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

Viral Rebound After Antiviral Treatment: A Mathematical Modeling Study of the Role of Antiviral Mechanism of Action

The development of antiviral treatments for SARS-CoV-2 was an important turning point for the pandemic. Availability of safe and effective antivirals has allowed people to return back to normal life. While SARS-CoV-2 antivirals are highly effective at preventing severe disease, there have been concerning reports of viral rebound in some patients after cessation of antiviral treatment. In this study, we use a mathematical model of viral infection to study the potential of different antivirals to prevent viral rebound. We find that antivirals that block production are most likely to result in viral rebound if the treatment time course is not sufficiently long. Since these antivirals do not prevent infection of cells, cells continue to be infected during treatment. When treatment is stopped, the infected cells will begin producing virus at the usual rate. Antivirals that prevent infection of cells are less likely to result in viral rebound since cells are not being infected during treatment. This study highlights the role of antiviral mechanism of action in increasing or reducing the probability of viral rebound.

CRISPR-Based Assays for Point-of-Need Detection and Subtyping of Influenza

The high disease burden of influenza virus poses a significant threat to human health. Optimized diagnostic technologies that combine speed, sensitivity, and specificity with minimal equipment requirements are urgently needed to detect the many circulating species, subtypes, and variants of influenza at the point of need. Here, we introduce such a method using Streamlined Highlighting of Infections to Navigate Epidemics (SHINE), a clustered regularly interspaced short palindromic repeats (CRISPR)-based RNA detection platform. Four SHINE assays were designed and validated for the detection and differentiation of clinically relevant influenza species (A and B) and subtypes (H1N1 and H3N2). When tested on clinical samples, these optimized assays achieved 100% concordance with quantitative RT-PCR. Duplex Cas12a/Cas13a SHINE assays were also developed to detect two targets simultaneously. This study demonstrates the utility of this duplex assay in discriminating two alleles of an oseltamivir resistance (H275Y) mutation as well as in simultaneously detecting influenza A and human RNAse P in patient samples. These assays have the potential to expand influenza detection outside of clinical laboratories for enhanced influenza diagnosis and surveillance.

Virus-mediated cell fusion of SARS-CoV-2 variants

SARS-CoV-2 has the ability to form large multi-nucleated cells known as syncytia. Little is known about how syncytia affect the dynamics of the infection or severity of the disease. In this manuscript, we extend a mathematical model of cell-cell fusion assays to estimate both the syncytia formation rate and the average duration of the fusion phase for five strains of SARS-CoV-2. We find that the original Wuhan strain has the slowest rate of syncytia formation (6.4×10-4/h), but takes only 4.0 h to complete the fusion process, while the Alpha strain has the fastest rate of syncytia formation (0.36 /h), but takes 7.6 h to complete the fusion process. The Beta strain also has a fairly fast syncytia formation rate (9.7×10-2/h), and takes the longest to complete fusion (8.4 h). The D614G strain has a fairly slow syncytia formation rate (2.8×10-3/h), but completes fusion in 4.0 h. Finally, the Delta strain is in the middle with a syncytia formation rate of 3.2×10-2/h and a fusing time of 6.1 h. We note that for these SARS-CoV-2 strains, there appears to be a tradeoff between the ease of forming syncytia and the speed at which they complete the fusion process.

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.

Antiviral Activity of Probenecid and Oseltamivir on Influenza Virus Replication

Influenza can cause respiratory infections, leading to significant morbidity and mortality in humans. While current influenza vaccines offer varying levels of protection, there remains a pressing need for effective antiviral drugs to supplement vaccine efforts. Currently, the FDA-approved antiviral drugs for influenza include oseltamivir, zanamivir, peramivir, and baloxavir marboxil. These antivirals primarily target the virus, making them vulnerable to drug resistance. In this study, we evaluated the efficacy of the neuraminidase inhibitor, oseltamivir, against probenecid, which targets the host cells and is less likely to engender resistance. Our results show that probenecid has superior antiviral efficacy compared to oseltamivir in both in vitro replication assays and in vivo mouse models of influenza infection.

The effect of random virus failure following cell entry on infection outcome and the success of antiviral therapy

A virus infection can be initiated with very few or even a single infectious virion, and as such can become extinct, i.e. stochastically fail to take hold or spread significantly. There are many ways that a fully competent infectious virion, having successfully entered a cell, can fail to cause a productive infection, i.e. one that yields infectious virus progeny. Though many stochastic models (SMs) have been developed and used to estimate a virus infection's establishment probability, these typically neglect infection failure post virus entry. The SM presented herein introduces parameter [Formula: see text] which corresponds to the probability that a virion's entry into a cell will result in a productive cell infection. We derive an expression for the likelihood of infection establishment in this new SM, and find that prophylactic therapy with an antiviral reducing [Formula: see text] is at least as good or better at decreasing the establishment probability, compared to antivirals reducing the rates of virus production or virus entry into cells, irrespective of the SM parameters. We investigate the difference in the fraction of cells consumed by so-called extinct versus established virus infections, and find that this distinction becomes biologically meaningless as the probability of establishment approaches zero. We explain why the release of virions continuously over an infectious cell's lifespan, rather than as a single burst at the end of the cell's lifespan, does not result in an increased risk of infection extinction. We show, instead, that the number of virus released, not the timing of the release, affects infection establishment and associated critical antiviral efficacy.

In Silico Design of an Oseltamivir Derivative with Increased Affinity against Wild-Type and Mutant Variants of Neuraminidase and Hemagglutinin of Influenza A H1N1 Virus

Antiviral resistance has turned into a world concern nowadays. Influenza A H1N1 emerged as a problem at the world level due to the neuraminidase (NA) mutations. The NA mutants conferred resistance to oseltamivir and zanamivir. Several efforts were conducted to develop better anti-influenza A H1N1 drugs. Our research group combined in silico methods to create a compound derived from oseltamivir to be tested in vitro against influenza A H1N1. Here we show the results of a new compound derived from oseltamivir but with specific chemical modifications, with significant affinity either on NA (in silico and in vitro assays) or HA (in silico) from influenza A H1N1 strain. We include docking and molecular dynamics (MD) simulations of the oseltamivir derivative at the binding site onto NA and HA of influenza A H1N1. Additionally, the biological experimental results show that oseltamivir derivative decreases the lytic-plaque formation on viral susceptibility assays, and it does not show cytotoxicity. Finally, oseltamivir derivative assayed on viral NA showed a concentration-dependent inhibition behavior at nM, depicting a high affinity of the compound for the enzyme, corroborated with the MD simulations results, placing our designed oseltamivir derivative as a potential antiviral against influenza A H1N1.

