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Both in vitro and in vivo models are employed for assessing the pandemic potential of novel and emerging influenza A viruses in laboratory settings, but systematic examinations of how well viral titer measurements obtained in vitro align with results from in vivo experimentation are not frequently performed. We show that certain viral titer measurements following infection of a human bronchial epithelial cell line are positively correlated with viral titers in specimens collected from virus-inoculated ferrets and employ mathematical modeling to identify commonalities between viral infection progression between both models.

As influenza A viruses (IAV) continue to cross species barriers and cause human infection, the establishment of risk assessment rubrics has improved pandemic preparedness efforts.

Agent-based models have been employed to describe numerous processes in immunology. Simulations based on these types of models have been used to enhance our understanding of immunology and disease pathology. We review various agent-based models relevant to host-pathogen systems and discuss their contributions to our understanding of biological processes. We then point out some limitations and challenges of agent-based models and encourage efforts towards reproducibility and model validation., LaTeX, 12 pages, 1 EPS figure, uses document class REVTeX 4, and packages hyperref, xspace, graphics, amsmath, verbatim, and SIunits

Most mathematical models used to study the dynamics of influenza A have thus far focused on the between-host population level, with the aim to inform public health decisions regarding issues such as drug and social distancing intervention strategies, antiviral stockpiling or vaccine distribution. Here, we investigate mathematical modeling of influenza infection spread at a different scale; namely that occurring within an individual host or a cell culture. We review the models that have been developed in the last decades and discuss their contributions to our understanding of the dynamics of influenza infections. We review kinetic parameters (e.g., viral clearance rate, lifespan of infected cells) and values obtained through fitting mathematical models, and contrast them with values obtained directly from experiments. We explore the symbiotic role of mathematical models and experimental assays in improving our quantitative understanding of influenza infection dynamics. We also discuss the challenges in developing better, more comprehensive models for the course of influenza infections within a host or cell culture. Finally, we explain the contributions of such modeling efforts to important public health issues, and suggest future modeling studies that can help to address additional questions relevant to public health.

Atherosclerosis results from the deposition and oxidation of low-density lipoprotein (LDL) and immune cell infiltration in the sub-arterial space leading to arterial occlusion. Numerous studies have now shown that transcytosis transports the circulating LDL across endothelial cells lining the blood vessel. LDL transcytosis is initiated by binding to either Scavenger Receptor B1 (SR-B1) or Activin A receptor-like kinase 1 (ALK1) on the apical side of endothelial cells leading to its transit to the basolateral side. Individuals with elevated levels of circulating high-density lipoprotein (HDL) are partly protected from atherosclerosis due to its ability to remove excess cholesterol and act as an antioxidant. Apolipoprotein A1 (ApoA1), an HDL constituent, can bind to SR-B1, suggesting that ApoA1/HDL may also compete with LDL for SR-B1 binding and thereby oppose its deposition in the sub-arterial space. To examine this possibility, we used in vitro approaches to quantify the internalization and transcytosis of fluorescently labelled LDL in coronary endothelial cells. Using microscale thermophoresis and affinity capture, we find that SR-B1 and ApoA1 directly interact and that binding is enhanced when using the cardioprotective variant of ApoA1 termed Milano (ApoA1-Milano). In vivo injection of either wild-type ApoA1 or ApoA1-Milano significantly reduced the acute accumulation of LDL in the atheroprone inner curvature of the murine aorta; inhibition was greater with Milano than the wild-type ApoA1. Together, the results suggest that an additional mechanism for HDL’s atheroprotective effects is attenuating LDL transcytosis through competition for the SR-B1 receptor.

The infectivity of a virus sample is measured by the infections it causes, via a plaque or focus forming assay (PFU or FFU) or an endpoint dilution (ED) assay (TCID$_{50}$, CCID$_{50}$, EID$_{50}$, etc., hereafter collectively ID$_{50}$). The counting of plaques or foci at a given dilution intuitively and directly provides the concentration of infectious doses in the undiluted sample. However, it has many technical and experimental limitations. For example, it relies on one's judgement in distinguishing between two merged plaques and a larger one, or between small plaques and staining artifacts. In this regard, ED assays are more robust because one need only determine whether infection occurred. The output of the ED assay, the 50% infectious dose (ID$_{50}$), is calculated using either the Spearman-Karber (SK, 1908,1931) or Reed-Muench (RM, 1938) mathematical approximations. However, these are often miscalculated and their ID$_{50}$ approximation is biased. We propose that the PFU and FFU assays be abandoned, and that the measured output of the ED assay, the ID$_{50}$, be replaced by a more useful measure we coined Specific INfections (SIN). We introduce a free, open-source web-application, midSIN, that computes the SIN concentration in a virus sample from a standard ED assay, requiring no changes to current experimental protocols. We demonstrate that the SIN/mL of a sample reliably corresponds to the number of infections the sample will cause per unit volume, and directly relates to the multiplicity of infection. midSIN estimates are shown to be more accurate and robust than those using the RM and SK approximations. The impact of ED plate design choices (dilution factor, replicates per dilution) on measurement accuracy is also explored. The simplicity of SIN as a measure and the greater accuracy of midSIN make them an easy, superior replacement for the PFU, FFU, and ID$_{50}$ measures., Comment: 22 pages, 8 figures

