Dynamics of influenza virus infection and pathology

Mammalian adaptation risk in HPAI H5N8: a comprehensive model bridging experimental data with mathematical insights

Understanding the mammalian pathogenesis and interspecies transmission of HPAI H5N8 virus hinges on mapping its adaptive markers. We used deep sequencing to track these markers over five passages in murine lung tissue. Subsequently, we evaluated the growth, selection, and RNA load of eight recombinant viruses with mammalian adaptive markers. By leveraging an integrated non-linear regression model, we quantitatively determined the influence of these markers on growth, adaptation, and RNA expression in mammalian hosts. Furthermore, our findings revealed that the interplay of these markers can lead to synergistic, additive, or antagonistic effects when combined. The elucidation distance method then transformed these results into distinct values, facilitating the derivation of a risk score for each marker. In vivo tests affirmed the accuracy of scores. As more mutations were incorporated, the overall risk score of virus heightened, and the optimal interplay between markers became essential for risk augmentation. Our study provides a robust model to assess risk from adaptive markers of HPAI H5N8, guiding strategies against future influenza threats.

Infection dynamics of subtype H9N2 low pathogenic avian influenza a virus in turkeys

While mammals can be infected by influenza A virus either sporadically or with well adapted lineages, aquatic birds are the natural reservoir of the pathogen. So far most of the knowledge on influenza virus dynamics was however gained on mammalian models. In this study, we infected turkeys using a low pathogenic avian influenza virus and determined the infection dynamics with a target-cell limited model. Results showed that turkeys had a different set of infection characteristics, compared with humans and ponies. The viral clearance rates were similar between turkeys and ponies but higher than that in humans. The cell death rates and cell to cell transmission rates were similar between turkeys and humans but higher than those in ponies. Overall, this study indicated the variations of within-host dynamics of influenza infection in avian, humans, and other mammalian systems.

Modeling the CD8＋ T cell immune response to influenza infection in adult and aged mice

The CD8＋ T cell response is the main determinant of viral clearance during influenza infection. However, influenza viral dynamics and the respective immune responses are affected by the host's age. To investigate age-related differences in the CD8＋ T cell immune response dynamics, we propose an 16 ordinary differential equation models of existing experimental data. These data consist of viral titer and CD8＋ T cell counts collected periodically over a period of 19 days from adult and aged mice infected with influenza A/Puerto Rico/8/34 (H1N1). We use the corrected Akaike Information Criterion to identify the models which best represent the considered data. Our model selection process indicates differences in mechanisms which reduce the CD8＋ T cell response: linear downregulation is favored for adult mice, while baseline exponential decay is favored for aged mice. Parameter fitting of the top ranked models suggests that the aged population has reduced CD8＋ T cell proliferation compared to the adult population. More experimental work is needed to determine the specific immunological features through which age might cause these differences. A better understanding of the immunological mechanisms by which aging leads to discrepant CD8＋ T cell dynamics may inform future treatment strategies.

Mathematical Modeling Suggests That Monocyte Activity May Drive Sex Disparities during Influenza Infection

In humans, females of reproductive age often experience a more severe disease during influenza A virus infection, which may be due to differences in their innate immune response. Sex-specific outcomes to influenza infection have been recapitulated in mice, enabling researchers to study viral and immune dynamics in vivo in order to identify immune mechanisms that are differently regulated between the sexes. This study is based on the hypothesis that sex-specific outcomes emerge due to differences in the rates/speeds that select immune components respond. Using publicly available sex-specific murine data, we utilized dynamic mathematical models of the innate immune response to identify candidate mechanisms that may lead to increased disease severity in female mice. We implemented a large computational screen using the Bayesian information criterion (BIC), wherein the goodness of fit of the competing model scenarios is balanced against complexity (i.e., the number of parameters). Our results suggest that having sex-specific rates for proinflammatory monocyte induction by interferon and monocyte inhibition of virus replication provides the simplest (lowest BIC) explanation for the difference observed in the male and female immune responses. Markov-chain Monte Carlo (MCMC) analysis and global sensitivity analysis of the top performing scenario were performed to provide rigorous estimates of the sex-specific parameter distributions and to provide insight into which parameters most affect innate immune responses. Simulations using the top-performing model suggest that monocyte activity could be a key target to reduce influenza disease severity in females. Overall, our Bayesian statistical and dynamic modeling approach suggests that monocyte activity and induction parameters are sex-specific and may explain sex-differences in influenza disease immune dynamics.

