suggest useful methods to control virus infection. These results can be applied to a variety of possible incidence functions that could be used in virus dynamics model as well as epidemic models.

A class of delayed virus dynamics models with multiple target cells

Two delayed virus dynamics models with multi-target cells and bilinear incidence rate or general incidence rate are studied in this paper. The delays correspond to be the time needed for a newly infected cell to start producing viruses and the time needed for a newly produced virus to become infectious, respectively. Our models include \(n\) uninfected target cells, \(n\) infected target cells and the virus particles. By constructing Lyapunov functionals, we establish the global asymptotic stabilities of the infection-free equilibria and positive equilibria of these models.

Turing Patterns from Dynamics of Early HIV Infection

We have developed a mathematical model for in-host virus dynamics that includes spatial chemotaxis and diffusion across a two-dimensional surface representing the vaginal or rectal epithelium at primary HIV infection. A linear stability analysis of the steady state solutions identified conditions for Turing instability pattern formation. We have solved the model equations numerically using parameter values obtained from previous experimental results for HIV infections. Simulations of the model for this surface show hot spots of infection. Understanding this localization is an important step in the ability to correctly model early HIV infection. These spatial variations also have implications for the development and effectiveness of microbicides against HIV.

847 ACH-2684 DEMONSTRATES POTENT VIRAL SUPPRESSION IN GENOTYPE 1 HEPATITIS C PATIENTS WITH AND WITHOUT CIRRHOSIS: SAFETY, PHARMACOKINETIC, AND VIRAL KINETIC ANALYSIS

Background: ACH-2684 is a second-generation HCV NS3 protease inhibitor in Phase Ib development for the treatment of chronic HCV infection. ACH-2684 demonstrates potent activity in vitro against genotype-1 (GT1) HCV and, as compared to other protease inhibitors, has improved activity against multiple viral variants. Presented here are phase I study results in cirrhotic and non-cirrhotic patients with chronic HCV GT1 infection. Methods: ACH-2684 or placebo was administered to non-cirrhotic (n = 30) and cirrhotic (n = 8) patients with chronic HCV GT1 infection. Pharmacokinetic, (PK) viral load and safety assessments were collected on Days 1 through 35. Serial blood samples were collected on Day 1 and Day 3, and plasma non-compartmental pharmacokinetic parameters were determined. Drug efficiency was estimated by applying a single population viral dynamics model (Neumann et al, Science 1998, 282,103). Results: ACH-2684 was safe and well tolerated in non-cirrhotic and cirrhotic patients. There were no serious adverse events, and no discontinuations for safety concerns. Mean maximum reductions in plasma HCV RNA were 3.36, 3.73 and 4.16 log10 (IU/ml) at doses of 100 mg daily, 400 mg daily and 400 mg twice daily, respectively. In cirrhotic patients administered 400 mg daily, mean maximum reduction was 3.67 log10 (IU/ml). The systemic exposures were generally greater than doseproportional for the dose range studied in non-cirrhotics, and approximately 2-fold higher in cirrhotic versus non-cirrhotic patients. The drug efficiency of the 400 mg daily dose in non-cirrhotic and cirrhotic subjects was similar at 0.9993 ± 0.0005 and 0.9991 ± 0.0007, respectively. Conclusions: ACH-2684 was safe and well-tolerated, and produced more than a 3 log10 (IU/ml) mean maximum reduction in plasma HCV RNA levels in all groups. A 400 mg dose of ACH-2684 yielded approximately a 2-fold higher exposure in cirrhotics than non-cirrhotics, but was still safe and well-tolerated, and was equally effective in reducing HCV RNA levels. Viral kinetics parameters were robust and demonstrated high drug efficiency. These data provide evidence that ACH-2684 is a safe and well-tolerated protease inhibitor with potent anti-viral activity in both cirrhotic and non-cirrhotic patients with chronic GT-1 HCV infection, making it a promising candidate for future treatment of chronic HCV infection.