Mathematical modelling of influenza A virus infection has seen increased use over the last several years. Models applied to both in vitro and in vivo data have provided important new understanding of the kinetics of the virus, the role of different components of the immune response, the importance of non-infectious influenza A virus particles, the issue of drug treatment and resistance, and the interaction mechanisms during bacterial co-infections. We review these contributions by mathematical models, with a focus on studies performed in the last several years. For continued progress, we emphasize robust data and parameter estimation approaches.

Background Developing a quantitative understanding of viral kinetics is useful for determining the pathogenesis and transmissibility of the virus, predicting the course of disease, and evaluating the effects of antiviral therapy. The availability of data in clinical, animal, and cell culture studies, however, has been quite limited. Many studies of virus infection kinetics have been based solely on measures of total or infectious virus count. Here, we introduce a new mathematical model which tracks both infectious and total viral load, as well as the fraction of infected and uninfected cells within a cell culture, and apply it to analyze time-course data of an SHIV infection in vitro. Results We infected HSC-F cells with SHIV-KS661 and measured the concentration of Nef-negative (target) and Nef-positive (infected) HSC-F cells, the total viral load, and the infectious viral load daily for nine days. The experiments were repeated at four different MOIs, and the model was fitted to the full dataset simultaneously. Our analysis allowed us to extract an infected cell half-life of 14.1 h, a half-life of SHIV-KS661 infectiousness of 17.9 h, a virus burst size of 22.1 thousand RNA copies or 0.19 TCID50, and a basic reproductive number of 62.8. Furthermore, we calculated that SHIV-KS661 virus-infected cells produce at least 1 infectious virion for every 350 virions produced. Conclusions Our method, combining in vitro experiments and a mathematical model, provides detailed quantitative insights into the kinetics of the SHIV infection which could be used to significantly improve the understanding of SHIV and HIV-1 pathogenesis. The method could also be applied to other viral infections and used to improve the in vitro determination of the effect and efficacy of antiviral compounds.

When analysing in vitro data, growth kinetics of influenza virus strains are often compared by computing their growth rates, which are sometimes used as proxies for fitness. However, analogous to mathematical models for epidemics, the growth rate can be defined as a function of mechanistic traits: the basic reproduction number (the average number of cells each infected cell infects) and the mean generation time (the average length of a replication cycle). Fitting a model to previously published and newly generated data from experiments in human lung cells, we compared estimates of growth rate, reproduction number and generation time for six influenza A strains. Of four strains in previously published data, A/Canada/RV733/2003 (seasonal H1N1) had the lowest basic reproduction number, followed by A/Mexico/INDRE4487/2009 (pandemic H1N1), then A/Indonesia/05/2005 (spill-over H5N1) and A/Anhui/1/2013 (spill-over H7N9). This ordering of strains was preserved for both generation time and growth rate, suggesting a positive biological correlation between these quantities which have not been previously observed. We further investigated these potential correlations using data from reassortant viruses with different internal proteins (from A/England/195/2009 (pandemic H1N1) and A/Turkey/05/2005 (H5N1)), and the same surface proteins (from A/Puerto Rico/8/34 (lab-adapted H1N1)). Similar correlations between traits were observed for these viruses, confirming our initial findings and suggesting that these patterns were related to the degree of human adaptation of internal genes. Also, the model predicted that strains with a smaller basic reproduction number, shorter generation time and slower growth rate underwent more replication cycles by the time of peak viral load, potentially accumulating mutations more quickly. These results illustrate the utility of mathematical models in inferring traits driving observed differences in in vitro growth of influenza strains.

Relativistic shocks propagating into a medium with low magnetization are generated and sustained by small-scale but very strong magnetic field turbulence. This so-called "microturbulence" modifies the typical shock acceleration process, and in particular that of electrons. In this work we perform Monte Carlo (MC) simulations of electrons encountering shocks with microturbulent fields. The simulations cover a three-dimensional parameter space in shock speed, acceleration efficiency, and peak magnetic field strength. From these, a Markov Chain Monte Carlo (MCMC) method was employed to estimate the maximum electron momentum from the MC-simulated electron spectra. Having estimated this quantity at many points well-distributed over an astrophysically relevant parameter space, an MCMC method was again used to estimate the parameters of an empirical formula that computes the maximum momentum of a Fermi-accelerated electron population anywhere in this parameter space. The maximum energy is well-approximated as a broken power-law in shock speed, with the break occurring when the shock decelerates to the point where electrons can begin to escape upstream from the shock., Comment: 18 pages, 2 figures, accepted in ApJ; arXiv version includes changes requested by referee