Modeling the emergence of viral resistance for SARS-CoV-2 during treatment with an anti-spike monoclonal antibody

To mitigate the loss of lives during the COVID-19 pandemic, emergency use authorization was given to several anti-SARS-CoV-2 monoclonal antibody (mAb) therapies for the treatment of mild-to-moderate COVID-19 in patients with a high risk of progressing to severe disease. Monoclonal antibodies used to treat SARS-CoV-2 target the spike protein of the virus and block its ability to enter and infect target cells. Monoclonal antibody therapy can thus accelerate the decline in viral load and lower hospitalization rates among high-risk patients with variants susceptible to mAb therapy. However, viral resistance has been observed, in some cases leading to a transient viral rebound that can be as large as 3-4 orders of magnitude. As mAbs represent a proven treatment choice for SARS-CoV-2 and other viral infections, evaluation of treatment-emergent mAb resistance can help uncover underlying pathobiology of SARS-CoV-2 infection and may also help in the development of the next generation of mAb therapies. Although resistance can be expected, the large rebounds observed are much more difficult to explain. We hypothesize replenishment of target cells is necessary to generate the high transient viral rebound. Thus, we formulated two models with different mechanisms for target cell replenishment (homeostatic proliferation and return from an innate immune response antiviral state) and fit them to data from persons with SARS-CoV-2 treated with a mAb. We showed that both models can explain the emergence of resistant virus associated with high transient viral rebounds. We found that variations in the target cell supply rate and adaptive immunity parameters have a strong impact on the magnitude or observability of the viral rebound associated with the emergence of resistant virus. Both variations in target cell supply rate and adaptive immunity parameters may explain why only some individuals develop observable transient resistant viral rebound. Our study highlights the conditions that can lead to resistance and subsequent viral rebound in mAb treatments during acute infection.

Mathematical Modeling of the Lethal Synergism of Coinfecting Pathogens in Respiratory Viral Infections: A Review

Influenza A virus (IAV) infections represent a substantial global health challenge and are often accompanied by coinfections involving secondary viruses or bacteria, resulting in increased morbidity and mortality. The clinical impact of coinfections remains poorly understood, with conflicting findings regarding fatality. Isolating the impact of each pathogen and mechanisms of pathogen synergy during coinfections is challenging and further complicated by host and pathogen variability and experimental conditions. Factors such as cytokine dysregulation, immune cell function alterations, mucociliary dysfunction, and changes to the respiratory tract epithelium have been identified as contributors to increased lethality. The relative significance of these factors depends on variables such as pathogen types, infection timing, sequence, and inoculum size. Mathematical biological modeling can play a pivotal role in shedding light on the mechanisms of coinfections. Mathematical modeling enables the quantification of aspects of the intra-host immune response that are difficult to assess experimentally. In this narrative review, we highlight important mechanisms of IAV coinfection with bacterial and viral pathogens and survey mathematical models of coinfection and the insights gained from them. We discuss current challenges and limitations facing coinfection modeling, as well as current trends and future directions toward a complete understanding of coinfection using mathematical modeling and computer simulation.

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.

Patch formation driven by stochastic effects of interaction between viruses and defective interfering particles

Defective interfering particles (DIPs) are virus-like particles that occur naturally during virus infections. These particles are defective, lacking essential genetic materials for replication, but they can interact with the wild-type virus and potentially be used as therapeutic agents. However, the effect of DIPs on infection spread is still unclear due to complicated stochastic effects and nonlinear spatial dynamics. In this work, we develop a model with a new hybrid method to study the spatial-temporal dynamics of viruses and DIPs co-infections within hosts. We present two different scenarios of virus production and compare the results from deterministic and stochastic models to demonstrate how the stochastic effect is involved in the spatial dynamics of virus transmission. We compare the spread features of the virus in simulations and experiments, including the formation and the speed of virus spread and the emergence of stochastic patchy patterns of virus distribution. Our simulations simultaneously capture observed spatial spread features in the experimental data, including the spread rate of the virus and its patchiness. The results demonstrate that DIPs can slow down the growth of virus particles and make the spread of the virus more patchy.

The role of Type I interferons in the pathogenesis of foot-and-mouth disease virus in cattle: A mathematical modelling analysis

Type I interferons (IFN) are the first line of immune response against infection. In this study, we explore the interaction between Type I IFN and foot-and-mouth disease virus (FMDV), focusing on the effect of this interaction on epithelial cell death. While several mathematical models have explored the interaction between interferon and viruses at a systemic level, with most of the work undertaken on influenza and hepatitis C, these cannot investigate why a virus such as FMDV causes extensive cell death in some epithelial tissues leading to the development of lesions, while other infected epithelial tissues exhibit negligible cell death. Our study shows how a model that includes epithelial tissue structure can explain the development of lesions in some tissues and their absence in others. Furthermore, we show how the site of viral entry in an epithelial tissue, the viral replication rate, IFN production, suppression of viral replication by IFN and IFN release by live cells, all have a major impact on results.

