Assessing the in vitro fitness of an oseltamivir-resistant seasonal A/H1N1 influenza strain using a mathematical model

Mathematical Modeling of Virus-Mediated Syncytia Formation: Past Successes and Future Directions

Many viruses have the ability to cause cells to fuse into large multi-nucleated cells, known as syncytia. While the existence of syncytia has long been known and its importance in helping spread viral infection within a host has been understood, few mathematical models have incorporated syncytia formation or examined its role in viral dynamics. This review examines mathematical models that have incorporated virus-mediated cell fusion and the insights they have provided on how syncytia can change the time course of an infection. While the modeling efforts are limited, they show promise in helping us understand the consequences of syncytia formation if future modeling efforts can be coupled with appropriate experimental efforts to help validate the models.

Different routes of infection of H5N1 lead to changes in infecting time

Influenza virus infection can result in a wide range of clinical outcomes from asymptomatic infection to severe disease and death. While there are undoubtedly many factors that contribute to the severity of disease, one possible contributing factor that needs more investigation is the route of infection. In this study, we use previously published data from cynomolgus macaques infected with A/Vietnam/1203/04 (H5N1) via either aerosol (with and without bronchoalveolar lavages (BAL)) or a combined intrabronchial, oral, and intranasal route. We fit a mathematical model of within host viral kinetics to the data and find that when the macaques are infected via the aerosol route with subsequent BAL, the infecting time is significantly lower than for the other two groups. A lower infecting time indicates that the virus spreads from cell to cell more rapidly for aerosol infection with BAL than for the combined deposition or aerosol deposition alone. This study helps elucidate the mechanism behind different infection outcomes caused by differences in routes of infection.

Ex Vivo Experiments Shed Light on the Innate Immune Response from Influenza Virus

The innate immune response is recognized as a key driver in controlling an influenza virus infection in a host. However, the mechanistic action of such innate response is not fully understood. Infection experiments on ex vivo explants from swine trachea represent an efficient alternative to animal experiments, as the explants conserved key characteristics of an organ from an animal. In the present work we compare three cellular automata models of influenza virus dynamics. The models are fitted to free virus and infected cells data from ex vivo swine trachea experiments. Our findings suggest that the presence of an immune response is necessary to explain the observed dynamics in ex vivo organ culture. Moreover, such immune response should include a refractory state for epithelial cells, and not just a reduced infection rate. Our results may shed light on how the immune system responds to an infection event.

Simplified within-host and Dose-response Models of SARS-CoV-2

Understanding the mechanistic dynamics of transmission is key to designing more targeted and effective interventions to limit the spread of infectious diseases. A well-described within-host model allows explicit simulation of how infectiousness changes over time at an individual level. This can then be coupled with dose-response models to investigate the impact of timing on transmission. We collected and compared a range of within-host models used in previous studies and identified a minimally-complex model that provides suitable within-host dynamics while keeping a reduced number of parameters to allow inference and limit unidentifiability issues. Furthermore, non-dimensionalised models were developed to further overcome the uncertainty in estimates of the size of the susceptible cell population, a common problem in many of these approaches. We will discuss these models, and their fit to data from the human challenge study (see Killingley et al. (2022)) for SARS-CoV-2 and the model selection results, which has been performed using ABC-SMC. The parameter posteriors have then used to simulate viral-load based infectiousness profiles via a range of dose-response models, which illustrate the large variability of the periods of infection window observed for COVID-19.

Emergence and competition of virus variants in respiratory viral infections

The emergence of new variants of concern (VOCs) of the SARS-CoV-2 infection is one of the main factors of epidemic progression. Their development can be characterized by three critical stages: virus mutation leading to the appearance of new viable variants; the competition of different variants leading to the production of a sufficiently large number of copies; and infection transmission between individuals and its spreading in the population. The first two stages take place at the individual level (infected individual), while the third one takes place at the population level with possible competition between different variants. This work is devoted to the mathematical modeling of the first two stages of this process: the emergence of new variants and their progression in the epithelial tissue with a possible competition between them. The emergence of new virus variants is modeled with non-local reaction–diffusion equations describing virus evolution and immune escape in the space of genotypes. The conditions of the emergence of new virus variants are determined by the mutation rate, the cross-reactivity of the immune response, and the rates of virus replication and death. Once different variants emerge, they spread in the infected tissue with a certain speed and viral load that can be determined through the parameters of the model. The competition of different variants for uninfected cells leads to the emergence of a single dominant variant and the elimination of the others due to competitive exclusion. The dominant variant is the one with the maximal individual spreading speed. Thus, the emergence of new variants at the individual level is determined by the immune escape and by the virus spreading speed in the infected tissue.

