Jessica M. Conway

Post-treatment control of HIV infection.

Significance Recent reports suggest that antiretroviral therapy (ART) initiated early after HIV infection increases the likelihood of post-treatment control (PTC) in which plasma virus remains undetectable after treatment cessation. However, only a small fraction of patients treated early attain PTC. We develop a mathematical model of HIV infection that provides insight into these phenomena, suggesting that treatments restricting or reducing the latent reservoir size may allow immune responses to control infection posttreatment. Our model makes predictions about immune response strengths and latent reservoir sizes needed for a patient taken off treatment to exhibit PTC that may help guide future studies. Antiretroviral therapy (ART) for HIV is not a cure. However, recent studies suggest that ART, initiated early during primary infection, may induce post-treatment control (PTC) of HIV infection with HIV RNA maintained at <50 copies per mL. We investigate the hypothesis that ART initiated early during primary infection permits PTC by limiting the size of the latent reservoir, which, if small enough at treatment termination, may allow the adaptive immune response to prevent viral rebound (VR) and control infection. We use a mathematical model of within host HIV dynamics to capture interactions among target cells, productively infected cells, latently infected cells, virus, and cytotoxic T lymphocytes (CTLs). Analysis of our model reveals a range in CTL response strengths where a patient may show either VR or PTC, depending on the size of the latent reservoir at treatment termination. Below this range, patients will always rebound, whereas above this range, patients are predicted to behave like elite controllers. Using data on latent reservoir sizes in patients treated during primary infection, we also predict population-level VR times for noncontrollers consistent with observations.

A Stochastic Model of Latently Infected Cell Reactivation and Viral Blip Generation in Treated HIV Patients

Motivated by viral persistence in HIV+ patients on long-term anti-retroviral treatment (ART), we present a stochastic model of HIV viral dynamics in the blood stream. We consider the hypothesis that the residual viremia in patients on ART can be explained principally by the activation of cells latently infected by HIV before the initiation of ART and that viral blips (clinically-observed short periods of detectable viral load) represent large deviations from the mean. We model the system as a continuous-time, multi-type branching process. Deriving equations for the probability generating function we use a novel numerical approach to extract the probability distributions for latent reservoir sizes and viral loads. We find that latent reservoir extinction-time distributions underscore the importance of considering reservoir dynamics beyond simply the half-life. We calculate blip amplitudes and frequencies by computing complete viral load probability distributions, and study the duration of viral blips via direct numerical simulation. We find that our model qualitatively reproduces short small-amplitude blips detected in clinical studies of treated HIV infection. Stochastic models of this type provide insight into treatment-outcome variability that cannot be found from deterministic models.

Impact of different oseltamivir regimens on treating influenza A virus infection and resistance emergence: insights from a modelling study.

Several studies have proven oseltamivir to be efficient in reducing influenza viral titer and symptom intensity. However, the usefulness of oseltamivir can be compromised by the emergence and spread of drug-resistant virus. The selective pressure exerted by different oseltamivir therapy regimens have received little attention. Combining models of drug pharmacokinetics, pharmacodynamics, viral kinetics and symptom dynamics, we explored the efficacy of oseltamivir in reducing both symptoms (symptom efficacy) and viral load (virological efficacy). We simulated samples of 1000 subjects using previously estimated between-subject variability in viral and symptom dynamic parameters to describe the observed heterogeneity in a patient population. We simulated random mutations conferring resistance to oseltamivir. We explored the effect of therapy initiation time, dose, intake frequency and therapy duration on influenza infection, illness dynamics, and emergence of viral resistance. Symptom and virological efficacies were strongly associated with therapy initiation time. The proportion of subjects shedding resistant virus was 27-fold higher when prophylaxis was initiated during the incubation period compared with no treatment. It fell to below 1% when treatment was initiated after symptom onset for twice-a-day intakes. Lower doses and prophylaxis regimens led to lower efficacies and increased risk of resistance emergence. We conclude that prophylaxis initiated during the incubation period is the main factor leading to resistance emergence.