Pulse HIV Vaccination: Feasibility for Virus Eradication and Optimal Vaccination Schedule

We modify the classical virus dynamics model by incorporating an immune response with fixed or fluctuating vaccination frequencies and dosages to obtain a system of impulsive differential equations for the virus dynamics of both the wild-type and mutant strains. This model framework permits us to obtain precise conditions for the virus elimination, which are much more feasible compared with existing results, which require frequent vaccine administration with large dosage. We also consider the corresponding impulsive optimal control problem to describe when and how much of the vaccine should be administered in order to maximize levels of healthy CD4(+) T cells and immune response cells. A gradient-based optimization method is applied to obtain the optimal schedule numerically. For a case study when the CTL vaccine is administered in a period of one year, our numerical studies support the optimal vaccination schedule consisting of vaccine administration three times, with the first dosage strong (to boost the immune system), followed by a second dosage shortly after (to strengthen the immune response) and then the third and final dosage long after (to ensure the immune system can handle viruses rebound).

Analysis of Hepatitis C Virus Decline during Treatment with the Protease Inhibitor Danoprevir Using a Multiscale Model

The current paradigm for studying hepatitis C virus (HCV) dynamics in patients utilizes a standard viral dynamic model that keeps track of uninfected (target) cells, infected cells, and virus. The model does not account for the dynamics of intracellular viral replication, which is the major target of direct-acting antiviral agents (DAAs). Here we describe and study a recently developed multiscale age-structured model that explicitly considers the potential effects of DAAs on intracellular viral RNA production, degradation, and secretion as virus into the circulation. We show that when therapy significantly blocks both intracellular viral RNA production and virus secretion, the serum viral load decline has three phases, with slopes reflecting the rate of serum viral clearance, the rate of loss of intracellular viral RNA, and the rate of loss of intracellular replication templates and infected cells, respectively. We also derive analytical approximations of the multiscale model and use one of them to analyze data from patients treated for 14 days with the HCV protease inhibitor danoprevir. Analysis suggests that danoprevir significantly blocks intracellular viral production (with mean effectiveness 99.2%), enhances intracellular viral RNA degradation about 5-fold, and moderately inhibits viral secretion (with mean effectiveness 56%). The multiscale model can be used to study viral dynamics in patients treated with other DAAs and explore their mechanisms of action in treatment of hepatitis C.

Modeling the Acute and Chronic Phases of Theiler Murine Encephalomyelitis Virus Infection

Theiler murine encephalomyelitis virus (TMEV) infection of a mouse's central nervous system is biphasic: first the virus infects motor neurons (acute phase), and this is followed by a chronic phase in which the virus infects glial cells (primarily microglia and macrophages [M]) of the spinal cord white matter, leading to inflammation and demyelination. As such, TMEV-induced demyelinating disease in mice provides a highly relevant experimental animal model for multiple sclerosis. Mathematical models have proven valuable in understanding the in vivo dynamics of persistent virus infections, such as HIV-1, hepatitis B virus, and hepatitis C virus infections. However, viral dynamic modeling has not been used for understanding TMEV infection. We constructed the first mathematical model of TMEV-host kinetics during acute and early chronic infections in mice and fit measured viral kinetic data with the model. The data fitting allowed us to estimate several unknown parameters, including the following: the rate of infection of neurons, 0.5 × 10(-8) to 5.6 × 10(-8) day(-1); the percent reduction of the infection rate due to the presence of virus-specific antibodies, which reaches 98.5 to 99.9% after day 15 postinfection (p.i.); the half-life of infected neurons, 0.1 to 1.2 days; and a cytokine-enhanced macrophage source rate of 25 to 350 M/day into the spinal cord starting at 10.9 to 12.9 days p.i. The model presented here is a first step toward building a comprehensive model for TMEV-induced demyelinating disease. Moreover, the model can serve as an important tool in understanding TMEV infectious mechanisms and may prove useful in evaluating antivirals and/or therapeutic modalities to prevent or inhibit demyelination.