Mathematical modeling of respiratory viral infection and applications to SARS-CoV-2 progression

Viral infection in cell culture and tissue is modeled with delay reaction-diffusion equations. It is shown that progression of viral infection can be characterized by the viral replication number, time-dependent viral load, and the speed of infection spreading. These three characteristics are determined through the original model parameters including the rates of cell infection and of virus production in the infected cells. The clinical manifestations of viral infection, depending on tissue damage, correlate with the speed of infection spreading, while the infectivity of a respiratory infection depends on the viral load in the upper respiratory tract. Parameter determination from the experiments on Delta and Omicron variants allows the estimation of the infection spreading speed and viral load. Different variants of the SARS-CoV-2 infection are compared confirming that Omicron is more infectious and has less severe symptoms than Delta variant. Within the same variant, spreading speed (symptoms) correlates with viral load allowing prognosis of disease progression.

Viral Infection Spreading and Mutation in Cell Culture

A new model of viral infection spreading in cell cultures is proposed taking into account virus mutation. This model represents a reaction-diffusion system of equations with time delay for the concentrations of uninfected cells, infected cells and viral load. Infection progression is characterized by the virus replication number Rv, which determines the total viral load. Analytical formulas for the speed of propagation and for the viral load are obtained and confirmed by numerical simulations. It is shown that virus mutation leads to the emergence of a new virus variant. Conditions of the coexistence of the two variants or competitive exclusion of one of them are found, and different stages of infection progression are identified.

The Influence of Immune Response on Spreading of Viral Infection

In this work we develop a model of viral infection in host tissues in order to study the influence of the immune response on the infection spreading speed and on the viral load characterizing, respectively, severity of symptoms and infection transmission rate. Dynamics of the interaction between viral infection and the immune response is studied with nonlocal reaction-diffusion equations for the concentrations of virus, interferon, immune cells and antibodies. Analytical results for infection spreading speed and viral load are completed by numerical simulations. At the first stage, progression of viral infection is confronted by the innate immune response mostly determined by the local interferon production. The modeling results show in this case that infection spreading speed does not depend on interferon concentration, while the total viral load decreases with the increase of its concentration. Next, we consider the influence of globally circulating interferon and show that, in contrast to local interferon diffusion, infection spreading speed decreases with increasing of global interferon level, and the total viral load also decreases. At the next stage, adaptive immune response mediated by antibodies and cytotoxic T cells (CTL) further influences infection progression. In this case, the infection propagation speed and the total viral load are decreased by the immune response. The humoral adaptive response (antibodies) increases the global interferon concentration through the viral load, while the cellular adaptive response (CTL) decreases it.

Space and Genotype-Dependent Virus Distribution during Infection Progression

The paper is devoted to a nonlocal reaction-diffusion equation describing the development of viral infection in tissue, taking into account virus distribution in the space of genotypes, the antiviral immune response, and natural genotype-dependent virus death. It is shown that infection propagates as a reaction-diffusion wave. In some particular cases, the 2D problem can be reduced to a 1D problem by separation of variables, allowing for proof of wave existence and stability. In general, this reduction provides an approximation of the 2D problem by a 1D problem. The analysis of the reduced problem allows us to determine how viral load and virulence depend on genotype distribution, the strength of the immune response, and the level of immunity.

Highly pathogenic avian influenza virus H5N2 (clade 2.3.4.4) challenge of mallards age appropriate to the 2015 midwestern poultry outbreak

Background

The 2015 highly pathogenic avian influenza virus (HPAIV) H5N2 clade 2.3.4.4 outbreak in upper midwestern U.S. poultry operations was not detected in wild birds to any great degree during the outbreak, despite wild waterfowl being implicated in the introduction, reassortment, and movement of the virus into North America from Asia. This outbreak led to the demise of over 50 million domestic birds and occurred mainly during the northward spring migration of adult avian populations.

Objectives

There have been no experimental examinations of the pathogenesis, transmission, and population impacts of this virus in adult wild waterfowl with varying exposure histories—the most relevant age class.

Methods

We captured, housed, and challenged adult wild mallards (Anas platyrhynchos) with HPAIV H5N2 clade 2.3.4.4 and measured viral infection, viral excretion, and transmission to other mallards.

Results

All inoculated birds became infected and excreted moderate amounts of virus, primarily orally, for up to 14 days. Cohoused, uninoculated birds also all became infected. Serological status had no effect on susceptibility. There were no obvious clinical signs of disease, and all birds survived to the end of the study (14 days).