Multiple cohort study of hospitalized SARS-CoV-2 in-host infection dynamics: Parameter estimates, identifiability, sensitivity and the eclipse phase profile

Within-host SARS-CoV-2 modelling studies have been published throughout the COVID-19 pandemic. These studies contain highly variable numbers of individuals and capture varying timescales of pathogen dynamics; some studies capture the time of disease onset, the peak viral load and subsequent heterogeneity in clearance dynamics across individuals, while others capture late-time post-peak dynamics. In this study, we curate multiple previously published SARS-CoV-2 viral load data sets, fit these data with a consistent modelling approach, and estimate the variability of in-host parameters including the basic reproduction number, R0, as well as the best-fit eclipse phase profile. We find that fitted dynamics can be highly variable across data sets, and highly variable within data sets, particularly when key components of the dynamic trajectories (e.g. peak viral load) are not represented in the data. Further, we investigated the role of the eclipse phase time distribution in fitting SARS-CoV-2 viral load data. By varying the shape parameter of an Erlang distribution, we demonstrate that models with either no eclipse phase, or with an exponentially-distributed eclipse phase, offer significantly worse fits to these data, whereas models with less dispersion around the mean eclipse time (shape parameter two or more) offered the best fits to the available data across all data sets used in this work. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Semi-infectious particles contribute substantially to influenza virus within-host dynamics when infection is dominated by spatial structure

Influenza is an ribonucleic acid virus with a genome that comprises eight segments. Experiments show that the vast majority of virions fail to express one or more gene segments and thus cannot cause a productive infection on their own. These particles, called semi-infectious particles (SIPs), can induce virion production through complementation when multiple SIPs are present in an infected cell. Previous within-host influenza models did not explicitly consider SIPs and largely ignore the potential effects of coinfection during virus infection. Here, we constructed and analyzed two distinct models explicitly keeping track of SIPs and coinfection: one without spatial structure and the other implicitly considering spatial structure. While the model without spatial structure fails to reproduce key aspects of within-host influenza virus dynamics, we found that the model implicitly considering the spatial structure of the infection process makes predictions that are consistent with biological observations, highlighting the crucial role that spatial structure plays during an influenza infection. This model predicts two phases of viral growth prior to the viral peak: a first phase driven by fully infectious particles at the initiation of infection followed by a second phase largely driven by coinfections of fully infectious particles and SIPs. Fitting this model to two sets of data, we show that SIPs can contribute substantially to viral load during infection. Overall, the model provides a new interpretation of the in vivo exponential viral growth observed in experiments and a mechanistic explanation for why the production of large numbers of SIPs does not strongly impede viral growth. Being simple and predictive, our model framework serves as a useful tool to understand coinfection dynamics in spatially structured acute viral infections.

Effect of cellular regeneration and viral transmission mode on viral spread

Illness negatively affects all aspects of life and one major cause of illness is viral infections. Some viral infections can last for weeks; others, like influenza (the flu), can resolve quickly. During infections, uninfected cells can replicate in order to replenish the cells that have died due to the virus. Many viral models, especially those for short-lived infections like influenza, tend to ignore cellular regeneration since many think that uncomplicated influenza resolves much faster than cells regenerate. This research accounts for cellular regeneration, using an agent-based framework, and varies the regeneration rate in order to understand how cell regeneration affects viral infection dynamics under assumptions of different modes of transmission. We find that although the general trends in peak viral load, time of viral peak, and chronic viral load as regeneration rate changes are the same for cell-free or cell-to-cell transmission, the changes are more extreme for cell-to-cell transmission due to limited access of infected cells to newly generated cells.

Utility of Human In Vitro Data in Risk Assessments of Influenza A Virus Using the Ferret Model

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. In vivo pathogenicity and transmissibility evaluations in the ferret model represent a critical component of this work. As the relative contribution of in vitro experimentation to these rubrics has not been closely examined, we sought to evaluate to what extent viral titer measurements over the course of in vitro infections are predictive or correlates of nasal wash and tissue measurements for IAV infections in vivo. We compiled data from ferrets inoculated with an extensive panel of over 50 human and zoonotic IAV (inclusive of swine-origin and high- and low-pathogenicity avian influenza viruses associated with human infection) under a consistent protocol, with all viruses concurrently tested in a human bronchial epithelial cell line (Calu-3). Viral titers in ferret nasal wash specimens and nasal turbinate tissue correlated positively with peak titer in Calu-3 cells, whereas additional phenotypic and molecular determinants of influenza virus virulence and transmissibility in ferrets varied in their association with in vitro viral titer measurements. Mathematical modeling was used to estimate more generalizable key replication kinetic parameters from raw in vitro viral titers, revealing commonalities between viral infection progression in vivo and in vitro. Meta-analyses inclusive of IAV that display a diverse range of phenotypes in ferrets, interpreted with mathematical modeling of viral kinetic parameters, can provide critical information supporting a more rigorous and appropriate contextualization of in vitro experiments toward pandemic preparedness. IMPORTANCE 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. These analyses provide a necessary first step in enhanced interpretation and incorporation of in vitro-derived data in risk assessment activities and highlight the utility of employing mathematical modeling approaches to more closely examine features of virus replication not identifiable by experimental studies alone.

Estimation of virus-mediated cell fusion rate of SARS-CoV-2

Several viruses have the ability to form large multinucleated cells known as syncytia. Many properties of syncytia and the role they play in the evolution of a viral infection are not well understood. One basic question that has not yet been answered is how quickly syncytia form. We use a novel mathematical model of cell-cell fusion assays and apply it to experimental data from SARS-CoV-2 fusion assays to provide the first estimates of virus-mediated cell fusion rate. We find that for SARS-CoV2, the fusion rate is in the range of 6 × 10-4-12×10-4/h. We also use our model to compare fusion rates when the protease TMPRSS2 is overexpressed (2-4 times larger fusion rate), when the protease furin is removed (one third the original fusion rate), and when the spike protein is altered (1/10th the original fusion rate). The use of mathematical models allows us to provide additional quantitative information about syncytia formation.