Immune response in influenza virus infection and modulation of immune injury by viral neuraminidase

Influenza A viruses cause severe respiratory illnesses in humans and animals. Overreaction of the innate immune response to influenza virus infection results in hypercytokinemia, which is responsible for mortality and morbidity. The influenza A virus surface glycoprotein neuraminidase (NA) plays a vital role in viral attachment, entry, and virion release from infected cells. NA acts as a sialidase, which cleaves sialic acids from cell surface proteins and carbohydrate side chains on nascent virions. Here, we review progress in understanding the role of NA in modulating host immune response to influenza virus infection. We also discuss recent exciting findings targeting NA protein to interrupt influenza-induced immune injury.

A target-cell limited model can reproduce influenza infection dynamics in hosts with differing immune responses

We consider a hierarchy of ordinary differential equation models that describe the within-host viral kinetics of influenza infections: the IR model explicitly accounts for an immune response to the virus, while the simpler, target-cell limited TEIV and TV models do not. We show that when the IR model is fitted to pooled experimental murine data of the viral load, fraction of dead cells, and immune response levels, its parameters values can be determined. However, if, as is common, only viral load data are available, we can estimate parameters of the TEIV and TV models but not the IR model. These results are substantiated by a structural and practical identifiability analysis. We then use the IR model to generate synthetic data representing infections in hosts whose immune responses differ. We fit the TV model to these synthetic datasets and show that it can reproduce the characteristic exponential increase and decay of viral load generated by the IR model. Furthermore, the values of the fitted parameters of the TV model can be mapped from the immune response parameters in the IR model. We conclude that, if only viral load data are available, a simple target-cell limited model can reproduce influenza infection dynamics and distinguish between hosts with differing immune responses.

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.

Mechanistic modeling of viral particle production

Viral systems such as wild-type viruses, viral vectors, and virus-like particles are essential components of modern biotechnology and medicine. Despite their importance, the commercial-scale production of viral systems remains highly inefficient for multiple reasons. Computational strategies are a promising avenue for improving process development, optimization, and control, but require a mathematical description of the system. This article reviews mechanistic modeling strategies for the production of viral particles, both at the cellular and bioreactor scales. In many cases, techniques and models from adjacent fields such as epidemiology and wild-type viral infection kinetics can be adapted to construct a suitable process model. These process models can then be employed for various purposes such as in-silico testing of novel process operating strategies and/or advanced process control.

Modelling of the Innate and Adaptive Immune Response to SARS Viral Infection, Cytokine Storm and Vaccination

In this work, we develop mathematical models of the immune response to respiratory viral infection, taking into account some particular properties of the SARS-CoV infections, cytokine storm and vaccination. Each model consists of a system of ordinary differential equations that describe the interactions of the virus, epithelial cells, immune cells, cytokines, and antibodies. Conventional analysis of the existence and stability of stationary points is completed by numerical simulations in order to study the dynamics of solutions. The behavior of the solutions is characterized by large peaks of virus concentration specific to acute respiratory viral infections. At the first stage, we study the innate immune response based on the protective properties of interferon secreted by virus-infected cells. Viral infection down-regulates interferon production. This competition can lead to the bistability of the system with different regimes of infection progression with high or low intensity. After that, we introduce the adaptive immune response with antigen-specific T- and B-lymphocytes. The resulting model shows how the incubation period and the maximal viral load depend on the initial viral load and the parameters of the immune response. In particular, an increase in the initial viral load leads to a shorter incubation period and higher maximal viral load. The model shows that a deficient production of antibodies leads to an increase in the incubation period and even higher maximum viral loads. In order to study the emergence and dynamics of cytokine storm, we consider proinflammatory cytokines produced by cells of the innate immune response. Depending on the parameters of the model, the system can remain in the normal inflammatory state specific for viral infections or, due to positive feedback between inflammation and immune cells, pass to cytokine storm characterized by the excessive production of proinflammatory cytokines. Finally, we study the production of antibodies due to vaccination. We determine the dose-response dependence and the optimal interval of vaccine dose. Assumptions of the model and obtained results correspond to the experimental and clinical data.