Conclusions

Based on these results, adult mallards are viable hosts of HPAIV H5N2 regardless of prior exposure history and are capable of transporting the virus over short and long distances. These findings have implications for surveillance efforts. The capture and sampling of wild waterfowl in the spring, when most surveillance programs are not operating, are important to consider in the design of future HPAIV surveillance programs.

Quantifying mechanistic traits of influenza viral dynamics using in vitro data

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.

In-host Mathematical Modelling of COVID-19 in Humans

COVID-19 pandemic has underlined the impact of emergent pathogens as a major threat to human health. The development of quantitative approaches to advance comprehension of the current outbreak is urgently needed to tackle this severe disease. Considering different starting times of infection, mathematical models are proposed to represent SARS-CoV-2 dynamics in infected patients. Based on the target cell limited model, the within-host reproductive number for SARS-CoV-2 is consistent with the broad values of human influenza infection. The best model to fit the data was including immune cell response, which suggests a slow immune response peaking between 5 to 10 days post-onset of symptoms. The model with the eclipse phase, time in a latent phase before becoming productively infected cells, was not supported. Interestingly, model simulations predict that SARS-CoV-2 may replicate very slowly in the first days after infection, and viral load could be below detection levels during the first 4 days post infection. A quantitative comprehension of SARS-CoV-2 dynamics and the estimation of standard parameters of viral infections is the key contribution of this pioneering work. These models can serve for future evaluation of control theoretical approaches to tailor new drugs against COVID-19.

Modeling Competitive Mixtures With the Lotka-Volterra Framework for More Complex Fitness Assessment Between Strains

With increasing resolution of microbial diversity at the genomic level, experimental and modeling frameworks that translate such diversity into phenotypes are highly needed. This is particularly important when comparing drug-resistant with drug-sensitive pathogen strains, when anticipating epidemiological implications of microbial diversity, and when designing control measures. Classical approaches quantify differences between microbial strains using the exponential growth model, and typically report a selection coefficient for the relative fitness differential between two strains. The apparent simplicity of such approaches comes with the costs of limiting the range of biological scenarios that can be captured, and biases strain fitness estimates to polarized extremes of competitive exclusion. Here, we propose a mathematical and statistical framework based on the Lotka-Volterra model, that can capture frequency-dependent competition between microbial strains within-host and upon transmission. As a proof-of-concept, the model is applied to a previously-published dataset from in-vivo competitive mixture experiments with influenza strains in ferrets (McCaw et al., 2011). We show that for the same data, our model predicts a scenario of coexistence between strains, and supports a higher bottleneck size in the range of 35–145 virions transmitted from donor to recipient host. Thanks to its simplicity and generality, such framework could be applied to other ecological scenarios of microbial competition, enabling a more complex and nuanced view of possible outcomes between two strains, beyond competitive exclusion.

The rate of viral transfer between upper and lower respiratory tracts determines RSV illness duration

Respiratory syncytial virus can lead to serious lower respiratory infection (LRI), particularly in children and the elderly. LRI can cause longer infections, lingering respiratory problems, and higher incidence of hospitalization. In this paper, we use a simplified ordinary differential equation model of viral dynamics to study the role of transport mechanisms in the occurrence of LRI. Our model uses two compartments to simulate the upper respiratory tract and the lower respiratory tract (LRT) and assumes two distinct types of viral transfer between the two compartments: diffusion and advection. We find that a range of diffusion and advection values lead to long-lasting infections in the LRT, elucidating a possible mechanism for the severe LRI infections observed in humans.

Uncovering critical properties of the human respiratory syncytial virus by combining in vitro assays and in silico analyses

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.

Superinfection and cell regeneration can lead to chronic viral coinfections

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Clinical researchers have found that coinfection of the respiratory tract can cause distinct disease outcome, sometimes leading to long-lasting infection, compared to single viral infection.

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The impact of coinfections in human respiratory tract have not yet been evaluated in either theoretical or experimental studies on a large scale.

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A few experiments confirm that different respiratory viruses can infect the same cell (superinfection).

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Superinfection alone cannot cause long-lasting viral coinfections.

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The combined mechanism of superinfection and cell regeneration provides a plausible mechanism for chronic viral coinfections.

Molecular diagnostic techniques have revealed that approximately 43% of the patients hospitalized with influenza-like illness are infected by more than one viral pathogen, sometimes leading to long-lasting infections. It is not clear how the heterologous viruses interact within the respiratory tract of the infected host to lengthen the duration of what are usually short, self-limiting infections. We develop a mathematical model which allows for single cells to be infected simultaneously with two different respiratory viruses (superinfection) to investigate the possibility of chronic coinfections. We find that a model with superinfection and cell regeneration has a stable chronic coinfection fixed point, while superinfection without cell regeneration produces only acute infections. This analysis suggests that both superinfection and cell regeneration are required to sustain chronic coinfection via this mechanism since coinfection is maintained by superinfected cells that allow slow-growing infections a chance to infect cells and continue replicating. This model provides a possible mechanism for chronic coinfection independent of any viral interactions via the immune response.