Heterogeneity of Rift Valley fever virus transmission potential across livestock hosts, quantified through a model-based analysis of host viral load and vector infection

Quantifying the variation of pathogens’ life history traits in multiple host systems is crucial to understand their transmission dynamics. It is particularly important for arthropod-borne viruses (arboviruses), which are prone to infecting several species of vertebrate hosts. Here, we focus on how host-pathogen interactions determine the ability of host species to transmit a virus to susceptible vectors upon a potentially infectious contact. Rift Valley fever (RVF) is a viral, vector-borne, zoonotic disease, chosen as a case study. The relative contributions of livestock species to RVFV transmission has not been previously quantified. To estimate their potential to transmit the virus over the course of their infection, we 1) fitted a within-host model to viral RNA and infectious virus measures, obtained daily from infected lambs, calves, and young goats, 2) estimated the relationship between vertebrate host infectious titers and probability to infect mosquitoes, and 3) estimated the net infectiousness of each host species over the duration of their infectious periods, taking into account different survival outcomes for lambs. Our results indicate that the efficiency of viral replication, along with the lifespan of infectious particles, could be sources of heterogeneity between hosts. Given available data on RVFV competent vectors, we found that, for similar infectious titers, infection rates in the Aedes genus were on average higher than in the Culex genus. Consequently, for Aedes-mediated infections, we estimated the net infectiousness of lambs to be 2.93 (median) and 3.65 times higher than that of calves and goats, respectively. In lambs, we estimated the overall infectiousness to be 1.93 times higher in individuals which eventually died from the infection than in those recovering. Beyond infectiousness, the relative contributions of host species to transmission depend on local ecological factors, including relative abundances and vector host-feeding preferences. Quantifying these contributions will ultimately help design efficient, targeted, surveillance and vaccination strategies.

Viruses spread by mosquitoes present a major threat to animal and public health worldwide. When these pathogenic viruses can infect multiple species, controlling their spread becomes difficult. Rift Valley fever virus (RVFV) is such a virus. It spreads predominantly among ruminant livestock but can also spill over and cause severe disease in humans. Understanding which of these ruminant species are most important for the transmission of RVFV can help for effective control. One piece of this puzzle is to assess how effective infected animals are at transmitting RVFV to mosquitoes. To answer this question, we combine mathematical models with observations from experimental infections in cattle, sheep, and goats, and model changes in viremia over time within individuals. We then quantify the relationship between hosts’ viremia and the probability to infect mosquitoes. In combining these two analyses, we estimate the overall transmission potential of sheep, when in contact with mosquitoes, to be 3 to 5 times higher than that of goats and cattle. Further, sheep that experience a lethal infection have an even larger overall transmission potential. Once applied at the level of populations, with setting-specific herd composition and exposure to mosquitoes, these results will help unravel species’ role in RVF outbreaks.

Predicting Permissive Mutations That Improve the Fitness of A(H1N1)pdm09 Viruses Bearing the H275Y Neuraminidase Substitution

Oseltamivir-resistant influenza viruses arise due to amino acid mutations in key residues of the viral neuraminidase (NA). These changes often come at a fitness cost; however, it is known that permissive mutations in the viral NA can overcome this cost. This result was observed in former seasonal A(H1N1) viruses in 2007 which expressed the H275Y substitution (N1 numbering) with no apparent fitness cost and lead to widespread oseltamivir resistance. Therefore, this study aims to predict permissive mutations that may similarly enable fit H275Y variants to arise in currently circulating A(H1N1)pdm09 viruses. The first approach in this study utilized in silico analyses to predict potentially permissive mutations. The second approach involved the generation of a virus library which encompassed all possible NA mutations while keeping H275Y fixed. Fit variants were then selected by serially passaging the virus library either through ferrets by transmission or passaging once in vitro. The fitness impact of selected substitutions was further evaluated experimentally. The computational approach predicted three candidate permissive NA mutations which, in combination with each other, restored the replicative fitness of an H275Y variant. The second approach identified a stringent bottleneck during transmission between ferrets; however, three further substitutions were identified which may improve transmissibility. A comparison of fit H275Y variants in vitro and in experimentally infected animals showed a statistically significant correlation in the variants that were positively selected. Overall, this study provides valuable tools and insights into potential permissive mutations that may facilitate the emergence of a fit H275Y A(H1N1)pdm09 variant.

IMPORTANCE Oseltamivir (Tamiflu) is the most widely used antiviral for the treatment of influenza infections. Therefore, resistance to oseltamivir is a public health concern. This study is important as it explores the different evolutionary pathways available to current circulating influenza viruses that may lead to widespread oseltamivir resistance. Specifically, this study develops valuable experimental and computational tools to evaluate the fitness landscape of circulating A(H1N1)pmd09 influenza viruses bearing the H275Y mutation. The H275Y substitution is most commonly reported to confer oseltamivir resistance but also leads to loss of virus replication and transmission fitness, which limits its spread. However, it is known from previous influenza seasons that influenza viruses can evolve to overcome this loss of fitness. Therefore, this study aims to prospectively predict how contemporary A(H1N1)pmd09 influenza viruses may evolve to overcome the fitness cost of bearing the H275Y NA substitution, which could result in widespread oseltamivir resistance.

Genetic Analysis of Influenza A/H1N1pdm Strains Isolated in Bangladesh in Early 2020

Influenza is one of the most common respiratory virus infections. We analyzed hemagglutinin (HA) and neuraminidase (NA) gene segments of viruses isolated from influenza patients who visited Evercare Hospital Dhaka, Bangladesh, in early 2020 immediately before the coronavirus disease 2019 (COVID-19) pandemic. All of them were influenza virus type A (IAV) H1N1pdm. Sequence analysis of the HA segments of the virus strains isolated from the clinical specimens and the subsequent phylogenic analyses of the obtained sequences revealed that all of the H1N1pdm recent subclades 6B.1A5A + 187V/A, 6B.1A5A + 156K, and 6B.1A5A + 156K with K209M were already present in Bangladesh in January 2020. Molecular clock analysis results suggested that the subclade 6B.1A5A + 156K emerged in Denmark, Australia, or the United States in July 2019, while subclades 6B.1A5A + 187V/A and 6B.1A5A + 156K with K209M emerged in East Asia in April and September 2019, respectively. On the other hand, sequence analysis of NA segments showed that the viruses lacked the H275Y mutation that confers oseltamivir resistance. Since the number of influenza cases in Bangladesh is usually small between November and January, these results indicated that the IAV H1N1pdm had spread extremely rapidly without acquiring oseltamivir resistance during a time of active international flow of people before the COVID-19 pandemic.