Virus dynamics in the presence of synaptic transmission

Traditionally, virus dynamics models consider populations of infected and target cells, and a population of free virus that can infect susceptible cells. In recent years, however, it has become. clear that direct cell-to-cell transmission can also play an important role for the in vivo spread of viruses, especially retroviruses such as human T lymphotropic virus-1 (HTLV-1) and Human immunodeficiency virus (HIV). Such cell-to-cell transmission is thought to occur through the formation of virological synapses that are formed between an infected source cell and a susceptible target cell. Here we formulate and analyze a class of virus dynamics models that include such cell–cell synaptic transmission. We explore different “strategies” of the virus defined by the number of viruses passed per synapse, and determine how the choice of strategy influences the basic reproductive ratio, R0, of the virus and thus its ability to establish a persistent infection. We show that depending on specific assumptions about the viral kinetics, strategies with low or intermediate numbers of viruses transferred may correspond to the highest values of R0. We also explore the evolutionary competition of viruses of different strains, which differ by their synaptic strategy, and show that viruses characterized by synaptic strategies with the highest R0 win the evolutionary competition and exclude other, inferior, strains.

A model of HIV drug resistance driven by heterogeneities in host immunity and adherence patterns

BackgroundPopulation transmission models of antiretroviral therapy (ART) and pre-exposure prophylaxis (PrEP) use simplistic assumptions – typically constant, homogeneous rates – to represent the short-term risk and long-term effects of drug resistance. In contrast, within-host models of drug resistance allow for more detailed dynamics of host immunity, latent reservoirs of virus, and drug PK/PD. Bridging these two levels of modeling detail requires an understanding of the “levers” – model parameters or combinations thereof – that change only one independent observable at a time. Using the example of accidental tenofovir-based pre-exposure prophyaxis (PrEP) use during HIV infection, we will explore methods of implementing host heterogeneities and their long-term effects on drug resistance.ResultsWe combined and extended existing models of virus dynamics by incorporating pharmacokinetics, pharmacodynamics, and adherence behavior. We identified two “levers” associated with the host immune pressure against the virus, which can be used to independently modify the setpoint viral load and the shape of the acute phase viral load peak. We propose parameter relationships that can explain differences in acute and setpoint viral load among hosts, and demonstrate their influence on the rates of emergence and reversion of drug resistance. The importance of these dynamics is illustrated by modeling long-lived latent reservoirs of virus, through which past intervals of drug resistance can lead to failure of suppressive drug regimens. Finally, we analyze assumptions about temporal patterns of drug adherence and their impact on resistance dynamics, finding that with the same overall level of adherence, the dwell times in drug-adherent versus not-adherent states can alter the levels of drug-resistant virus incorporated into latent reservoirs.ConclusionsWe have shown how a diverse range of observable viral load trajectories can be produced from a basic model of virus dynamics using immunity-related “levers”. Immune pressure, in turn, influences the dynamics of drug resistance, with increased immune activity delaying drug resistance and driving more rapid return to dominance of drug-susceptible virus after drug cessation. Both immune pressure and patterns of drug adherence influence the long-term risk of drug resistance. In the case of accidental PrEP use during infection, rapid transitions between adherence states and/or weak immunity fortifies the “memory” of previous PrEP exposure, increasing the risk of future drug resistance. This model framework provides a means for analyzing individual-level risks of drug resistance and implementing heterogeneities among hosts, thereby achieving a crucial prerequisite for improving population-level models of drug resistance.

Mathematical Modeling of Triphasic Viral Dynamics in Patients with HBeAg-Positive Chronic Hepatitis B Showing Response to 24-Week Clevudine Therapy

BackgroundModeling of short-term viral dynamics of hepatitis B with traditional biphasic model might be insufficient to explain long-term viral dynamics. The aim was to develop a novel method of mathematical modeling to shed light on the dissociation between early and long-term dynamics in previous studies.MethodsWe investigated the viral decay pattern in 50 patients from the phase III clinical trial of 24-week clevudine therapy, who showed virological response and HBsAg decline. Immune effectors were added as a new compartment in the model equations. We determined some parameter values in the model using the non-linear least square minimization method.ResultsMedian baseline viral load was 8.526 Log10copies/mL, and on-treatment viral load decline was 5.683 Log10copies/mL. The median half-life of free virus was 24.89 hours. The median half-life of infected hepatocytes was 7.39 days. The viral decay patterns were visualized as triphasic curves with decreasing slopes over time: fastest decay in the first phase; slowest in the third phase; the second phase in between.ConclusionsIn the present study, mathematical modeling of hepatitis B in patients with virological response and HBsAg decline during 24-week antiviral therapy showed triphasic viral dynamics with direct introduction of immune effectors as a new compartment, which was thought to reflect the reduction of clearance rate of infected cells over time. This modeling method seems more appropriate to describe long-term viral dynamics compared to the biphasic model, and needs further validation.