Host-pathogen kinetics during influenza infection and coinfection: insights from predictive modeling

Influenza virus infections are a leading cause of morbidity and mortality worldwide. This is due in part to the continual emergence of new viral variants and to synergistic interactions with other viruses and bacteria. There is a lack of understanding about how host responses work to control the infection and how other pathogens capitalize on the altered immune state. The complexity of multi-pathogen infections makes dissecting contributing mechanisms, which may be non-linear and occur on different time scales, challenging. Fortunately, mathematical models have been able to uncover infection control mechanisms, establish regulatory feedbacks, connect mechanisms across time scales, and determine the processes that dictate different disease outcomes. These models have tested existing hypotheses and generated new hypotheses, some of which have been subsequently tested and validated in the laboratory. They have been particularly a key in studying influenza-bacteria coinfections and will be undoubtedly be useful in examining the interplay between influenza virus and other viruses. Here, I review recent advances in modeling influenza-related infections, the novel biological insight that has been gained through modeling, the importance of model-driven experimental design, and future directions of the field.

PK/PD-based adaptive tailoring of oseltamivir doses to treat within-host influenza viral infections

Influenza A virus (IAV) is a latent global threat to human health. In view of the risk of pandemics, prophylactic and curative treatments are essential. Oseltamivir is a neuraminidase inhibitor efficiently supporting recovery from influenza infections. Current common clinical practice is a constant drug dose (75 or 150 mg) administered at regular time intervals twice a day. We aim to use quantitative systems pharmacology to propose an efficient adaptive drug scheduling. We combined the mathematical model for IAV infections validated by murine data, which captures the viral dynamics and the dynamics of the immune host response, with a pharmacokinetic (PK)/pharmacodynamic (PD) model of oseltamivir. Next, we applied an adaptive impulsive feedback control method to systematically calculate the adaptive dose of oseltamivir in dependence on the viral load and the number of immune effectors at the time of drug administration. Our in silico results revealed that the treatment with adaptive control-based drug scheduling is able to either increase the drug virological efficacy or reduce the drug dose while keeping the same virological efficacy. Thus, adaptive adjustment of the drug dose would reduce not only the potential side effects but also the amount of stored oseltamivir required for the prevention of outbreaks.

Mathematical Analysis of Viral Replication Dynamics and Antiviral Treatment Strategies: From Basic Models to Age-Based Multi-Scale Modeling

Viral infectious diseases are a global health concern, as is evident by recent outbreaks of the middle east respiratory syndrome, Ebola virus disease, and re-emerging zika, dengue, and chikungunya fevers. Viral epidemics are a socio-economic burden that causes short- and long-term costs for disease diagnosis and treatment as well as a loss in productivity by absenteeism. These outbreaks and their socio-economic costs underline the necessity for a precise analysis of virus-host interactions, which would help to understand disease mechanisms and to develop therapeutic interventions. The combination of quantitative measurements and dynamic mathematical modeling has increased our understanding of the within-host infection dynamics and has led to important insights into viral pathogenesis, transmission, and disease progression. Furthermore, virus-host models helped to identify drug targets, to predict the treatment duration to achieve cure, and to reduce treatment costs. In this article, we review important achievements made by mathematical modeling of viral kinetics on the extracellular, intracellular, and multi-scale level for Human Immunodeficiency Virus, Hepatitis C Virus, Influenza A Virus, Ebola Virus, Dengue Virus, and Zika Virus. Herein, we focus on basic mathematical models on the population scale (so-called target cell-limited models), detailed models regarding the most important steps in the viral life cycle, and the combination of both. For this purpose, we review how mathematical modeling of viral dynamics helped to understand the virus-host interactions and disease progression or clearance. Additionally, we review different types and effects of therapeutic strategies and how mathematical modeling has been used to predict new treatment regimens.