Mathematical modelling of SARS-CoV-2 infection of human and animal host cells reveals differences in the infection rates and delays in viral particle production by infected cells

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV -2), a causative agent of COVID-19 disease, poses a significant threat to public health. Since its outbreak in December 2019, Wuhan, China, extensive collection of diverse data from cell culture and animal infections as well as population level data from an ongoing pandemic, has been vital in assessing strategies to battle its spread. Mathematical modelling plays a key role in quantifying determinants that drive virus infection dynamics, especially those relevant for epidemiological investigations and predictions as well as for proposing efficient mitigation strategies. We utilized a simple mathematical model to describe and explain experimental results on viral replication cycle kinetics during SARS-CoV-2 infection of animal and human derived cell lines, green monkey kidney cells, Vero-E6, and human lung epithelium cells, A549-ACE2, respectively. We conducted cell infections using two distinct initial viral concentrations and quantified viral loads over time. We then fitted the model to our experimental data and quantified the viral parameters. We showed that such cellular tropism generates significant differences in the infection rates and incubation times of SARS-CoV-2, that is, the times to the first release of newly synthesised viral progeny by SARS-CoV-2-infected cells. Specifically, the rate at which A549-ACE2 cells were infected by SARS-CoV-2 was 15 times lower than that in the case of Vero-E6 cell infection and the duration of latent phase of A549-ACE2 cells was 1.6 times longer than that of Vero-E6 cells. On the other hand, we found no statistically significant differences in other viral parameters, such as viral production rate or infected cell death rate. Since in vitro infection assays represent the first stage in the development of antiviral treatments against SARS-CoV-2, discrepancies in the viral parameter values across different cell hosts have to be identified and quantified to better target vaccine and antiviral research.

Dynamical Differences in Respiratory Syncytial Virus

Respiratory syncytial virus (RSV) is a leading viral cause of pediatric respiratory infections and early infant mortality. Despite extensive development efforts currently underway, there remain no vaccines available for the prevention of RSV. RSV is an enveloped, negative-strand RNA virus that utilizes two different proteins (G and F) to mediate attachment and entry into host cells. These G and F proteins are the primary determinants of viral strain-specific differences and elicit protective neutralizing antibodies during natural infection in humans. Earlier studies have demonstrated that these proteins play an additional role in regulating the stability of RSV particles in response to temperature and pH. However, it remains unclear how much variability exists in the stability of RSV strains and what contribution changes in temperature and pH make to the clearance of virus during an active infection. In this study, we evaluated the impacts of changes in temperature and pH on the inactivation of four different chimeric recombinant RSV strains that differ exclusively in G and F protein expression. Using these data, we developed predictive mathematical models to examine the specific contributions and variations in susceptibility that exist between viral strains. Our data provide strain-specific clearance rates and temperature–pH landscapes that shed light on the optimal contributions of temperature and pH to viral clearance. These provide new insight into how much variation exists in the clearance of a major respiratory pathogen and may offer new guidance on optimization of viral strains for development of live-attenuated vaccine preparations.

Estimation of viral kinetics model parameters in young and aged SARS-CoV-2 infected macaques

The SARS-CoV-2 virus disproportionately causes serious illness and death in older individuals. In order to have the greatest impact in decreasing the human toll caused by the virus, antiviral treatment should be targeted to older patients. For this, we need a better understanding of the differences in viral dynamics between SARS-CoV-2 infection in younger and older adults. In this study, we use previously published averaged viral titre measurements from the nose and throat of SARS-CoV-2 infection in young and aged cynomolgus macaques to parametrize a viral kinetics model. We find that all viral kinetics parameters differ between young and aged macaques in the nasal passages, but that there are fewer differences in parameter estimates from the throat. We further use our parametrized model to study the antiviral treatment of young and aged animals, finding that early antiviral treatment is more likely to lead to a lengthening of the infection in aged animals, but not in young animals.

Genotypic Variants of Pandemic H1N1 Influenza A Viruses Isolated from Severe Acute Respiratory Infections in Ukraine during the 2015/16 Influenza Season

Human type A influenza viruses A(H1N1)pdm09 have caused seasonal epidemics of influenza since the 2009-2010 pandemic. A(H1N1)pdm09 viruses had a leading role in the severe epidemic season of 2015/16 in the Northern Hemisphere and caused a high incidence of acute respiratory infection (ARI) in Ukraine. Serious complications of influenza-associated severe ARI (SARI) were observed in the very young and individuals at increased risk, and 391 fatal cases occurred in the 2015/16 epidemic season. We analyzed the genetic changes in the genomes of A(H1N1)pdm09 influenza viruses isolated from SARI cases in Ukraine during the 2015/16 season. The viral hemagglutinin (HA) fell in H1 group 6B.1 for all but four isolates, with known mutations affecting glycosylation, the Sa antigenic site (S162N in all 6B.1 isolates), or virulence (D222G/N in two isolates). Other mutations occurred in antigenic site Ca (A141P and S236P), and a subgroup of four strains were in group 6B.2, with potential alterations to antigenicity in A(H1N1)pdm09 viruses circulating in 2015/16 in Ukraine. A cluster of Ukrainian isolates exhibited novel D2E and N48S mutations in the RNA binding domain, and E125D in the effector domain, of immune evasion nonstructural protein 1 (NS1). The diverse spectrum of amino-acid substitutions in HA, NS1, and other viral proteins including nucleoprotein (NP) and the polymerase complex suggested the concurrent circulation of multiple lineages of A(H1N1)pdm09 influenza viruses in the human population in Ukraine, a country with low vaccination coverage, complicating public health measures against influenza.

A study of the effects of age on the dynamics of RSV in animal models

Respiratory syncytial virus can cause severe illness and even death, particularly in infants. The increased severity of disease in young children is thought to be due to a lack of previous exposure to the virus as well as the limited immune response in infants. While studies have examined the clinical differences in disease between infants and adults, there has been limited examination of how the viral dynamics differ as infants develop. In this study, we apply a mathematical model to data from cotton rats and ferrets of different ages to assess how viral kinetics parameters change as the animals age. We find no clear trend in the viral decay rate, infecting time, and basic reproduction number as the animals age. We discuss possible reasons for the null result including the limited data, lack of detail of the mathematical model, and the limitations of animal models.