Global dynamics of IAV/SARS-CoV-2 coinfection model with eclipse phase and antibody immunity

Coronavirus disease 2019 (COVID-19) and influenza are two respiratory infectious diseases of high importance widely studied around the world. COVID-19 is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), while influenza is caused by one of the influenza viruses, A, B, C, and D. Influenza A virus (IAV) can infect a wide range of species. Studies have reported several cases of respiratory virus coinfection in hospitalized patients. IAV mimics the SARS-CoV-2 with respect to the seasonal occurrence, transmission routes, clinical manifestations and related immune responses. The present paper aimed to develop and investigate a mathematical model to study the within-host dynamics of IAV/SARS-CoV-2 coinfection with the eclipse (or latent) phase. The eclipse phase is the period of time that elapses between the viral entry into the target cell and the release of virions produced by that newly infected cell. The role of the immune system in controlling and clearing the coinfection is modeled. The model simulates the interaction between nine compartments, uninfected epithelial cells, latent/active SARS-CoV-2-infected cells, latent/active IAV-infected cells, free SARS-CoV-2 particles, free IAV particles, SARS-CoV-2-specific antibodies and IAV-specific antibodies. The regrowth and death of the uninfected epithelial cells are considered. We study the basic qualitative properties of the model, calculate all equilibria, and prove the global stability of all equilibria. The global stability of equilibria is established using the Lyapunov method. The theoretical findings are demonstrated via numerical simulations. The importance of considering the antibody immunity in the coinfection dynamics model is discussed. It is found that without modeling the antibody immunity, the case of IAV and SARS-CoV-2 coexistence will not occur. Further, we discuss the effect of IAV infection on the dynamics of SARS-CoV-2 single infection and vice versa.

Characterizing viral within-host diversity in fast and non-equilibrium demo-genetic dynamics

High-throughput sequencing has opened the route for a deep assessment of within-host genetic diversity that can be used, e.g., to characterize microbial communities and to infer transmission links in infectious disease outbreaks. The performance of such characterizations and inferences cannot be analytically assessed in general and are often grounded on computer-intensive evaluations. Then, being able to simulate within-host genetic diversity across time under various demo-genetic assumptions is paramount to assess the performance of the approaches of interest. In this context, we built an original model that can be simulated to investigate the temporal evolution of genotypes and their frequencies under various demo-genetic assumptions. The model describes the growth and the mutation of genotypes at the nucleotide resolution conditional on an overall within-host viral kinetics, and can be tuned to generate fast non-equilibrium demo-genetic dynamics. We ran simulations of this model and computed classic diversity indices to characterize the temporal variation of within-host genetic diversity (from high-throughput amplicon sequences) of virus populations under three demographic kinetic models of viral infection. Our results highlight how demographic (viral load) and genetic (mutation, selection, or drift) factors drive variations in within-host diversity during the course of an infection. In particular, we observed a non-monotonic relationship between pathogen population size and genetic diversity, and a reduction of the impact of mutation on diversity when a non-specific host immune response is activated. The large variation in the diversity patterns generated in our simulations suggests that the underlying model provides a flexible basis to produce very diverse demo-genetic scenarios and test, for instance, methods for the inference of transmission links during outbreaks.

Compositional modelling of immune response and virus transmission dynamics

Transmission models for infectious diseases are typically formulated in terms of dynamics between individuals or groups with processes such as disease progression or recovery for each individual captured phenomenologically, without reference to underlying biological processes. Furthermore, the construction of these models is often monolithic: they do not allow one to readily modify the processes involved or include the new ones, or to combine models at different scales. We show how to construct a simple model of immune response to a respiratory virus and a model of transmission using an easily modifiable set of rules allowing further refining and merging the two models together. The immune response model reproduces the expected response curve of PCR testing for COVID-19 and implies a long-tailed distribution of infectiousness reflective of individual heterogeneity. This immune response model, when combined with a transmission model, reproduces the previously reported shift in the population distribution of viral loads along an epidemic trajectory. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Calibration and Validation of a Mechanistic COVID-19 Model for Translational Quantitative Systems Pharmacology - A Proof-of-Concept Model Development for Remdesivir

With the ongoing global pandemic of coronavirus disease 2019 (COVID‐19), there is an urgent need to accelerate the traditional drug development process. Many studies identified potential COVID‐19 therapies based on promising nonclinical data. However, the poor translatability from nonclinical to clinical settings has led to failures of many of these drug candidates in the clinical phase. In this study, we propose a mechanism‐based, quantitative framework to translate nonclinical findings to clinical outcome. Adopting a modularized approach, this framework includes an in silico disease model for COVID‐19 (virus infection and human immune responses) and a pharmacological component for COVID‐19 therapies. The disease model was able to reproduce important longitudinal clinical data for patients with mild and severe COVID‐19, including viral titer, key immunological cytokines, antibody responses, and time courses of lymphopenia. Using remdesivir as a proof‐of‐concept example of model development for the pharmacological component, we developed a pharmacological model that describes the conversion of intravenously administered remdesivir as a prodrug to its active metabolite nucleoside triphosphate through intracellular metabolism and connected it to the COVID‐19 disease model. After being calibrated with the placebo arm data, our model was independently and quantitatively able to predict the primary endpoint (time to recovery) of the remdesivir clinical study, Adaptive Covid‐19 Clinical Trial (ACTT). Our work demonstrates the possibility of quantitatively predicting clinical outcome based on nonclinical data and mechanistic understanding of the disease and provides a modularized framework to aid in candidate drug selection and clinical trial design for COVID‐19 therapeutics.