Influenza Virus Infection Model With Density Dependence Supports Biphasic Viral Decay

Mathematical models that describe infection kinetics help elucidate the time scales, effectiveness, and mechanisms underlying viral growth and infection resolution. For influenza A virus (IAV) infections, the standard viral kinetic model has been used to investigate the effect of different IAV proteins, immune mechanisms, antiviral actions, and bacterial coinfection, among others. We sought to further define the kinetics of IAV infections by infecting mice with influenza A/PR8 and measuring viral loads with high frequency and precision over the course of infection. The data highlighted dynamics that were not previously noted, including viral titers that remain elevated for several days during mid-infection and a sharp 4–5 log₁₀ decline in virus within 1 day as the infection resolves. The standard viral kinetic model, which has been widely used within the field, could not capture these dynamics. Thus, we developed a new model that could simultaneously quantify the different phases of viral growth and decay with high accuracy. The model suggests that the slow and fast phases of virus decay are due to the infected cell clearance rate changing as the density of infected cells changes. To characterize this model, we fit the model to the viral load data, examined the parameter behavior, and connected the results and parameters to linear regression estimates. The resulting parameters and model dynamics revealed that the rate of viral clearance during resolution occurs 25 times faster than the clearance during mid-infection and that small decreases to this rate can significantly prolong the infection. This likely reflects the high efficiency of the adaptive immune response. The new model provides a well-characterized representation of IAV infection dynamics, is useful for analyzing and interpreting viral load dynamics in the absence of immunological data, and gives further insight into the regulation of viral control.

A comparison of RSV and influenza in vitro kinetic parameters reveals differences in infecting time

Influenza and respiratory syncytial virus (RSV) cause acute infections of the respiratory tract. Since the viruses both cause illnesses with similar symptoms, researchers often try to apply knowledge gleaned from study of one virus to the other virus. This can be an effective and efficient strategy for understanding viral dynamics or developing treatment strategies, but only if we have a full understanding of the similarities and differences between the two viruses. This study used mathematical modeling to quantitatively compare the viral kinetics of in vitro RSV and influenza virus infections. Specifically, we determined the viral kinetics parameters for RSV A2 and three strains of influenza virus, A/WSN/33 (H1N1), A/Puerto Rico/8/1934 (H1N1), and pandemic H1N1 influenza virus. We found that RSV viral titer increases at a slower rate and reaches its peak value later than influenza virus. Our analysis indicated that the slower increase of RSV viral titer is caused by slower spreading of the virus from one cell to another. These results provide estimates of dynamical differences between influenza virus and RSV and help provide insight into the virus-host interactions that cause observed differences in the time courses of the two illnesses in patients.

Exploring virus release as a bottleneck for the spread of influenza A virus infection in vitro and the implications for antiviral therapy with neuraminidase inhibitors

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.

Modelling the emergence of influenza drug resistance: The roles of surface proteins, the immune response and antiviral mechanisms

The emergence of influenza drug resistance has become of particular interest as current planning for an influenza pandemic involves using massive amounts of antiviral drugs. We use semi-stochastic simulations to examine the emergence of drug resistant mutants during the course of a single infection within a patient in the presence and absence of antiviral therapy. We specifically examine three factors and their effect on the emergence of drug-resistant mutants: antiviral mechanism, the immune response, and surface proteins. We find that adamantanes, because they act at the start of the replication cycle to prevent infection, are less likely to produce drug-resistant mutants than NAIs, which act at the end of the replication cycle. A mismatch between surface proteins and internal RNA results in drug-resistant mutants being less likely to emerge, and emerging later in the infection because the mismatch gives antivirals a second chance to prevent propagation of the mutation. The immune response subdues slow growing infections, further reducing the probability that a drug resistant mutant will emerge and yield a drug-resistant infection. These findings improve our understanding of the factors that contribute to the emergence of drug resistance during the course of a single influenza infection.

The impact of cell regeneration on the dynamics of viral coinfection

Many mathematical models of respiratory viral infections do not include regeneration of cells within the respiratory tract, arguing that the infection is resolved before there is significant cellular regeneration. However, recent studies have found that ∼40% of patients hospitalized with influenza-like illness are infected with at least two different viruses, which could potentially lead to longer-lasting infections. In these longer infections, cell regeneration might affect the infection dynamics, in particular, allowing for the possibility of chronic coinfections. Several mathematical models have been used to describe cell regeneration in infection models, though the effect of model choice on the predicted time course of viral coinfections is not clear. We investigate four mathematical models incorporating different mechanisms of cell regeneration during respiratory viral coinfection to determine the effect of cell regeneration on infection dynamics. We perform linear stability analysis for each of the models and find the steady states analytically. The analysis suggests that chronic illness is possible but only with one viral species; chronic coexistence of two different viral species is not possible with the regeneration models considered here.

The in vivo efficacy of neuraminidase inhibitors cannot be determined from the decay rates of influenza viral titers observed in treated patients

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.