Kinetics of Asian and African Zika virus lineages over single-cycle and multi-cycle growth in culture: Gene expression, cell killing, virus production, and mathematical modeling

Since 2014, an Asian lineage of Zika virus has caused outbreaks, and it has been associated with neurological disorders in adults and congenital defects in newborns. The resulting threat of the Zika virus to human health has prompted the development of new vaccines, which have yet to be approved for human use. Vaccines based on the attenuated or chemically inactivated virus will require large-scale production of the intact virus to meet potential global demands. Intact viruses are produced by infecting cultures of susceptible cells, a dynamic process that spans from hours to days and has yet to be optimized. Here, we infected Vero cells adhesively cultured in well-plates with two Zika virus strains: a recently isolated strain from the Asian lineage, and a cell-culture-adapted strain from the African lineage. At different time points post-infection, virus particles in the supernatant were quantified; further, microscopy images were used to quantify cell density and the proportion of cells expressing viral protein. These measurements were performed across multiple replicate samples of one-step infections every four hours over 60 h and for multi-step infections every four to 24 h over 144 h, generating a rich data set. For each set of data, mathematical models were developed to estimate parameters associated with cell infection and virus production. The African-lineage strain was found to produce a 14-fold higher yield than the Asian-lineage strain in one-step growth and a sevenfold higher titer in multi-step growth, suggesting a benefit of cell-culture adaptation for developing a vaccine strain. We found that image-based measurements were critical for discriminating among different models, and different parameters for the two strains could account for the experimentally observed differences. An exponential-distributed delay model performed best in accounting for multi-step infection of the Asian strain, and it highlighted the significant sensitivity of virus titer to the rate of viral degradation, with implications for optimization of vaccine production. More broadly, this study highlights how image-based measurements can contribute to the discrimination of virus-culture models for the optimal production of inactivated and attenuated whole-virus vaccines.

Interferon Lambda Delays the Emergence of Influenza Virus Resistance to Oseltamivir

Influenza viruses are a leading cause of morbidity and mortality worldwide. These air-borne pathogens are able to cross the species barrier, leading to regular seasonal epidemics and sporadic pandemics. Influenza viruses also possess a high genetic variability, which allows for the acquisition of resistance mutations to antivirals. Combination therapies with two or more drugs targeting different mechanisms of viral replication have been considered an advantageous option to not only enhance the effectiveness of the individual treatments, but also reduce the likelihood of resistance emergence. Using an in vitro infection model, we assessed the barrier to viral resistance of a combination therapy with the neuraminidase inhibitor oseltamivir and human interferon lambda against the pandemic H1N1 A/Netherlands/602/2009 (H1N1pdm09) virus. We serially passaged the virus in a cell line derived from human bronchial epithelial cells in the presence or absence of increasing concentrations of oseltamivir alone or oseltamivir plus interferon lambda. While the treatment with oseltamivir alone quickly induced the emergence of antiviral resistance through a single mutation in the neuraminidase gene, the co-administration of interferon lambda delayed the emergence of drug-resistant influenza virus variants. Our results suggest a possible clinical application of interferon lambda in combination with oseltamivir to treat influenza.

Quantifying the effect of trypsin and elastase on in vitro SARS-CoV infections

The SARS coronavirus (SARS-CoV) has the potential to cause serious disease that can spread rapidly around the world. Much of our understanding of SARS-CoV pathogenesis comes from in vitro experiments. Unfortunately, in vitro experiments cannot replicate all the complexity of the in vivo infection. For example, proteases in the respiratory tract cleave the SARS-CoV surface protein to facilitate viral entry, but these proteases are not present in vitro. Unfortunately, proteases might also have an effect on other parts of the replication cycle. Here, we use mathematical modeling to estimate parameters characterizing viral replication for SARS-CoV in the presence of trypsin or elastase, and in the absence of either. In addition to increasing the infection rate, the addition of trypsin and elastase causes lengthening of the eclipse phase duration and the infectious cell lifespan.

Phylogenetic analysis of the neuraminidase segment gene of Influenza A/H1N1 strains isolated from Monastir Region (Tunisia) during the 2017-2018 outbreak

Influenza A/H1N1 is widely considered to be a very evolutionary virus causing major public health problems. Since the pandemic of 2009, there has been a rapid rise in human Influenza virus characterization. However, little data is available in Tunisia regarding its genetic evolution. In light of this fact, our paper aim is to genetically characterize the Neuraminidase, known as the target of antiviral inhibitors, in Tunisian isolates circulating in Monastir region during 2017-2018. In total of 31 positive Influenza A/H1N1 detected by multiplex real-time PCR, RT-PCR of neuraminidase was performed. Among the 31 positive samples, 7 samples representing fatal and most severe cases were conducted for sequencing and genetic analysis. The results thus obtained showed genetic evolution of the A/H1N1 neuraminidase between 2009 and 2010 and 2018-2019 outbreaks. All Tunisian isolates were genetically related to the recommended vaccine strain with a specific evolution. Moreover, the phylogenetic analysis demonstrated that France and especially Italian strains were the major related strains. Interestingly, our results revealed a specific cluster of Tunisian isolates where two intragroup were evolved in correlation with the severity and the fatalities cases. From the outcome of our investigation, this study confirms the genetic evolution of the Influenza A virus circulating in Tunisia and gives a preliminary analysis for a better comprehension of new emerging Tunisian strain's virulence and thus, a more appropriate monitoring of Influenza virus A/H1N1 during each round of outbreaks.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11756-021-00723-y.

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.

Quantification of Ebola virus replication kinetics in vitro

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.

Initial Inoculum and the Severity of COVID-19: A Mathematical Modeling Study of the Dose-Response of SARS-CoV-2 Infections

SARS-CoV-2 (Severe acute respiratory syndrome coronavirus 2) causes a variety of responses in those who contract the virus, ranging from asymptomatic infections to acute respiratory failure and death. While there are likely multiple mechanisms triggering severe disease, one potential cause of severe disease is the size of the initial inoculum. For other respiratory diseases, larger initial doses lead to more severe outcomes. We investigate whether there is a similar link for SARS-CoV-2 infections using the combination of an agent-based model (ABM) and a partial differential equation model (PDM). We use the model to examine the viral time course for different sizes of initial inocula, generating dose-response curves for peak viral load, time of viral peak, viral growth rate, infection duration, and area under the viral titer curve. We find that large initial inocula lead to short infections, but with higher viral titer peaks; and that smaller initial inocula lower the viral titer peak, but make the infection last longer.