Which 'imperfect vaccines' encourage the evolution of higher virulence?

Background and objectives

Theory suggests that some types of vaccines against infectious pathogens may lead to the evolution of variants that cause increased harm, particularly when they infect unvaccinated individuals. This theory was supported by the observation that the use of an imperfect vaccine to control Marek's disease virus in chickens resulted in the virus evolving to be more lethal to unvaccinated birds. This raises the concern that the use of some other vaccines may lead to similar pernicious outcomes. We examine that theory with a focus on considering the regimes in which such outcomes are expected.

Methodology

We evaluate the plausibility of assumptions in the original theory. The previous theory rested heavily on a particular form of transmission-mortality-recovery trade-off and invoked other assumptions about the pathways of evolution. We review alternatives to mortality in limiting transmission and consider evolutionary pathways that were omitted in the original theory.

Results

The regime where the pernicious evolutionary outcome occurs is narrowed by our analysis but remains possible in various scenarios. We propose a more nuanced consideration of alternative models for the within-host dynamics of infections and for factors that limit virulence. Our analysis suggests imperfect vaccines against many pathogens will not lead to the evolution of pathogens with increased virulence in unvaccinated individuals.

Conclusions and implications

Evolution of greater pathogen mortality driven by vaccination remains difficult to predict, but the scope for such outcomes appears limited. Incorporation of mechanistic details into the framework, especially regarding immunity, may be requisite for prediction accuracy.

Lay Summary

A virus of chickens appears to have evolved high mortality in response to a vaccine that merely prevented disease symptoms. Theory has predicted this type of evolution in response to a variety of vaccines and other interventions such as drug treatment. Under what circumstances is this pernicious result likely to occur? Analysis of the theory in light of recent changes in our understanding of viral biology raises doubts that medicine-driven, pernicious evolution is likely to be common. But we are far from a mechanistic understanding of the interaction between pathogen and host that can predict when vaccines and other medical interventions will lead to the unwanted evolution of more virulent pathogens. So, while the regime where a pernicious result obtains may be limited, caution remains warranted in designing many types of interventions.

Recent Advances in Surface Plasmon Resonance Sensors for Sensitive Optical Detection of Pathogens

The advancement of science and technology has led to the recent development of highly sensitive pathogen biosensing techniques. The effective treatment of pathogen infections requires sensing technologies to not only be sensitive but also render results in real-time. This review thus summarises the recent advances in optical surface plasmon resonance (SPR) sensor technology, which possesses the aforementioned advantages. Specifically, this technology allows for the detection of specific pathogens by applying nano-sized materials. This review focuses on various nanomaterials that are used to ensure the performance and high selectivity of SPR sensors. This review will undoubtedly accelerate the development of optical biosensing technology, thus allowing for real-time diagnosis and the timely delivery of appropriate treatments as well as preventing the spread of highly contagious pathogens.

SARS-coronavirus-2 infections: biological instabilities characterized by order parameters

A four-variable virus dynamics TIIV model was considered that involves infected cells in an eclipse phase. The state space description of the model was transferred into an amplitude space description which is the appropriate general, nonlinear physics framework to describe instabilities. In this context, the unstable eigenvector or order parameter of the model was determined. Subsequently, a model-based analysis of viral load data from eight symptomatic COVID-19 patients was conducted. For all patients, it was found that the initial SARS-CoV-2 infection evolved along the respective patient-specific order parameter, as expected by theoretical considerations. The order parameter amplitude that described the initial virus multiplication showed doubling times between 30 minutes and 3 hours. Peak viral loads of patients were linearly related to the amplitudes of the patient order parameters. Finally, it was found that the patient order parameters determined qualitatively and quantitatively the relationships between the increases in virus-producing infected cells and infected cells in the eclipse phase. Overall, the study echoes the 40 years old suggestion by Mackey and Glass to consider diseases as instabilities.

Equine Influenza

Horses are the third major mammalian species, along with humans and swine, long known to be subject to acute upper respiratory disease from influenza A virus infection. The viruses responsible are subtype H7N7, which is believed extinct, and H3N8, which circulates worldwide. The equine influenza lineages are clearly divergent from avian influenza lineages of the same subtypes. Their genetic evolution and potential for interspecies transmission, as well as clinical features and epidemiology, are discussed. Equine influenza is spread internationally and vaccination is central to control efforts. The current mechanism of international surveillance and virus strain recommendations for vaccines is described.