Analysis of Practical Identifiability of a Viral Infection Model

Mathematical modelling approaches have granted a significant contribution to life sciences and beyond to understand experimental results. However, incomplete and inadequate assessments in parameter estimation practices hamper the parameter reliability, and consequently the insights that ultimately could arise from a mathematical model. To keep the diligent works in modelling biological systems from being mistrusted, potential sources of error must be acknowledged. Employing a popular mathematical model in viral infection research, existing means and practices in parameter estimation are exemplified. Numerical results show that poor experimental data is a main source that can lead to erroneous parameter estimates despite the use of innovative parameter estimation algorithms. Arbitrary choices of initial conditions as well as data asynchrony distort the parameter estimates but are often overlooked in modelling studies. This work stresses the existence of several sources of error buried in reports of modelling biological systems, voicing the need for assessing the sources of error, consolidating efforts in solving the immediate difficulties, and possibly reconsidering the use of mathematical modelling to quantify experimental data.

Viral factors in influenza pandemic risk assessment

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.

Models of Viral Population Dynamics

Models of viral population dynamics have contributed enormously to our understanding of the pathogenesis and transmission of several infectious diseases, the coevolutionary dynamics of viruses and their hosts, the mechanisms of action of drugs, and the effectiveness of interventions. In this chapter, we review major advances in the modeling of the population dynamics of the human immunodeficiency virus (HIV) and briefly discuss adaptations to other viruses.

Coinfections of the Respiratory Tract: Viral Competition for Resources

Studies have shown that simultaneous infection of the respiratory tract with at least two viruses is common in hospitalized patients, although it is not clear whether these infections are more or less severe than single virus infections. We use a mathematical model to study the dynamics of viral coinfection of the respiratory tract in an effort to understand the kinetics of these infections. Specifically, we use our model to investigate coinfections of influenza, respiratory syncytial virus, rhinovirus, parainfluenza virus, and human metapneumovirus. Our study shows that during coinfections, one virus can block another simply by being the first to infect the available host cells; there is no need for viral interference through immune response interactions. We use the model to calculate the duration of detectable coinfection and examine how it varies as initial viral dose and time of infection are varied. We find that rhinovirus, the fastest-growing virus, reduces replication of the remaining viruses during a coinfection, while parainfluenza virus, the slowest-growing virus is suppressed in the presence of other viruses.

Avian influenza viruses that cause highly virulent infections in humans exhibit distinct replicative properties in contrast to human H1N1 viruses

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.

Modeling Influenza Virus Infection: A Roadmap for Influenza Research

Influenza A virus (IAV) infection represents a global threat causing seasonal outbreaks and pandemics. Additionally, secondary bacterial infections, caused mainly by Streptococcus pneumoniae, are one of the main complications and responsible for the enhanced morbidity and mortality associated with IAV infections. In spite of the significant advances in our knowledge of IAV infections, holistic comprehension of the interplay between IAV and the host immune response (IR) remains largely fragmented. During the last decade, mathematical modeling has been instrumental to explain and quantify IAV dynamics. In this paper, we review not only the state of the art of mathematical models of IAV infection but also the methodologies exploited for parameter estimation. We focus on the adaptive IR control of IAV infection and the possible mechanisms that could promote a secondary bacterial coinfection. To exemplify IAV dynamics and identifiability issues, a mathematical model to explain the interactions between adaptive IR and IAV infection is considered. Furthermore, in this paper we propose a roadmap for future influenza research. The development of a mathematical modeling framework with a secondary bacterial coinfection, immunosenescence, host genetic factors and responsiveness to vaccination will be pivotal to advance IAV infection understanding and treatment optimization.

Assessing Uncertainty in A2 Respiratory Syncytial Virus Viral Dynamics

Respiratory syncytial virus (RSV) is the most common cause of bronchiolitis and pneumonia in children younger than 1 year of age in the United States. Moreover, RSV is being recognized more often as a significant cause of respiratory illness in older adults. Although RSV has been studied both clinically and in vitro, a quantitative understanding of the infection dynamics is still lacking. In this paper, we study the effect of uncertainty in the main parameters of a viral kinetics model of RSV. We first characterize the RSV replication cycle and extract parameter values by fitting the mathematical model to in vivo data from eight human subjects. We then use Monte Carlo numerical simulations to determine how uncertainty in the parameter values will affect model predictions. We find that uncertainty in the infection rate, eclipse phase duration, and infectious lifespan most affect the predicted dynamics of RSV. This study provides the first estimate of in vivo RSV infection parameters, helping to quantify RSV dynamics. Our assessment of the effect of uncertainty will help guide future experimental design to obtain more precise parameter values.