Modeling the efficiency of filovirus entry into cells in vitro: Effects of SNP mutations in the receptor molecule

Interaction between filovirus glycoprotein (GP) and the Niemann-Pick C1 (NPC1) protein is essential for membrane fusion during virus entry. Some single-nucleotide polymorphism (SNPs) in two surface-exposed loops of NPC1 are known to reduce viral infectivity. However, the dependence of differences in entry efficiency on SNPs remains unclear. Using vesicular stomatitis virus pseudotyped with Ebola and Marburg virus GPs, we investigated the cell-to-cell spread of viruses in cultured cells expressing NPC1 or SNP derivatives. Eclipse and virus-producing phases were assessed by in vitro infection experiments, and we developed a mathematical model describing spatial-temporal virus spread. This mathematical model fit the plaque radius data well from day 2 to day 6. Based on the estimated parameters, we found that SNPs causing the P424A and D508N substitutions in NPC1 most effectively reduced the entry efficiency of Ebola and Marburg viruses, respectively. Our novel approach could be broadly applied to other virus plaque assays.

Ebola (EBOV) and Marburg (MARV) viruses, which are included viruses of the family Filoviridae, cause severe hemorrhagic fever in humans. Filovirus particles is adsorbed to the cell through glycoprotein (GP), which is the only viral surface protein. Interaction between the filovirus sugar protein (GP) and the Niemann-Pick C1 (NPC1) protein plays a key role in membrane fusion during virus entry. Although some single-nucleotide polymorphism (SNPs) in two surface-exposed loops of NPC1 are known to reduce viral infectivity, the dependence of differences in entry efficiency on SNPs has not been studied. We therefore investigated the cell-to-cell spread of viruses in cultured cells expressing NPC1 or SNP derivatives. Using a mathematical model describing spatial-temporal virus spread, we quantitatively analyze viral entry efficiency and how this affected cell-to-cell spread. Our approach may be applied to not only understanding the roles of genetic polymorphisms in human susceptibility to filoviruses, but also other virus plaque assays.

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.

Modelling Degradation and Replication Kinetics of the Zika Virus In Vitro Infection

Mathematical models of in vitro viral kinetics help us understand and quantify the main determinants underlying the virus–host cell interactions. We aimed to provide a numerical characterization of the Zika virus (ZIKV) in vitro infection kinetics, an arthropod-borne emerging virus that has gained public recognition due to its association with microcephaly in newborns. The mathematical model of in vitro viral infection typically assumes that degradation of extracellular infectious virus proceeds in an exponential manner, that is, each viral particle has the same probability of losing infectivity at any given time. We incubated ZIKV stock in the cell culture media and sampled with high frequency for quantification over the course of 96 h. The data showed a delay in the virus degradation in the first 24 h followed by a decline, which could not be captured by the model with exponentially distributed decay time of infectious virus. Thus, we proposed a model, in which inactivation of infectious ZIKV is gamma distributed and fit the model to the temporal measurements of infectious virus remaining in the media. The model was able to reproduce the data well and yielded the decay time of infectious ZIKV to be 40 h. We studied the in vitro ZIKV infection kinetics by conducting cell infection at two distinct multiplicity of infection and measuring viral loads over time. We fit the mathematical model of in vitro viral infection with gamma distributed degradation time of infectious virus to the viral growth data and identified the timespans and rates involved within the ZIKV-host cell interplay. Our mathematical analysis combined with the data provides a well-described example of non-exponential viral decay dynamics and presents numerical characterization of in vitro infection with ZIKV.

A mathematical model describing the localization and spread of influenza A virus infection within the human respiratory tract

Within the human respiratory tract (HRT), virus diffuses through the periciliary fluid (PCF) bathing the epithelium. But virus also undergoes advection: as the mucus layer sitting atop the PCF is pushed along by the ciliated cell's beating cilia, the PCF and its virus content are also pushed along, upwards towards the nose and mouth. While many mathematical models (MMs) have described the course of influenza A virus (IAV) infections in vivo, none have considered the impact of both diffusion and advection on the kinetics and localization of the infection. The MM herein represents the HRT as a one-dimensional track extending from the nose down towards the lower HRT, wherein stationary cells interact with IAV which moves within (diffusion) and along with (advection) the PCF. Diffusion was found to be negligible in the presence of advection which effectively sweeps away IAV, preventing infection from disseminating below the depth at which virus first deposits. Higher virus production rates (10-fold) are required at higher advection speeds (40 μm/s) to maintain equivalent infection severity and timing. Because virus is entrained upwards, upper parts of the HRT see more virus than lower parts. As such, infection peaks and resolves faster in the upper than in the lower HRT, making it appear as though infection progresses from the upper towards the lower HRT, as reported in mice. When the spatial MM is expanded to include cellular regeneration and an immune response, it reproduces tissue damage levels reported in patients. It also captures the kinetics of seasonal and avian IAV infections, via parameter changes consistent with reported differences between these strains, enabling comparison of their treatment with antivirals. This new MM offers a convenient and unique platform from which to study the localization and spread of respiratory viral infections within the HRT.

Lung Aerosol Dynamics of Airborne Influenza A Virus-Laden Droplets and the Resultant Immune System Responses: An In Silico Study

Influenza A Virus (IAV) replications start from the deposition of inhaled virus-laden droplets on the epithelial cells in the pulmonary tracts. In order to understand the local deposition patterns and within-host dynamics of infectious aerosols, accurate information of high-resolution imaging capabilities, as well as real-time flow cytometry analysis, are required for tracking infected cells, virus agents, and immune system responses. However, clinical and animal studies are in deficit to meet the above-mentioned demands, due to their limited operational flexibility and imaging resolution. Therefore, this study developed an experimentally validated multiscale epidemiological computational model, i.e., the Computational Fluid-Particle Dynamics (CFPD) plus Host Cell Dynamics (HCD) model, to predict the transport and deposition of the low-strain IAV-laden droplets, as well as the resultant regional immune system responses. The hygroscopic growth and shrinkage of IAV-laden droplets were accurately modeled. The subject-specific respiratory system was discretized by generating the new polyhedral-core mesh. By simulating both mouth and nasal breathing scenarios, the inhalations of isotonic IAV-laden droplets with three different compositions were achieved. It is the first time that parametric analysis was performed using the multiscale model on how different exposure conditions can influence the virus aerodynamics in the lung and the subsequent immune system responses. Numerical results show a higher viral accretion followed by a faster immune system response in the supraglottic region when droplets with the higher salt concentration were inhaled. Consequently, more severe symptoms and longer recovery are expected at the pharynx. Furthermore, local deposition maps of IAV-laden droplets and post-deposition infection dynamics provide informative and direct evidence which significantly enhance the fundamental understanding of the underlying mechanisms for upper airway and lower airway infections.