Vaccination against 2009 pandemic H1N1 in a population dynamical model of Vancouver, Canada: timing is everything

BackgroundMuch remains unknown about the effect of timing and prioritization of vaccination against pandemic (pH1N1) 2009 virus on health outcomes. We adapted a city-level contact network model to study different campaigns on influenza morbidity and mortality.MethodsWe modeled different distribution strategies initiated between July and November 2009 using a compartmental epidemic model that includes age structure and transmission network dynamics. The model represents the Greater Vancouver Regional District, a major North American city and surrounding suburbs with a population of 2 million, and is parameterized using data from the British Columbia Ministry of Health, published studies, and expert opinion. Outcomes are expressed as the number of infections and deaths averted due to vaccination.ResultsThe model output was consistent with provincial surveillance data. Assuming a basic reproduction number = 1.4, an 8-week vaccination campaign initiated 2 weeks before the epidemic onset reduced morbidity and mortality by 79-91% and 80-87%, respectively, compared to no vaccination. Prioritizing children and parents for vaccination may have reduced transmission compared to actual practice, but the mortality benefit of this strategy appears highly sensitive to campaign timing. Modeling the actual late October start date resulted in modest reductions in morbidity and mortality (13-25% and 16-20%, respectively) with little variation by prioritization scheme.ConclusionDelays in vaccine production due to technological or logistical barriers may reduce potential benefits of vaccination for pandemic influenza, and these temporal effects can outweigh any additional theoretical benefits from population targeting. Careful modeling may provide decision makers with estimates of these effects before the epidemic peak to guide production goals and inform policy. Integration of real-time surveillance data with mathematical models holds the promise of enabling public health planners to optimize the community benefits from proposed interventions before the pandemic peak.

Residual Viremia in Treated HIV+ Individuals

Antiretroviral therapy (ART) effectively controls HIV infection, suppressing HIV viral loads. However, some residual virus remains, below the level of detection, in HIV-infected patients on ART. The source of this viremia is an area of debate: does it derive primarily from activation of infected cells in the latent reservoir, or from ongoing viral replication? Observations seem to be contradictory: there is evidence of short term evolution, implying that there must be ongoing viral replication, and viral strains should thus evolve. However, phylogenetic analyses, and rare emergent drug resistance, suggest no long-term viral evolution, implying that virus derived from activated latent cells must dominate. We use simple deterministic and stochastic models to gain insight into residual viremia dynamics in HIV-infected patients. Our modeling relies on two underlying assumptions for patients on suppressive ART: that latent cell activation drives viral dynamics and that the reproductive ratio of treated infection is less than 1. Nonetheless, the contribution of viral replication to residual viremia in patients on ART may be non-negligible. However, even if the portion of viremia attributable to viral replication is significant, our model predicts (1) that latent reservoir re-seeding remains negligible, and (2) some short-term viral evolution is permitted, but long-term evolution can still be limited: stochastic analysis of our model shows that de novo emergence of drug resistance is rare. Thus, our simple models reconcile the seemingly contradictory observations on residual viremia and, with relatively few parameters, recapitulates HIV viral dynamics observed in patients on suppressive therapy.

STOCHASTIC ANALYSIS OF PRE- AND POSTEXPOSURE PROPHYLAXIS AGAINST HIV INFECTION ∗

The events that occur following HIV exposure, preceding any detectable infection, are difficult to study experimentally. However, there is considerable evidence that these events can be influenced by the action of antiretroviral drugs, taken either as pre- or postexposure prophylaxis (PrEP and PEP, respectively). We present simple theoretical models of HIV dynamics immediately following exposure, and apply these models to understanding how drug prophylaxis can act to reduce the risk of infection. Because HIV infection following exposure is a relatively rare event, we work with stochastic models which we base on continuous-time branching processes, allowing us to compute the risk of infection under different scenarios. We obtain analytical solutions for viral extinction probabilities, allowing us to avoid extensive computer simulations. We predict in the case of PrEP that reverse transcriptase inhibitors should be somewhat more effective than protease inhibitors and also that single drugs should be nearly ...

Recombination enhances HIV-1 envelope diversity by facilitating the survival of latent genomic fragments in the plasma virus population

HIV-1 is subject to immune pressure exerted by the host, giving variants that escape the immune response an advantage. Virus released from activated latent cells competes against variants that have continually evolved and adapted to host immune pressure. Nevertheless, there is increasing evidence that virus displaying a signal of latency survives in patient plasma despite having reduced fitness due to long-term immune memory. We investigated the survival of virus with latent envelope genomic fragments by simulating within-host HIV-1 sequence evolution and the cycling of viral lineages in and out of the latent reservoir. Our model incorporates a detailed mutation process including nucleotide substitution, recombination, latent reservoir dynamics, diversifying selection pressure driven by the immune response, and purifying selection pressure asserted by deleterious mutations. We evaluated the ability of our model to capture sequence evolution in vivo by comparing our simulated sequences to HIV-1 envelope sequence data from 16 HIV-infected untreated patients. Empirical sequence divergence and diversity measures were qualitatively and quantitatively similar to those of our simulated HIV-1 populations, suggesting that our model invokes realistic trends of HIV-1 genetic evolution. Moreover, reconstructed phylogenies of simulated and patient HIV-1 populations showed similar topological structures. Our simulation results suggest that recombination is a key mechanism facilitating the persistence of virus with latent envelope genomic fragments in the productively infected cell population. Recombination increased the survival probability of latent virus forms approximately 13-fold. Prevalence of virus with latent fragments in productively infected cells was observed in only 2% of simulations when we ignored recombination, while the proportion increased to 27% of simulations when we allowed recombination. We also found that the selection pressures exerted by different fitness landscapes influenced the shape of phylogenies, diversity trends, and survival of virus with latent genomic fragments. Our model predicts that the persistence of latent genomic fragments from multiple different ancestral origins increases sequence diversity in plasma for reasonable fitness landscapes.