Quantifying relative within-host replication fitness in influenza virus competition experiments

Through accumulation of genetic mutations in the neuraminidase gene, the influenza virus can become resistant to antiviral drugs such as oseltamivir. Quantifying the fitness of emergent drug-resistant influenza viruses, relative to contemporary circulating viruses, provides valuable information to complement existing efforts in the surveillance of drug-resistance. We have previously developed a co-infection based method for the assessment of the relative in vivo fitness of two competing viruses. We have also introduced a model of within-host co-infection dynamics that enables relative within-host fitness to be quantified in these competitive-mixtures experiments. The model assumed that fitness differences between co-infecting strains were mediated by strain-dependent viral production rates from infected epithelial cells. Here we extend the model to enable a more complete exploration of biological processes that may differ between virus pairs and hence generate fitness differences. We use the extended model to re-analyse data from competitive-mixtures experiments that investigated the fitness of oseltamivir-resistant (OR) H1N1 pandemic 2009 ("H1N1pdm09") viruses that emerged during a community outbreak in Australia in 2011. Results are consistent with those of our previous analysis, suggesting that the within-host replication fitness of these OR viruses is not compromised relative to that of related oseltamivir-susceptible (OS) strains, and that potentially permissive mutations in the neuraminidase gene (V241I and N369K) significantly enhance the fitness of H1N1pdm09 OR viruses. These results are consistent regardless of the hypothesised biological cause of fitness difference.

Ebola virus infection modeling and identifiability problems

The recent outbreaks of Ebola virus (EBOV) infections have underlined the impact of the virus as a major threat for human health. Due to the high biosafety classification of EBOV (level 4), basic research is very limited. Therefore, the development of new avenues of thinking to advance quantitative comprehension of the virus and its interaction with the host cells is urgently needed to tackle this lethal disease. Mathematical modeling of the EBOV dynamics can be instrumental to interpret Ebola infection kinetics on quantitative grounds. To the best of our knowledge, a mathematical modeling approach to unravel the interaction between EBOV and the host cells is still missing. In this paper, a mathematical model based on differential equations is used to represent the basic interactions between EBOV and wild-type Vero cells in vitro. Parameter sets that represent infectivity of pathogens are estimated for EBOV infection and compared with influenza virus infection kinetics. The average infecting time of wild-type Vero cells by EBOV is slower than in influenza infection. Simulation results suggest that the slow infecting time of EBOV could be compensated by its efficient replication. This study reveals several identifiability problems and what kind of experiments are necessary to advance the quantification of EBOV infection. A first mathematical approach of EBOV dynamics and the estimation of standard parameters in viral infections kinetics is the key contribution of this work, paving the way for future modeling works on EBOV infection.

Trade-offs between and within scales: environmental persistence and within-host fitness of avian influenza viruses

Trade-offs between different components of a pathogen's replication and transmission cycle are thought to be common. A number of studies have identified trade-offs that emerge across scales, reflecting the tension between strategies that optimize within-host proliferation and large-scale population spread. Most of these studies are theoretical in nature, with direct experimental tests of such cross-scale trade-offs still rare. Here, we report an analysis of avian influenza A viruses across scales, focusing on the phenotype of temperature-dependent viral persistence. Taking advantage of a unique dataset that reports both environmental virus decay rates and strain-specific viral kinetics from duck challenge experiments, we show that the temperature-dependent environmental decay rate of a strain does not impact within-host virus load. Hence, for this phenotype, the scales of within-host infection dynamics and between-host environmental persistence do not seem to interact: viral fitness may be optimized on each scale without cross-scale trade-offs. Instead, we confirm the existence of a temperature-dependent persistence trade-off on a single scale, with some strains favouring environmental persistence in water at low temperatures while others reduce sensitivity to increasing temperatures. We show that this temperature-dependent trade-off is a robust phenomenon and does not depend on the details of data analysis. Our findings suggest that viruses might employ different environmental persistence strategies, which facilitates the coexistence of diverse strains in ecological niches. We conclude that a better understanding of the transmission and evolutionary dynamics of influenza A viruses probably requires empirical information regarding both within-host dynamics and environmental traits, integrated within a combined ecological and within-host framework.

Relating plaque morphology to respiratory syncytial virus subgroup, viral load, and disease severity in children

BACKGROUND

Viral culture plaque morphology in human cell lines are markers for growth capability and cytopathic effect, and have been used to assess viral fitness and select preattenuation candidates for live viral vaccines. We classified respiratory syncytial virus (RSV) plaque morphology and analyzed the relationship between plaque morphology as compared to subgroup, viral load and clinical severity of infection in infants and children.

METHODS

We obtained respiratory secretions from 149 RSV-infected children. Plaque morphology and viral load was assessed within the first culture passage in HEp-2 cells. Viral load was measured by polymerase chain reaction (PCR), as was RSV subgroup. Disease severity was determined by hospitalization, length of stay, intensive care requirement, and respiratory failure.