Effect of stochasticity on coinfection dynamics of respiratory viruses

Background

Respiratory viral infections are a leading cause of mortality worldwide. As many as 40% of patients hospitalized with influenza-like illness are reported to be infected with more than one type of virus. However, it is not clear whether these infections are more severe than single viral infections. Mathematical models can be used to help us understand the dynamics of respiratory viral coinfections and their impact on the severity of the illness. Most models of viral infections use ordinary differential equations (ODE) that reproduce the average behavior of the infection, however, they might be inaccurate in predicting certain events because of the stochastic nature of viral replication cycle. Stochastic simulations of single virus infections have shown that there is an extinction probability that depends on the size of the initial viral inoculum and parameters that describe virus-cell interactions. Thus the coinfection dynamics predicted by the ODE might be difficult to observe in reality.

Results

In this work, a continuous-time Markov chain (CTMC) model is formulated to investigate probabilistic outcomes of coinfections. This CTMC model is based on our previous coinfection model, expressed in terms of a system of ordinary differential equations. Using the Gillespie method for stochastic simulation, we examine whether stochastic effects early in the infection can alter which virus dominates the infection.

Conclusions

We derive extinction probabilities for each virus individually as well as for the infection as a whole. We find that unlike the prediction of the ODE model, for similar initial growth rates stochasticity allows for a slower growing virus to out-compete a faster growing virus.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2793-6) contains supplementary material, which is available to authorized users.

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.

Model-based analysis of influenza A virus replication in genetically engineered cell lines elucidates the impact of host cell factors on key kinetic parameters of virus growth

The best measure to limit spread of contagious diseases caused by influenza A viruses (IAVs) is annual vaccination. The growing global demand for low-cost vaccines requires the establishment of high-yield production processes. One possible option to address this challenge is the engineering of novel vaccine producer cell lines by manipulating gene expression of host cell factors relevant for virus replication. To support detailed characterization of engineered cell lines, we fitted an ordinary differential equation (ODE)-based model of intracellular IAV replication previously established by our group to experimental data obtained from infection studies in human A549 cells. Model predictions indicate that steps of viral RNA synthesis, their regulation and particle assembly and virus budding are promising targets for cell line engineering. The importance of these steps was confirmed in four of five single gene overexpression cell lines (SGOs) that showed small, but reproducible changes in early dynamics of RNA synthesis and virus release. Model-based analysis suggests, however, that overexpression of the selected host cell factors negatively influences specific RNA synthesis rates. Still, virus yield was rescued by an increase in the virus release rate. Based on parameter estimations obtained for SGOs, we predicted that there is a potential benefit associated with overexpressing multiple host cell genes in one cell line, which was validated experimentally. Overall, this model-based study on IAV replication in engineered cell lines provides a step forward in the dynamic and quantitative characterization of IAV-host cell interactions. Furthermore, it suggests targets for gene editing and indicates that overexpression of multiple host cell factors may be beneficial for the design of novel producer cell lines.

Mathematical Analysis of a Transformed ODE from a PDE Multiscale Model of Hepatitis C Virus Infection

Mathematical modeling has revealed the quantitative dynamics during the process of viral infection and evolved into an important tool in modern virology. Coupled with analyses of clinical and experimental data, the widely used basic model of viral dynamics described by ordinary differential equations (ODEs) has been well parameterized. In recent years, age-structured models, called "multiscale model," formulated by partial differential equations (PDEs) have also been developed and become useful tools for more detailed data analysis. However, in general, PDE models are considerably more difficult to subject to mathematical and numerical analyses. In our recently reported study, we successfully derived a mathematically identical ODE model from a PDE model, which helps to overcome the limitations of the PDE model with regard to clinical data analysis. Here, we derive the basic reproduction number from the identical ODE model and provide insight into the global stability of all possible steady states of the ODE model.

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.

Sequential infection experiments for quantifying innate and adaptive immunity during influenza infection

Laboratory models are often used to understand the interaction of related pathogens via host immunity. For example, recent experiments where ferrets were exposed to two influenza strains within a short period of time have shown how the effects of cross-immunity vary with the time between exposures and the specific strains used. On the other hand, studies of the workings of different arms of the immune response, and their relative importance, typically use experiments involving a single infection. However, inferring the relative importance of different immune components from this type of data is challenging. Using simulations and mathematical modelling, here we investigate whether the sequential infection experiment design can be used not only to determine immune components contributing to cross-protection, but also to gain insight into the immune response during a single infection. We show that virological data from sequential infection experiments can be used to accurately extract the timing and extent of cross-protection. Moreover, the broad immune components responsible for such cross-protection can be determined. Such data can also be used to infer the timing and strength of some immune components in controlling a primary infection, even in the absence of serological data. By contrast, single infection data cannot be used to reliably recover this information. Hence, sequential infection data enhances our understanding of the mechanisms underlying the control and resolution of infection, and generates new insight into how previous exposure influences the time course of a subsequent infection.

Investigating Different Mechanisms of Action in Combination Therapy for Influenza

Combination therapy for influenza can have several benefits, from reducing the emergence of drug resistant virus strains to decreasing the cost of antivirals. However, there are currently only two classes of antivirals approved for use against influenza, limiting the possible combinations that can be considered for treatment. However, new antivirals are being developed that target different parts of the viral replication cycle, and their potential for use in combination therapy should be considered. The role of antiviral mechanism of action in the effectiveness of combination therapy has not yet been systematically investigated to determine whether certain antiviral mechanisms of action pair well in combination. Here, we use a mathematical model of influenza to model combination treatment with antivirals having different mechanisms of action to measure peak viral load, infection duration, and synergy of different drug combinations. We find that antivirals that lower the infection rate and antivirals that increase the duration of the eclipse phase perform poorly in combination with other antivirals.