Severity of liver disease affects HCV kinetics in patients treated with intravenous silibinin monotherapy

BACKGROUND HCV kinetic analysis and modelling during antiviral therapy have not been performed in decompensated cirrhotic patients awaiting liver transplantation. Here, viral and host parameters were compared in three groups of patients treated with daily intravenous silibinin (SIL) monotherapy for 7 days according to the severity of their liver disease. METHODS Data were obtained from 25 patients, 12 non-cirrhotic, 8 with compensated cirrhosis and 5 with decompensated cirrhosis. The standard-biphasic model with time-varying SIL effectiveness (from 0 to final effectiveness [εmax]) was fitted to viral kinetic data. RESULTS Baseline viral load and age were significantly associated with the severity of liver disease (P<0.0001). A biphasic viral decline was observed in most patients with a higher first phase decline in patients with less severe liver disease. The εmax was significantly (P≤0.032) associated with increasing severity of liver disease (non-cirrhotic εmax [se]=0.86 [0.05], compensated cirrhotic εmax=0.69 [0.06] and decompensated cirrhotic εmax=0.59 [0.1]). The second phase decline slope was not significantly different among groups (mean 1.88 ±0.15 log10 IU/ml/week, P=0.75) as was the rate of change of SIL effectiveness (k=2.12/day [se=0.18/day]). HCV-infected cell loss rate (δ [se]=0.62/day [0.05/day]) was high and similar among groups. CONCLUSIONS The high loss rate of HCV-infected cells suggests that sufficient dose and duration of SIL might achieve viral suppression in advanced liver disease.

Superlattice Patterns in the Complex Ginzburg–Landau Equation with Multiresonant Forcing

Motivated by the rich variety of complex patterns observed on the surface of fluid layers that are vibrated at multiple frequencies, we investigate the effect of such resonant forcing on systems undergoing a Hopf bifurcation to spatially homogeneous oscillations. We use an extension of the complex Ginzburg–Landau equation that systematically captures weak forcing functions with a spectrum consisting of frequencies close to the 1:1-, the 1:2-, and the 1:3-resonance. By slowly modulating the amplitude of the 1:2-forcing component, we render the bifurcation to subharmonic patterns supercritical despite the quadratic interaction introduced by the 1:3-forcing. Our weakly nonlinear analysis shows that quite generally the forcing function can be tuned such that resonant triad interactions with weakly damped modes stabilize subharmonic superlattice patterns comprising four or five Fourier modes. Using direct simulations of the extended complex Ginzburg–Landau equation, we confirm our weakly nonlinear analysis. In...

A Hepatitis C Virus Infection Model with Time-Varying Drug Effectiveness: Solution and Analysis

Simple models of therapy for viral diseases such as hepatitis C virus (HCV) or human immunodeficiency virus assume that, once therapy is started, the drug has a constant effectiveness. More realistic models have assumed either that the drug effectiveness depends on the drug concentration or that the effectiveness varies over time. Here a previously introduced varying-effectiveness (VE) model is studied mathematically in the context of HCV infection. We show that while the model is linear, it has no closed-form solution due to the time-varying nature of the effectiveness. We then show that the model can be transformed into a Bessel equation and derive an analytic solution in terms of modified Bessel functions, which are defined as infinite series, with time-varying arguments. Fitting the solution to data from HCV infected patients under therapy has yielded values for the parameters in the model. We show that for biologically realistic parameters, the predicted viral decay on therapy is generally biphasic and resembles that predicted by constant-effectiveness (CE) models. We introduce a general method for determining the time at which the transition between decay phases occurs based on calculating the point of maximum curvature of the viral decay curve. For the parameter regimes of interest, we also find approximate solutions for the VE model and establish the asymptotic behavior of the system. We show that the rate of second phase decay is determined by the death rate of infected cells multiplied by the maximum effectiveness of therapy, whereas the rate of first phase decline depends on multiple parameters including the rate of increase of drug effectiveness with time.