RESULTS

Plaque morphology varied between individual subjects; however, similar results were observed among viruses collected from upper and lower respiratory tracts of the same subject. Significant differences in plaque morphology were observed between RSV subgroups. No correlations were found among plaque morphology and viral load. Plaque morphology did not correlate with disease severity.

CONCLUSION

Plaque morphology measures parameters that are viral-specific and independent of the human host. Morphologies vary between patients and are related to RSV subgroup. In HEp-2 cells, RSV plaque morphology appears unrelated to disease severity in RSV-infected children.

Epitope mapping of the 2009 pandemic and the A/Brisbane/59/2007 seasonal (H1N1) influenza virus haemagglutinins using mAbs and escape mutants

mAbs constitute an important biological tool for influenza virus haemagglutinin (HA) epitope mapping through the generation of escape mutants, which could provide insights into immune evasion mechanisms and may benefit the future development of vaccines. Several influenza A (H1N1) pandemic 2009 (pdm09) HA escape mutants have been recently described. However, the HA antigenic sites of the previous seasonal A/Brisbane/59/2007 (H1N1) (Bris07) virus remain poorly documented. Here, we produced mAbs against pdm09 and Bris07 HA proteins expressed in human HEK293 cells. Escape mutants were generated using mAbs that exhibited HA inhibition and neutralizing activities. The resulting epitope mapping of the pdm09 HA protein revealed 11 escape mutations including three that were previously described (G172E, N173D and K256E) and eight novel ones (T89R, F128L, G157E, K180E, A212E, R269K, N311T and G478E). Among the six HA mutations that were part of predicted antigenic sites (Ca1, Ca2, Cb, Sa or Sb), three (G172E, N173D and K180E) were within the Sa site. Eight escape mutations (H54N, N55D, N55K, L60H, N203D, A231T, V314I and K464E) were obtained for Bris07 HA, and all but one (N203D, Sb site) were outside the predicted antigenic sites. Our results suggest that the Sa antigenic site is immunodominant in pdm09 HA, whereas the N203D mutation (Sb site), present in three different Bris07 escape mutants, appears as the immunodominant epitope in that strain. The fact that some mutations were not part of predicted antigenic sites reinforces the necessity of further characterizing the HA of additional H1N1 strains.

Reducing uncertainty in within-host parameter estimates of influenza infection by measuring both infectious and total viral load

For in vivo studies of influenza dynamics where within-host measurements are fit with a mathematical model, infectivity assays (e.g. 50% tissue culture infectious dose; TCID₅₀) are often used to estimate the infectious virion concentration over time. Less frequently, measurements of the total (infectious and non-infectious) viral particle concentration (obtained using real-time reverse transcription-polymerase chain reaction; rRT-PCR) have been used as an alternative to infectivity assays. We investigated the degree to which measuring both infectious (via TCID₅₀) and total (via rRT-PCR) viral load allows within-host model parameters to be estimated with greater consistency and reduced uncertainty, compared with fitting to TCID₅₀ data alone. We applied our models to viral load data from an experimental ferret infection study. Best-fit parameter estimates for the “dual-measurement” model are similar to those from the TCID₅₀-only model, with greater consistency in best-fit estimates across different experiments, as well as reduced uncertainty in some parameter estimates. Our results also highlight how variation in TCID₅₀ assay sensitivity and calibration may hinder model interpretation, as some parameter estimates systematically vary with known uncontrolled variations in the assay. Our techniques may aid in drawing stronger quantitative inferences from in vivo studies of influenza virus dynamics.

The H275Y neuraminidase mutation of the pandemic A/H1N1 influenza virus lengthens the eclipse phase and reduces viral output of infected cells, potentially compromising fitness in ferrets

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.

A review of mathematical models of influenza A infections within a host or cell culture: lessons learned and challenges ahead

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.

Influenza A virus infection kinetics: quantitative data and models

Influenza A virus is an important respiratory pathogen that poses a considerable threat to public health each year during seasonal epidemics and even more so when a pandemic strain emerges. Understanding the mechanisms involved in controlling an influenza infection within a host is important and could result in new and effective treatment strategies. Kinetic models of influenza viral growth and decay can summarize data and evaluate the biological parameters governing interactions between the virus and the host. Here we discuss recent viral kinetic models for influenza. We show how these models have been used to provide insight into influenza pathogenesis and treatment, and we highlight the challenges of viral kinetic analysis, including accurate model formulation, estimation of important parameters, and the collection of detailed data sets that measure multiple variables simultaneously. WIREs Syst Biol Med 2011 3 429-445 DOI: 10.1002/wsbm.129