In vivo kinetics of SARS-CoV-2 infection and its relationship with a person's infectiousness

The within-host viral kinetics of SARS-CoV-2 infection and how they relate to a person's infectiousness are not well understood. This limits our ability to quantify the impact of interventions on viral transmission. Here, we develop viral dynamic models of SARS-CoV-2 infection and fit them to data to estimate key within-host parameters such as the infected cell half-life and the within-host reproductive number. We then develop a model linking viral load (VL) to infectiousness and show a person's infectiousness increases sublinearly with VL and that the logarithm of the VL in the upper respiratory tract is a better surrogate of infectiousness than the VL itself. Using data on VL and the predicted infectiousness, we further incorporated data on antigen and RT-PCR tests and compared their usefulness in detecting infection and preventing transmission. We found that RT-PCR tests perform better than antigen tests assuming equal testing frequency; however, more frequent antigen testing may perform equally well with RT-PCR tests at a lower cost but with many more false-negative tests. Overall, our models provide a quantitative framework for inferring the impact of therapeutics and vaccines that lower VL on the infectiousness of individuals and for evaluating rapid testing strategies.

Multicellular spatial model of RNA virus replication and interferon responses reveals factors controlling plaque growth dynamics

Respiratory viruses present major public health challenges, as evidenced by the 1918 Spanish Flu, the 1957 H2N2, 1968 H3N2, and 2009 H1N1 influenza pandemics, and the ongoing severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic. Severe RNA virus respiratory infections often correlate with high viral load and excessive inflammation. Understanding the dynamics of the innate immune response and its manifestations at the cell and tissue levels is vital to understanding the mechanisms of immunopathology and to developing strain-independent treatments. Here, we present a novel spatialized multicellular computational model of RNA virus infection and the type-I interferon-mediated antiviral response that it induces within lung epithelial cells. The model is built using the CompuCell3D multicellular simulation environment and is parameterized using data from influenza virus-infected cell cultures. Consistent with experimental observations, it exhibits either linear radial growth of viral plaques or arrested plaque growth depending on the local concentration of type I interferons. The model suggests that modifying the activity of signaling molecules in the JAK/STAT pathway or altering the ratio of the diffusion lengths of interferon and virus in the cell culture could lead to plaque growth arrest. The dependence of plaque growth arrest on diffusion lengths highlights the importance of developing validated spatial models of cytokine signaling and the need for in vitro measurement of these diffusion coefficients. Sensitivity analyses under conditions leading to continuous or arrested plaque growth found that plaque growth is more sensitive to variations of most parameters and more likely to have identifiable model parameters when conditions lead to plaque arrest. This result suggests that cytokine assay measurements may be most informative under conditions leading to arrested plaque growth. The model is easy to extend to include SARS-CoV-2-specific mechanisms or to use as a component in models linking epithelial cell signaling to systemic immune models.

Quantifying dose-, strain-, and tissue-specific kinetics of parainfluenza virus infection

Human parainfluenza viruses (HPIVs) are a leading cause of acute respiratory infection hospitalization in children, yet little is known about how dose, strain, tissue tropism, and individual heterogeneity affects the processes driving growth and clearance kinetics. Longitudinal measurements are possible by using reporter Sendai viruses, the murine counterpart of HPIV 1, that express luciferase, where the insertion location yields a wild-type (rSeV-luc(M-F*)) or attenuated (rSeV-luc(P-M)) phenotype. Bioluminescence from individual animals suggests that there is a rapid increase in expression followed by a peak, biphasic clearance, and resolution. However, these kinetics vary between individuals and with dose, strain, and whether the infection was initiated in the upper and/or lower respiratory tract. To quantify the differences, we translated the bioluminescence measurements from the nasopharynx, trachea, and lung into viral loads and used a mathematical model together a nonlinear mixed effects approach to define the mechanisms distinguishing each scenario. The results confirmed a higher rate of virus production with the rSeV-luc(M-F*) virus compared to its attenuated counterpart, and suggested that low doses result in disproportionately fewer infected cells. The analyses indicated faster infectivity and infected cell clearance rates in the lung and that higher viral doses, and concomitantly higher infected cell numbers, resulted in more rapid clearance. This parameter was also highly variable amongst individuals, which was particularly evident during infection in the lung. These critical differences provide important insight into distinct HPIV dynamics, and show how bioluminescence data can be combined with quantitative analyses to dissect host-, virus-, and dose-dependent effects.

Human parainfluenza viruses (HPIVs) cause acute respiratory infections and can lead to the hospitalization of children. HPIV infection severity may vary due to dose, strain, patient, and whether the infection initiates within the upper or lower respiratory tract. There is a need to determine how the rates of virus spread and clearance change in different infection scenarios in order to better understand varying clinical manifestations. The significance of our research is in identifying the dominant mechanisms driving strain-, dose-, and tissue-specific HPIV infection kinetics, and in pairing bioluminescence data with quantitative analyses to determine how the same virus can yield patient-specific outcomes. This work enhances our understanding of HPIV infection and broadens our knowledge viral dynamics in the upper and lower respiratory tracts.