Mathematical modelling has successfully been used to provide quantitative descriptions of many viral infections, but for the Ebola virus, which requires biosafety level 4 facilities for experimentation, modelling can play a crucial role. Ebola virus modelling efforts have primarily focused on in vivo virus kinetics, e.g., in animal models, to aid the development of antivirals and vaccines. But, thus far, these studies have not yielded a detailed specification of the infection cycle, which could provide a foundational description of the virus kinetics and thus a deeper understanding of their clinical manifestation. Here, we obtain a diverse experimental data set of the Ebola virus infection in vitro, and then make use of Bayesian inference methods to fully identify parameters in a mathematical model of the infection. Our results provide insights into the distribution of time an infected cell spends in the eclipse phase (the period between infection and the start of virus production), as well as the rate at which infectious virions lose infectivity. We suggest how these results can be used in future models to describe co-infection with defective interfering particles, which are an emerging alternative therapeutic., Author summary The two deadliest Ebola virus epidemics have both occurred in the past five years, with one of these epidemics still ongoing. Mathematical modelling has already provided insights into the spread of disease at the population level as well as the effect of antiviral therapy in Ebola virus-infected animals. However, a quantitative description of the replication cycle is still missing. Here, we report results from a set of in vitro experiments involving infection with the Ecran strain of Ebola virus. By parameterizing a mathematical model, we are able to determine robust estimates for the duration of the replication cycle, the infectious burst size, and the viral clearance rate.

Many aspects of the respiratory syncytial virus (RSV) are still poorly understood. Yet these knowledge gaps have had and could continue to have adverse, unintended consequences for the efficacy and safety of antivirals and vaccines developed against RSV. Mathematical modelling was used to test and evaluate hypotheses about the rate of loss of RSV infectivity and the mechanisms and kinetics of RSV infection spread in SIAT cells in vitro. While the rate of loss of RSV integrity, as measured via qRT-PCR, is well-described by an exponential decay, the latter mechanism failed to describe the rate at which RSV A Long loses infectivity over time in vitro based on the data presented herein. This is unusual given that other viruses (HIV, HCV, influenza) have been shown to lose their infectivity exponentially in vitro, and indeed an exponential rate of loss of infectivity is always assumed in mathematical modelling and experimental analyses. The infectivity profile of RSV in HEp-2 and SIAT cells remained consistent over the course of an RSV infection, over time and a large range of infectivity. However, SIAT cells were found to be ∼ 100× less sensitive to RSV infection than HEp-2 cells. In particular, we found that RSV spreads inefficiently in SIAT cells, in a manner we show is consistent with the establishment of infection resistance in uninfected cells. SIAT cells are a good in vitro model in which to study RSV in vivo dissemination, yielding similar infection timescales. However, the higher sensitivity of HEp-2 cells to RSV together with its RSV infectivity profile being similar to that of SIAT cells, makes HEp-2 cells more suitable for quantifying RSV infectivity over the course of in vitro RSV infections in SIAT cells. Our findings highlight the importance and urgency of resolving the mechanisms at play in the dissemination of RSV infections in vitro, and the processes by which this infectivity is lost.

This study's objective was to develop models of endurance time (ET), as a function of load level (LL), and of resumption time (RT) after loading as a function of both LL and loading time (LT) for repeated loadings. Ten male participants with experience in construction work each performed 15 different one-handed repetaed pushing tasks at shoulder height with varied exerted force and duration. These data were used to create regression models predicting ET and RT. It is concluded that power law relationships are most appropriate to use when modelling ET and RT. While the data the equations are based on are limited regarding number of participants, gender, postures, magnitude and type of exerted force, the paper suggests how this kind of modelling can be used in job design and in further research. Practitioner Summary: Adequate muscular recovery during work-shifts is important to create sustainable jobs. This paper describes mathematical modelling and presents models for endurance times and resumption times (an aspect of recovery need), based on data from an empirical study. The models can be used to help manage fatigue levels in job design.

The duration of the eclipse phase, from cell infection to the production and release of the first virion progeny, immediately followed by the virus-production phase, from the first to the last virion progeny, are important steps in a viral infection, by setting the pace of infection progression and modulating the response to antiviral therapy. Using a mathematical model (MM) and data for the infection of HSC-F cells with SHIV in vitro, we reconfirm our earlier finding that the eclipse phase duration follows a fat-tailed distribution, lasting 19 h (18–20 h). Most importantly, for the first time, we show that the virus-producing phase duration, which lasts 11 h (9.8–12 h), follows a normal-like distribution, and not an exponential distribution as is typically assumed. We explore the significance of this finding and its impact on analysis of plasma viral load decays in HIV patients under antiviral therapy. We find that incorrect assumptions about the eclipse and virus-producing phase distributions can lead to an overestimation of antiviral efficacy. Additionally, our predictions for the rate of plasma HIV decay under integrase inhibitor therapy offer an opportunity to confirm whether HIV production duration in vivo also follows a normal distribution, as demonstrated here for SHIV infections in vitro.