Comparison of early and recent influenza A(H1N1)pdm09 isolates harboring or not the H275Y neuraminidase mutation, in vitro and in animal models

After 6 years of circulation in humans, a novel antigenic variant of influenza A(H1N1)pdm09 (i.e., A/Michigan/45/2015) emerged in 2015-16 and has predominated thereafter worldwide. Herein, we compared in vitro and in vivo properties of 2016 wild-type (WT) A/Michigan/45/15-like isolate and its H275Y neuraminidase (NA) variant to the original A/California/07/09-like counterparts. The H275Y mutation induced comparable levels of resistance to oseltamivir and peramivir without altering zanamivir susceptibility in both 2009 and 2016 isolates. In vitro, the two WT isolates had comparable replicative properties. The 2016-H275Y isolate had lower titers at 36 h post-inoculation (PI) (P < 0.05) while the 2009-H275Y titers were lower at both 24 h (P < 0.01) and 36 h PI (P < 0.001) vs the respective WTs. In mice, the 2016-WT isolate caused less weight losses (P < 0.001) and lower lung viral titers (LVTs) (P < 0.01) vs the 2009-WT. The LVTs of 2016-WT and 2016-H275Y groups were comparable whereas the 2009-H275Y LVTs were lower vs the respective WT (P < 0.01). Ferrets infected with the 2016-WT isolate and their contacts had higher nasal viral titers (NVTs) at early time points vs the 2009-WT group (P < 0.01). Also, NVTs of 2016-H275Y animals were lower vs the 2016-WT group at early time points in both infected (P < 0.01) and contact animals (P < 0.001). In conclusion, while the H275Y mutation similarly impacts the A/California/07/2009- and A/Michigan/45/2015-like A(H1N1)pdm09 NAs, the fitness of these isolates differs according to animal models with the 2016 virus being less virulent in mice but slightly more virulent in ferrets, potentially reflecting a period of cumulative changes in surface and internal genes.

Effects of Transmission Bottlenecks on the Diversity of Influenza A Virus

We investigate the fate of de novo mutations that occur during the in-host replication of a pathogenic virus, predicting the probability that such mutations are passed on during disease transmission to a new host. Using influenza A virus as a model organism, we develop a life-history model of the within-host dynamics of the infection, deriving a multitype branching process with a coupled deterministic model to capture the population of available target cells. We quantify the fate of neutral mutations and mutations affecting five life-history traits: clearance, attachment, budding, cell death, and eclipse phase timing. Despite the severity of disease transmission bottlenecks, our results suggest that in a single transmission event, several mutations that appeared de novo in the donor are likely to be transmitted to the recipient. Even in the absence of a selective advantage for these mutations, the sustained growth phase inherent in each disease transmission cycle generates genetic diversity that is not eliminated during the transmission bottleneck.

Mathematical modeling of within-host Zika virus dynamics

Recent Zika virus outbreaks have been associated with severe outcomes, especially during pregnancy. A great deal of effort has been put toward understanding this virus, particularly the immune mechanisms responsible for rapid viral control in the majority of infections. Identifying and understanding the key mechanisms of immune control will provide the foundation for the development of effective vaccines and antiviral therapy. Here, we outline a mathematical modeling approach for analyzing the within-host dynamics of Zika virus, and we describe how these models can be used to understand key aspects of the viral life cycle and to predict antiviral efficacy.

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.

A quantitative assessment of dynamical differences of RSV infections in vitro and in vivo

Experimental results in vitro and in animal models are used to guide researchers in testing vaccines or treatment in humans. However, viral kinetics are different in vitro, in animals, and in humans, so it is sometimes difficult to translate results from one system to another. In this study, we use a mathematical model to fit experimental data from multiple cycle respiratory syncytial virus (RSV) infections in vitro, in african green monkey (AGM), and in humans in order to quantitatively compare viral kinetics in the different systems. We find that there are differences in viral clearance rate, productively infectious cell lifespan, and eclipse phase duration between in vitro and in vivo systems and among different in vivo systems. We show that these differences in viral kinetics lead to different estimates of drug effectiveness of fusion inhibitors in vitro and in AGM than in humans.

Modeling of fusion inhibitor treatment of RSV in African green monkeys

Respiratory syncytial virus (RSV) is a respiratory infection that can cause serious illness, particularly in infants. In this study, we test four different model implementations for the effect of a fusion inhibitor, including one model that combines different drug effects, by fitting the models to data from a study of TMC353121 in African green monkeys. We use mathematical modeling to estimate the drug efficacy parameters, ε_max, the maximum efficacy of the drug, and EC₅₀, the drug concentration needed to achieve half the maximum effect. We find that if TMC353121 is having multiple effects on viral kinetics, more detailed data, using different treatment delays, is needed to detect this effect.

The effect of delay in viral production in within-host models during early infection

Delay in viral production may have a significant impact on the early stages of infection. During the eclipse phase, the time from viral entry until active production of viral particles, no viruses are produced. This delay affects the probability that a viral infection becomes established and timing of the peak viral load. Deterministic and stochastic models are formulated with either multiple latent stages or a fixed delay for the eclipse phase. The deterministic model with multiple latent stages approaches in the limit the model with a fixed delay as the number of stages approaches infinity. The deterministic model framework is used to formulate continuous-time Markov chain and stochastic differential equation models. The probability of a minor infection with rapid viral clearance as opposed to a major full-blown infection with a high viral load is estimated from a branching process approximation of the Markov chain model and the results are confirmed through numerical simulations. In addition, parameter values for influenza A are used to numerically estimate the time to peak viral infection and peak viral load for the deterministic and stochastic models. Although the average length of the eclipse phase is the same in each of the models, as the number of latent stages increases, the numerical results show that the time to viral peak and the peak viral load increase.

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.

Intermittent treatment of severe influenza

Severe, long-lasting influenza infections are often caused by new strains of the virus. The long duration of these infections leads to an increased opportunity for the emergence of drug resistant mutants. This is particularly problematic since for new strains there is often no vaccine, so drug treatment is the first line of defense. One strategy for trying to minimize drug resistance is to apply drugs periodically. During treatment phases the wild-type virus decreases, but resistant virus might increase; when there is no treatment, wild-type virus will hopefully out-compete the resistant virus, driving down the number of resistant virus. A stochastic model of severe influenza is combined with a model of drug resistance to simulate long-lasting infections and intermittent treatment with two types of antivirals: neuraminidase inhibitors, which block release of virions; and adamantanes, which block replication of virions. Each drug's ability to reduce emergence of drug resistant mutants is investigated. We find that cell regeneration is required for successful implementation of intermittent treatment and that the optimal cycling parameters change with regeneration rate.