Decoding the dynamics of multilayered stochastic antiviral IFN-I responses

Type I Interferon (IFN-I) responses were first recognized for their role in antiviral immunity, but it is now widely appreciated that IFN-Is have many immunomodulatory functions, influencing antitumor responses, autoimmune manifestations, and antimicrobial defenses. Given these pivotal roles, it may be surprising that multilayered stochastic events create highly heterogeneous, but tightly regulated, all-or-nothing cellular decisions. Recently, mathematical models have provided crucial insights into the stochastic nature of antiviral IFN-I responses, which we critically evaluate in this review. In this context, we emphasize the need for innovative single-cell technologies combined with mathematical models to further reveal, understand, and predict the complexity of the IFN-I system in physiological and pathological conditions that may be relevant to a plethora of diseases.

In vivo kinetics of SARS-CoV-2 infection and its relationship with a person's infectiousness

The within-host viral kinetics of SARS-CoV-2 infection and how they relate to a person's infectiousness are not well understood. This limits our ability to quantify the impact of interventions on viral transmission. Here, we develop data-driven viral dynamic models of SARS-CoV-2 infection and estimate key within-host parameters such as the infected cell half-life and the within-host reproductive number. We then develop a model linking VL to infectiousness, showing that a person's infectiousness increases sub-linearly with VL. We show that the logarithm of the VL in the upper respiratory tract (URT) is a better surrogate of infectiousness than the VL itself. Using data on VL and the predicted infectiousness, we further incorporated data on antigen and reverse transcription polymerase chain reaction (RT-PCR) tests and compared their usefulness in detecting infection and preventing transmission. We found that RT-PCR tests perform better than antigen tests assuming equal testing frequency; however, more frequent antigen testing may perform equally well with RT-PCR tests at a lower cost, but with many more false-negative tests. Overall, our models provide a quantitative framework for inferring the impact of therapeutics and vaccines that lower VL on the infectiousness of individuals and for evaluating rapid testing strategies.

SIGNIFICANCE

Quantifying the kinetics of SARS-CoV-2 infection and individual infectiousness is key to quantitatively understanding SARS-CoV-2 transmission and evaluating intervention strategies. Here we developed data-driven within-host models of SARS-CoV-2 infection and by fitting them to clinical data we estimated key within-host viral dynamic parameters. We also developed a mechanistic model for viral transmission and show that the logarithm of the viral load in the upper respiratory tract serves an appropriate surrogate for a person's infectiousness. Using data on how viral load changes during infection, we further evaluated the effectiveness of PCR and antigen-based testing strategies for averting transmission and identifying infected individuals.

Equine influenza: a comprehensive review from etiology to treatment

Influenza is an extremely contagious respiratory disease, which predominantly affects the upper respiratory tract. There are four types of influenza virus, and pigs and chickens are considered two key reservoirs of this virus. Equine influenza (EI) virus was first identified in horses in 1956, in Prague. The influenza A viruses responsible for EI are H7N7 and H3N8. Outbreaks of EI are characterized by their visible and rapid spread, and it has been possible to isolate and characterize H3N8 outbreaks in several countries. The clinical diagnosis of this disease is based on the clinical signs presented by the infected animals, which can be confirmed by performing complementary diagnostic tests. In the diagnosis of EI, in the field, rapid antigen detection tests can be used for a first approach. Treatment is based on the management of the disease and rest for the animal. Regarding the prognosis, it will depend on several factors, such as the animal's vaccination status. One of the important points in this disease is its prevention, which can be done through vaccination. In addition to decreasing the severity of clinical signs and morbidity during outbreaks, vaccination ensures immunity for the animals, reducing the economic impact of this disease.

Compartmental Model Suggests Importance of Innate Immune Response to COVID-19 Infection in Rhesus Macaques

The pandemic outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has quickly spread worldwide, creating a serious health crisis. The virus is primarily associated with flu-like symptoms but can also lead to severe pathologies and death. We here present an ordinary differential equation model of the intrahost immune response to SARS-CoV-2 infection, fitted to experimental data gleaned from rhesus macaques. The model is calibrated to data from a nonlethal infection, but the model can replicate behavior from various lethal scenarios as well. We evaluate the sensitivity of the model to biologically relevant parameters governing the strength and efficacy of the immune response. We also simulate the effect of both anti-inflammatory and antiviral drugs on the host immune response and demonstrate the ability of the model to lessen the severity of a formerly lethal infection with the addition of the appropriately calibrated drug. Our model emphasizes the importance of tight control of the innate immune response for host survival and viral clearance.