Antiviral therapy is a first line of defence against new influenza strains. Current pandemic preparations involve stock- piling oseltamivir, an oral neuraminidase inhibitor (NAI), so rapidly determining the effectiveness of NAIs against new viral strains is vital for deciding how to use the stockpile. Previous studies have shown that it is possible to extract the drug efficacy of antivirals from the viral decay rate of chronic infections. In the present work, we use a nonlinear mathematical model representing the course of an influenza infection to explore the possibility of extracting NAI drug efficacy using only the observed viral titer decay rates seen in patients. We first show that the effect of a time-varying antiviral concentration can be accurately approximated by a constant efficacy. We derive a relationship relating the true treatment dose and time elapsed between doses to the constant drug dose required to approximate the time- varying dose. Unfortunately, even with the simplification of a constant drug efficacy, we show that the viral decay rate depends not just on drug efficacy, but also on several viral infection parameters, such as infection and production rate, so that it is not possible to extract drug efficacy from viral decay rate alone.

Mathematical models (MMs) have been used to study the kinetics of influenza A virus infections under antiviral therapy, and to characterize the efficacy of antivirals such as neuraminidase inhibitors (NAIs). NAIs prevent viral neuraminidase from cleaving sialic acid receptors that bind virus progeny to the surface of infected cells, thereby inhibiting their release, suppressing infection spread. When used to study treatment with NAIs, MMs represent viral release implicitly as part of viral replication. Consequently, NAIs in such MMs do not act specifically and exclusively on virus release. We compared a MM with an explicit representation of viral release (i.e., distinct from virus production) to a simple MM without explicit release, and investigated whether parameter estimation and the estimation of NAI efficacy were affected by the use of a simple MM. Since the release rate of influenza A virus is not well-known, a broad range of release rates were considered. If the virus release rate is greater than ∼0.1 h-1, the simple MM provides accurate estimates of infection parameters, but underestimates NAI efficacy, which could lead to underdosing and the emergence of NAI resistance. In contrast, when release is slower than ∼0.1 h-1, the simple MM accurately estimates NAI efficacy, but it can significantly overestimate the infectious lifespan (i.e., the time a cell remains infectious and producing free virus), and it will significantly underestimate the total virus yield and thus the likelihood of resistance emergence. We discuss the properties of, and a possible lower bound for, the influenza A virus release rate.

The threat of an influenza A virus pandemic stems from continual virus spillovers from reservoir species, a tiny fraction of which spark sustained transmission in humans. To date, no pandemic emergence of a new influenza strain has been preceded by detection of a closely related precursor in an animal or human. Nonetheless, influenza surveillance efforts are expanding, prompting a need for tools to assess the pandemic risk posed by a detected virus. The goal would be to use genetic sequence and/or biological assays of viral traits to identify those non-human influenza viruses with the greatest risk of evolving into pandemic threats, and/or to understand drivers of such evolution, to prioritize pandemic prevention or response measures. We describe such efforts, identify progress and ongoing challenges, and discuss three specific traits of influenza viruses (hemagglutinin receptor binding specificity, hemagglutinin pH of activation, and polymerase complex efficiency) that contribute to pandemic risk. DOI: http://dx.doi.org/10.7554/eLife.18491.001

Avian influenza viruses present an emerging epidemiological concern as some strains of H5N1 avian influenza can cause severe infections in humans with lethality rates of up to 60%. These have been in circulation since 1997 and recently a novel H7N9-subtyped virus has been causing epizootics in China with lethality rates around 20%. To better understand the replication kinetics of these viruses, we combined several extensive viral kinetics experiments with mathematical modelling of in vitro infections in human A549 cells. We extracted fundamental replication parameters revealing that, while both the H5N1 and H7N9 viruses replicate faster and to higher titers than two low-pathogenicity H1N1 strains, they accomplish this via different mechanisms. While the H7N9 virions exhibit a faster rate of infection, the H5N1 virions are produced at a higher rate. Of the two H1N1 strains studied, the 2009 pandemic H1N1 strain exhibits the longest eclipse phase, possibly indicative of a less effective neuraminidase activity, but causes infection more rapidly than the seasonal strain. This explains, in part, the pandemic strain’s generally slower growth kinetics and permissiveness to accept mutations causing neuraminidase inhibitor resistance without significant loss in fitness. Our results highlight differential growth properties of H1N1, H5N1 and H7N9 influenza viruses.

Experimentation in vitro is a vital part of the process by which the clinical and epidemiological characteristics of a particular influenza virus strain are determined. We detail the considerations which must be made in designing appropriate theoretical/mathematical models of these experiments and show how modeling can increase the information output of such experiments. Starting from a traditional system of ordinary differential equations, common to infectious disease modeling, we broaden the approach by using an agent-based model, applicable to more general experimental geometries and assumptions about the biological properties of viruses, cell and their interaction. Within this framework, we explore the limits of the assumptions made by more traditional models and the conditions under which these assumptions begin to break down, requiring the use of more sophisticated models. We apply the agent-based model to experimental plaque growth of two influenza strains, one resistant to the antiviral oseltamivir, and extract the values of key infection parameters specific to each strain.