Nested model reveals potential amplification of an HIV epidemic due to drug resistance

The use of antiretroviral therapy (ART) is the most efficient measure in controlling the HIV epidemic. However, emergence of drug-resistant strains can reduce the potential benefits of ART. The viral dynamics of drug-sensitive and drug-resistant strains at the individual level may play a crucial role in the emergence and spread of drug resistance in a population.We investigate the effect of the viral dynamics within an infected individual on the epidemiological dynamics of HIV using a nested model that links both dynamical levels. A time-dependent between-host transmission rate that receives feedback from a model of two-strain virus dynamics within a host is incorporated into an epidemiological model of HIV. We analyze the resulting dynamics of the model and identify model parameters such as time when ART is initiated, fraction of cases treated, and the probability that a patient develops drug resistance, as having the greatest impact on total infection and prevalence of drug resistance. Importantly, for small values of the risk of a patient developing drug resistance, increasing the fraction of cases treated can increase the cumulative number of infected individuals. Such a pattern is the result of the balance between not treating a patient and having future cases still sensitive to treatment, and treating the patient and increasing the chances for future (untreatable) drug-resistant infections.The current modeling framework incorporates important aspects of virus dynamics within a host into an epidemic model. This approach provides useful insights on the drug resistance dynamics of an epidemic of HIV, which may assist in identifying an optimal use of ART.

Stability of the virus dynamics model with Beddington–DeAngelis functional response and delays

A virus dynamics model with Beddington–DeAngelis functional response and delays is introduced. By analyzing the characteristic equations, the local stability of an infection-free equilibrium and a chronic-infection equilibrium of the model is established. By using suitable Lyapunov functionals and the LaSalle invariance principle, we show that the infection-free equilibrium is globally asymptotically stable if R0⩽1 and the chronic-infection equilibrium is globally asymptotically stable if R0>1. Numerical simulations are also given to explain our results.

Pre-existence and emergence of drug resistance in a generalized model of intra-host viral dynamics

Understanding the source of drug resistance emerging within a treated patient is an important problem, from both clinical and basic evolutionary perspectives. Resistant mutants may arise de novo either before or after treatment is initiated, with different implications for prevention. Here we investigate this problem in the context of chronic viral diseases, such as human immunodeficiency virus (HIV) and hepatitis B and C viruses (HBV and HCV). We present a unified model of viral population dynamics within a host, which can capture a variety of viral life cycles. This allows us to identify which results generalize across various viral diseases, and which are sensitive to the particular virus's life cycle. Accurate analytical approximations are derived that allow for a solid understanding of the parameter dependencies in the system. We find that the mutation-selection balance attained prior to treatment depends on the step at which mutations occur and the viral trait that incurs the cost of resistance. Life cycle effects and key parameters, including mutation rate, infected cell death rate, cost of resistance, and drug efficacy, play a role in determining when mutations arising during treatment are important relative to those pre-existing.

Systems mapping of HIV-1 infection

Mathematical models of viral dynamics in vivo provide incredible insights into the mechanisms for the nonlinear interaction between virus and host cell populations, the dynamics of viral drug resistance, and the way to eliminate virus infection from individual patients by drug treatment. The integration of these mathematical models with high-throughput genetic and genomic data within a statistical framework will raise a hope for effective treatment of infections with HIV virus through developing potent antiviral drugs based on individual patients’ genetic makeup. In this opinion article, we will show a conceptual model for mapping and dictating a comprehensive picture of genetic control mechanisms for viral dynamics through incorporating a group of differential equations that quantify the emergent properties of a system.