The pathogenicity and transmission of influenza A viruses are likely determined in part by replication efficiency in human cells, which is the net effect of complex virus-host interactions. H5N1 avian, H1N1 seasonal, and H1N1 2009 pandemic influenza virus strains were compared by infecting human differentiated bronchial epithelial cells in air-liquid interface cultures at relatively low virus particle/cell ratios. Differential equation and computational models were used to characterize the in vitro kinetic behaviors of the three strains. The models were calibrated by fitting experimental data in order to estimate difficult-to-measure parameters. Both models found marked differences in the relative values of p , the virion production rate per cell, and R 0 , an index of the spread of infection through the monolayer, with the values for the strains in the following rank order (from greatest to least): pandemic strain, followed by seasonal strain, followed by avian strain, as expected. In the differential equation model, which treats virus and cell populations as well mixed, R 0 and p varied proportionately for all 3 strains, consistent with a primary role for productivity. In the spatially explicit computational model, R 0 and p also varied proportionately except that R 0 derived for the pandemic strain was reduced, consistent with constrained viral spread imposed by multiple host defenses, including mucus and paracrine antiviral effects. This synergistic experimental-computational strategy provides relevant parameters for identifying and phenotyping potential pandemic strains.

Both direct and indirect experimental evidence has shown signaling, communication and conductivity in microtubules (MTs). Theoretical models have predicted that MTs can be potentially used for both classical and quantum information processing although controversies arose in regard to physiological temperature effects on these capabilities. In this paper, MTs have been studied using well-established principles of classical statistical physics as applied to information processing, information storage and signal propagation. To investigate the existence of information processing in MTs we used cellular automata (CA) models with neighbor rules based on the electrostatic properties of the molecular structure of tubulin, and both synchronous and asynchronous updating methods. We obtained a phase diagram of possible dynamic behaviors in MTs that depend on the values of characteristic physical parameters that can be experimentally verified.

We analyzed the dynamics of an influenza A/Albany/1/98 (H3N2) viral infection, using a set of mathematical models highlighting the differences between in vivo and in vitro infection. For example, we found that including virion loss due to cell entry was critical for the in vitro model but not for the in vivo model. Experiments were performed on influenza virus-infected MDCK cells in vitro inside a hollow-fiber (HF) system, which was used to continuously deliver the drug amantadine. The HF system captures the dynamics of an influenza infection, and is a controlled environment for producing experimental data which lend themselves well to mathematical modeling. The parameter estimates obtained from fitting our mathematical models to the HF experimental data are consistent with those obtained earlier for a primary infection in a human model. We found that influenza A/Albany/1/98 (H3N2) virions under normal experimental conditions at 37 degrees C rapidly lose infectivity with a half-life of approximately 6.6+/-0.2 h, and that the lifespan of productively infected MDCK cells is approximately 13 h. Finally, using our models we estimated that the maximum efficacy of amantadine in blocking viral infection is approximately 74%, and showed that this low maximum efficacy is likely due to the rapid development of drug resistance.

The recent application of two-photon microscopy to the visualization of T cell movement has presented trajectories of individual T cells within lymphoid organs both in the presence and in the absence of Ag-loaded dendritic cells. Remarkably, even though T cells largely move along conduits of the fibroblastic reticular cell network, they appear to execute random walks in lymphoid organs rather than chemotaxis. In this study, we analyze experimental trajectories of T cells using computer simulations of idealized random walks. Comparisons of simulations with experimental data provide estimates of key parameters that characterize T cell motion in vivo. For example, we find that the distance moved before turning is about twice the distance between intersections in the fibroblastic reticular cell network, suggesting that at an intersection a T cell will turn onto a new fiber ∼50% of the time. Although the calibrated model appears to offer an accurate representation of T cell movement, it has also uncovered inconsistencies across different experimental data sets.

The time elapsed between successful cell infection and the start of virus production is called the eclipse phase. Its duration is specific to each virus strain and, along with an effective virus production rate, plays a key role in infection kinetics. How the eclipse phase varies amongst cells infected with the same virus strain and therefore how best to mathematically represent its duration is not clear. Most mathematical models either neglect this phase or assume it is exponentially distributed, such that at least some if not all cells can produce virus immediately upon infection. Biologically, this is unrealistic (one must allow for the translation, transcription, export, etc. to take place), but could be appropriate if the duration of the eclipse phase is negligible on the time-scale of the infection. If it is not, however, ignoring this delay affects the accuracy of the mathematical model, its parameter estimates and predictions. Here, we introduce a new approach, consisting in a carefully designed experiment and simple analytical expressions, to determine the duration and distribution of the eclipse phase in vitro. We find that the eclipse phase of SHIV-KS661 lasts on average one day and is consistent with an Erlang distribution.