Modeling of Viral Dynamics after Liver Transplantation in Patients with Chronic Hepatitis B and D

Viral kinetic models have become an important tool for understanding the main biological processes behind the dynamics of chronic viral diseases and optimizing effectiveness of anti-viral therapy. We analyzed the dynamics of hepatitis B and D co-infection (HBV/HDV) and the pharmacokinetics/pharmacodynamics of the reinfection prophylaxis with polyclonal antibodies after liver transplantation. Therefore we developed a mechanistic model consisting of a system of ordinary differential equations. This model was fitted by analyzing the kinetics of HBV/HDV viremia after liver transplantation in patient data and correlated with the reinfection prophylaxis dosing schemes. The results suggest that this modeling approach may help to optimize reinfection prophylaxis.

Mathematical modeling of viral infection dynamics in spherical organs

A general mathematical model of viral infections inside a spherical organ is presented. Transported quantities are used to represent external cells or viral particles that penetrate the organ surface to either promote or combat the infection. A diffusion mechanism is considered for the migration of transported quantities to the organ inner tissue. Cases that include the effect of penetration, diffusion and proliferation of immune system cells, the generation of latently infected cells and the delivery of antiviral treatment are analyzed. Different antiviral mechanisms are modeled in the context of spatial variation. Equilibrium conditions are also calculated to determine the radial profile after the infection progresses and antiviral therapy is delivered for a long period of time. The dynamic and equilibrium solutions obtained in this paper provide insight into the temporal and spatial evolution of viral infections.

Viral Dynamic Model of Antiretroviral Therapy Including the Integrase Inhibitor Raltegravir in Patients with HIV-1

Antiviral combination therapies consisting of reverse transcriptase inhibitors, protease inhibitors and an integrase inhibitor, have been developed to suppress HIV below the limit of detection. We introduce a mathematical model for the effect of different combination treatment regimens on the dynamics of HIV RNA and CD4 T-cell counts. We will especially focus on modelling the treatment effect of the integrase inhibitor-Raltegravir. The model consists of a system of ordinary differential equations and the parameters were chosen or estimated in order to agree with clinical data of a recent clinical trial. All the numerical simulations were calculated with Matlab.

Viral dynamics model with CTL immune response incorporating antiretroviral therapy

We present two HIV models that include the CTL immune response, antiretroviral therapy and a full logistic growth term for uninfected CD4+ T-cells. The difference between the two models lies in the inclusion or omission of a loss term in the free virus equation. We obtain critical conditions for the existence of one, two or three steady states, and analyze the stability of these steady states. Through numerical simulation we find substantial differences in the reproduction numbers and the behaviour at the infected steady state between the two models, for certain parameter sets. We explore the effect of varying the combination drug efficacy on model behaviour, and the possibility of reconstituting the CTL immune response through antiretroviral therapy. Furthermore, we employ Latin hypercube sampling to investigate the existence of multiple infected equilibria.

Analysis of the Virus Dynamics Model Reveals That Early Treatment of HCV Infection May Lead to the Sustained Virological Response

Considerable progress has been made towards understanding hepatitis C virus, its pathogenesis and the effect of the drug therapy on the viral load, yet around 50% of patients do not achieve the sustained virological response (SVR) by the standard treatment. Although several personalized factors such as patients’ age and weight may be important, by mathematical modeling we show that the time of the start of the therapy is a significant factor in determining the outcome. Toward this end, we first performed sensitivity analysis on the standard virus dynamics model. The analysis revealed four phases when the sensitivity of the infection to drug treatment differs. Further, we added a perturbation term in the model to simulate the drug treatment period and predict the outcome when the therapy is carried out during each of the four phases. The study shows that while the infection may be difficult to treat in the late phases, the therapy is likely to result in SVR if it is carried out in the first or second phase. Thus, development of newer and more sensitive screening methods is needed for the early detection of the infection. Moreover, the analysis predicts that the drug that blocks new infections is more effective than the drug that blocks the virus production.