A population drug-disease model was developed to describe the time course of influenza virus with and without oseltamivir treatment and to investigate opportunities for antiviral combination therapy. Data included viral titers from 208 subjects, across 4 studies, receiving placebo and oseltamivir at 20 to 200 mg twice daily for 5 days. A 3-compartment mathematical model, comprising target cells infected at rate β, free virus produced at rate p and cleared at rate c , and infected cells cleared at rate δ, was implemented in NONMEM with an inhibitory Hill function on virus production ( p ), accounting for the oseltamivir effect. In congruence with clinical data, the model predicts that the standard 75-mg regimen initiated 2 days after infection decreased viral shedding duration by 1.5 days versus placebo; the 150-mg regimen decreased shedding by an additional average 0.25 day. The model also predicts that initiation of oseltamivir sooner postinfection, specifically at day 0.5 or 1, results in proportionally greater decreases in viral shedding duration of 5 and 3.5 days, respectively. Furthermore, the model suggests that combining oseltamivir (acting to subdue virus production rate) with an antiviral whose activity decreases viral infectivity (β) results in a moderate additive effect dependent on therapy initiation time. In contrast, the combination of oseltamivir with an antiviral whose activity increases viral clearance ( c ) shows significant additive effects independent of therapy initiation time. The utility of the model for investigating the pharmacodynamic effects of novel antivirals alone or in combination on emergent influenza virus strains warrants further investigation.

Currently, little is known about the viral kinetics of influenza A during infection within an individual. We utilize a series of mathematical models of increasing complexity, which incorporate target cell limitation and the innate interferon response, to examine influenza A virus kinetics in the upper respiratory tracts of experimentally infected adults. The models were fit to data from an experimental H1N1 influenza A/Hong Kong/123/77 infection and suggest that it is important to include the eclipse phase of the viral life cycle in viral dynamic models. Doing so, we estimate that after a delay of ∼6 h, infected cells begin producing influenza virus and continue to do so for ∼5 h. The average lifetime of infected cells is ∼11 h, and the half-life of free infectious virus is ∼3 h. We calculated the basic reproductive number,R0, which indicated that a single infected cell could produce ∼22 new productive infections. This suggests that antiviral treatments have a large hurdle to overcome in moderating symptoms and limiting infectiousness and that treatment has to be initiated as early as possible. For about 50% of patients, the curve of viral titer versus time has two peaks. This bimodal behavior can be explained by incorporating the antiviral effects of interferon into the model. Our model also compared well to an additional data set on viral titer after experimental infection and treatment with the neuraminidase inhibitor zanamivir, which suggests that such models may prove useful in estimating the efficacies of different antiviral therapies for influenza A infection.

Conservation laws are among the most important properties of a physical system, but are not commonplace in biology. We derived a conservation law from the basic model for viral infections which consists in a small set of ordinary differential equations. We challenged the conservation law experimentally for the case of a virus infection in a cell culture. We found that the derived, conserved quantity remained almost constant throughout the infection period, implying that the derived conservation law holds in this biological system. We also suggest a potential use for the conservation law in evaluating the accuracy of experimental measurements.

The role of the host immune response in determining the severity and duration of an influenza infection is still unclear. Inorder to identify severity factors and more accurately predict the course of an influenza infection within a human host, anunderstanding of the impact of host factors on the infection process is required. Despite the lack of sufficiently diverseexperimental data describing the time course of the various immune response components, published mathematical models were constructed from limited human or animal data using various strategies and simplifying assumptions. Toassess the validity of these models, we assemble previously published experimental data of the dynamics and role ofcytotoxic T lymphocytes, antibodies, and interferon and determined qualitative key features of their effect that should becaptured by mathematical models. We test these existing models by confronting them with experimental data and find thatno single model agrees completely with the variety of influenza viral kinetics responses observed experimentally whenvarious immune response components are suppressed. Our analysis highlights the strong and weak points of eachmathematical model and highlights areas where additional experimental data could elucidate specific mechanisms,constrain model design, and complete our understanding of the immune response to influenza.

A defective interfering particle (DIP) in the context of influenza A virus is a virion with a significantly shortened RNA segment substituting one of eight full-length parent RNA segments, such that it is preferentially amplified. Hence, a cell co-infected with DIPs will produce mainly DIPs, suppressing infectious virus yields and affecting infection kinetics. Unfortunately, the quantification of DIPs contained in a sample is difficult because they are indistinguishable from standard virus (STV). Using a mathematical model, we investigated the standard experimental method for counting DIPs based on the reduction in STV yield (Bellett & Cooper, 1959, Journal of General Microbiology 21 , 498–509 ( doi:10.1099/00221287-21-3-498 )). We found the method is valid for counting DIPs provided that: (i) an STV-infected cell's co-infection window is approximately half its eclipse phase (it blocks infection by other virions before it begins producing progeny virions), (ii) a cell co-infected by STV and DIP produces less than 1 STV per 1000 DIPs and (iii) a high MOI of STV stock (more than 4 PFU per cell) is added to perform the assay. Prior work makes no mention of these criteria such that the method has been applied incorrectly in several publications discussed herein. We determined influenza A virus meets these criteria, making the method suitable for counting influenza A DIPs.

Volume 59, no. 9, p. [5388–5395][1], 2015. Page 5391, Table 2: It was brought to our attention that there was an inadvertent error in reporting the residual error term (σerror, Table 2) in our model. The minor error is isolated and has no impact on the stated objectives of the paper, the

The H275Y amino acid substitution of the neuraminidase gene is the most common mutation conferring oseltamivir resistance in the N1 subtype of the influenza virus. Using a mathematical model to analyze a set of in vitro experiments that allow for the full characterization of the viral replication cycle, we show that the primary effects of the H275Y substitution on the pandemic H1N1 (H1N1pdm09) strain are to lengthen the mean eclipse phase of infected cells (from 6.6 to 9.1 h) and decrease (by 7-fold) the viral burst size, i.e., the total number of virions produced per cell. We also find, however, that the infectious-unit-to-particle ratio of the H275Y mutant strain is 12-fold higher than that of the oseltamivir-susceptible strain (0.19 versus 0.016 per RNA copy). A parallel analysis of the H275Y mutation in the prior seasonal A/Brisbane/59/2007 background shows similar changes in the infection kinetic parameters, but in this background, the H275Y mutation also allows the mutant to infect cells five times more rapidly. Competitive mixed-strain infections in vitro , where the susceptible and resistant H1N1pdm09 strains must compete for cells, are characterized by higher viral production by the susceptible strain but suggest equivalent fractions of infected cells in the culture. In ferrets, however, the mutant strain appears to suffer a delay in its infection of the respiratory tract that allows the susceptible strain to dominate mixed-strain infections.

Oseltamivir-resistant A/H3N2 influenza isolates with or without the E119V and I222V neuraminidase (NA) mutations were recovered from an immunocompromised patient. Based on plaque size, yield assays, and NA activity, the impaired viral fitness of the E119V mutant was partially restored by the I222V NA mutation.

Several mechanisms have been proposed to account for the marked increase in severity of human infections with avian compared to human influenza strains, including increased cytokine expression, poor immune response, and differences in target cell receptor affinity. Here, the potential effect of target cell tropism on disease severity is studied using a mathematical model for in-host influenza viral infection in a cell population consisting of two different cell types. The two cell types differ only in their susceptibility to infection and rate of virus production. We show the existence of a parameter regime which is characterized by high viral loads sustained long after the onset of infection. This finding suggests that differences in cell tropism between influenza strains could be sufficient to cause significant differences in viral titer profiles, similar to those observed in infections with certain strains of influenza A virus. The two target cell mathematical model offers good agreement with experimental data from severe influenza infections, as does the usual, single target cell model albeit with biologically unrealistic parameters. Both models predict that while neuraminidase inhibitors and adamantanes are only effective when administered early to treat an uncomplicated seasonal infection, they can be effective against more severe influenza infections even when administered late.

In 2007, the A/Brisbane/59/2007 (H1N1) seasonal influenza virus strain acquired the oseltamivir-resistance mutation H275Y in its neuraminidase (NA) gene. Although previous studies had demonstrated that this mutation impaired the replication capacity of the influenza virus in vitro and in vivo, the A/Brisbane/59/2007 H275Y oseltamivir-resistant mutant completely out-competed the wild-type (WT) strain and was, in the 2008-2009 influenza season, the primary A/H1N1 circulating strain. Using a combination of plaque and viral yield assays, and a simple mathematical model, approximate values were extracted for two basic viral kinetics parameters of the in vitro infection. In the ST6GalI-MDCK cell line, the latent infection period (i.e., the time for a newly infected cell to start releasing virions) was found to be 1-3 h for the WT strain and more than 7 h for the H275Y mutant. The infecting time (i.e., the time for a single infectious cell to cause the infection of another one) was between 30 and 80 min for the WT, and less than 5 min for the H275Y mutant. Single-cycle viral yield experiments have provided qualitative confirmation of these findings. These results, though preliminary, suggest that the increased fitness success of the A/Brisbane/59/2007 H275Y mutant may be due to increased infectivity compensating for an impaired or delayed viral release, and are consistent with recent evidence for the mechanistic origins of fitness reduction and recovery in NA expression. The method applied here can reconcile seemingly contradictory results from the plaque and yield assays as two complementary views of replication kinetics, with both required to fully capture a strain's fitness.

Treatment of seasonal influenza viral infections using antivirals such as neuraminidase inhibitors (NAIs) has been proven effective if administered within 48 h post-infection. However, there is growing evidence that antiviral treatment of infections with avian-derived strains even as late as 6 days post-infection (dpi) can significantly reduce infection severity and duration. Using a mathematical model of in-host influenza viral infections which can capture the kinetics of both a short-lived, typical, seasonal infection and a severe infection exhibiting sustained viral titer, we explore differences in the effects of NAI treatment on both types of influenza viral infections. Comparison of our model's behavior against experimental data from patients naturally infected with avian strains yields estimates for the times at which patients were infected that are consistent with those reported by the patients, and estimates of drug efficacies that are lower for patients who died than for those who recovered. In addition, our model suggests that the sustained, high, viral titers often seen in more severe influenza virus infections are the reason why antiviral treatment delayed by as much as 6 dpi will still lead to reduced viral titers and shortened illness. We conclude that NAIs may be an effective and beneficial treatment strategy against more severe strains of influenza virus characterized by high, sustained, viral titers. We believe that our mathematical model will be an effective tool in guiding treatment of severe influenza viral infections with antivirals.

The 2009 pandemic H1N1 (H1N1pdm09) influenza virus is naturally susceptible to neuraminidase (NA) inhibitors, but mutations in the NA protein can cause oseltamivir resistance. The H275Y and I223V amino acid substitutions in the NA of the H1N1pdm09 influenza strain have been separately observed in patients exhibiting oseltamivir-resistance. Here, we apply mathematical modelling techniques to compare the fitness of the wild-type H1N1pdm09 strain relative to each of these two mutants. We find that both the H275Y and I223V mutations in the H1N1pdm09 background significantly lengthen the duration of the eclipse phase (by 2.5 h and 3.6 h, respectively), consistent with these NA mutations delaying the release of viral progeny from newly infected cells. Cells infected by H1N1pdm09 virus carrying the I223V mutation display a disadvantageous, shorter infectious lifespan (17 h shorter) than those infected with the wild-type or MUT-H275Y strains. In terms of compensating traits, the H275Y mutation in the H1N1pdm09 background results in increased virus infectiousness, as we reported previously, whereas the I223V exhibits none, leaving it overall less fit than both its wild-type counterpart and the MUT-H275Y strain. Using computer simulated competition experiments, we determine that in the presence of oseltamivir at doses even below standard therapy, both the MUT-H275Y and MUT-I223V dominate their wild-type counterpart in all aspects, and the MUT-H275Y outcompetes the MUT-I223V. The H275Y mutation should therefore be more commonly observed than the I223V mutation in circulating H1N1pdm09 strains, assuming both mutations have a similar impact or no significant impact on between-host transmission. We also show that mathematical modelling offers a relatively inexpensive and reliable means to quantify inter-experimental variability and assess the reproducibility of results.

Predicting the virulence of new Influenza strains is an important problem. The solution to this problem will likely require a combination of in vitro and in silico tools that are used iteratively. We describe the agent-based modeling component of this program and report preliminary results from both the in vitro and in silico experiments.

Viral kinetics have been extensively studied in the past through the use of spatially well-mixed ordinary differential equations describing the time evolution of the diseased state. However, emerging spatial structures such as localized populations of dead cells might adversely affect the spread of infection, similar to the manner in which a counter-fire can stop a forest fire from spreading. In a previous publication (Beauchemin et al., 2005), a simple 2-D cellular automaton model was introduced and shown to be accurate enough to model an uncomplicated infection with influenza A. Here, this model is used to investigate the effects of relaxing the well-mixed assumption. Particularly, the effects of the initial distribution of infected cells, the regeneration rule for dead epithelial cells, and the proliferation rule for immune cells are explored and shown to have an important impact on the development and outcome of the viral infection in our model., LaTeX, 12 pages, 22 EPS figures, uses document class REVTeX 4, and packages float, graphics, amsmath, and SIunits

Viral kinetics have been extensively studied in the past through the use of spatially homogeneous ordinary differential equations describing the time evolution of the diseased state. However, spatial characteristics such as localized populations of dead cells might adversely affect the spread of infection, similar to the manner in which a counter-fire can stop a forest fire from spreading. In order to investigate the influence of spatial heterogeneities on viral spread, a simple 2-D cellular automaton (CA) model of a viral infection has been developed. In this initial phase of the investigation, the CA model is validated against clinical immunological data for uncomplicated influenza A infections. Our results will be shown and discussed., Comment: LaTeX, 12 pages, 18 EPS figures, uses document class ReTeX4, and packages amsmath and SIunits

Background For a typical influenza infection in vivo, viral titers over time are characterized by 1–2 days of exponential growth followed by an exponential decay. This simple dynamic can be reproduced by a broad range of mathematical models which makes model selection and the extraction of biologically-relevant infection parameters from experimental data difficult. Results We analyze in vitro experimental data from the literature, specifically that of single-cycle viral yield experiments, to narrow the range of realistic models of infection. In particular, we demonstrate the viability of using a normal or lognormal distribution for the time a cell spends in a given infection state (e.g., the time spent by a newly infected cell in the latent state before it begins to produce virus), while exposing the shortcomings of ordinary differential equation models which implicitly utilize exponential distributions and delay-differential equation models with fixed-length delays. Conclusions By fitting published viral titer data from challenge experiments in human volunteers, we show that alternative models can lead to different estimates of the key infection parameters.