Within-host model of respiratory virus shedding and antibody response to H9N2 avian influenza virus vaccination and infection in chickens

Avian influenza virus (AIV) H9N2 subtype is an infectious pathogen that can affect both the respiratory and gastrointestinal systems in chickens and continues to have an important economic impact on the poultry industry. While the host innate immune response provides control of virus replication in early infection, the adaptive immune response aids to clear infections and prevent future invasion. Modelling virus-innate immune response pathways can improve our understanding of early infection dynamics and help to guide our understanding of virus shedding dynamics that could lead to reduced transmission between hosts. While some countries use vaccines for the prevention of H9N2 AIV in poultry, the virus continues to be endemic in regions of Eurasia and Africa, indicating a need for improved vaccine efficacy or vaccination strategies. Here we explored how three type-I interferon (IFN) pathways affect respiratory virus shedding patterns in infected chickens using a within-host model. Additionally, prime and boost vaccination strategies for a candidate H9N2 AIV vaccine are assessed for the ability to elicit seroprotective antibody titres. The model demonstrates that inclusion of virus sensitivity to intracellular type-I IFN pathways results in a shedding pattern most consistent with virus titres observed in infected chickens, and the inclusion of a cellular latent period does not improve model fit. Furthermore, early administration of a booster dose two weeks after the initial vaccine is administered results in seroprotective titres for the greatest length of time for both broilers and layers. These results demonstrate that type-I IFN intracellular mechanisms are required in a model of respiratory virus shedding in H9N2 AIV infected chickens, and also highlights the need for improved vaccination strategies for laying hens.

Autocrine and paracrine interferon signalling as 'ring vaccination' and 'contact tracing' strategies to suppress virus infection in a host

The innate immune response, particularly the interferon response, represents a first line of defence against viral infections. The interferon molecules produced from infected cells act through autocrine and paracrine signalling to turn host cells into an antiviral state. Although the molecular mechanisms of IFN signalling have been well characterized, how the interferon response collectively contribute to the regulation of host cells to stop or suppress viral infection during early infection remain unclear. Here, we use mathematical models to delineate the roles of the autocrine and the paracrine signalling, and show that their impacts on viral spread are dependent on how infection proceeds. In particular, we found that when infection is well-mixed, the paracrine signalling is not as effective; by contrast, when infection spreads in a spatial manner, a likely scenario during initial infection in tissue, the paracrine signalling can impede the spread of infection by decreasing the number of susceptible cells close to the site of infection. Furthermore, we argue that the interferon response can be seen as a parallel to population-level epidemic prevention strategies such as ‘contact tracing’ or ‘ring vaccination’. Thus, our results here may have implications for the outbreak control at the population scale more broadly.

Structure and Hierarchy of SARS-CoV-2 Infection Dynamics Models Revealed by Reaction Network Analysis

This work provides a mathematical technique for analyzing and comparing infection dynamics models with respect to their potential long-term behavior, resulting in a hierarchy integrating all models. We apply our technique to coupled ordinary and partial differential equation models of SARS-CoV-2 infection dynamics operating on different scales, that is, within a single organism and between several hosts. The structure of a model is assessed by the theory of chemical organizations, not requiring quantitative kinetic information. We present the Hasse diagrams of organizations for the twelve virus models analyzed within this study. For comparing models, each organization is characterized by the types of species it contains. For this, each species is mapped to one out of four types, representing uninfected, infected, immune system, and bacterial species, respectively. Subsequently, we can integrate these results with those of our former work on Influenza-A virus resulting in a single joint hierarchy of 24 models. It appears that the SARS-CoV-2 models are simpler with respect to their long term behavior and thus display a simpler hierarchy with little dependencies compared to the Influenza-A models. Our results can support further development towards more complex SARS-CoV-2 models targeting the higher levels of the hierarchy.

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.

An approximate solution of the interferon-dependent viral kinetics model of influenza

The analysis of viral kinetics models is mostly achieved by numerical methods. We present an approach via a Magnus expansion that allows us to give an approximate solution to the interferon-dependent viral infection model of influenza which is compared with numerical results. The time of peak viral load is calculated from the approximation and stays within 10% in the studied range of interferon (IFN) efficacy ϵ ∈ [0, 1000]. We utilize our solution to interpret the effect of varying IFN efficacy, suggesting a competition between virions and interferon that can cause an additional peak in the usually exponential increase in the viral load.

A within-host mathematical model of H9N2 avian influenza infection and type-I interferon response pathways in chickens

Chickens infected with avian influenza virus (AIV) transmit the virus via respiratory and cloacal shedding. While previous mathematical models have shown that the innate immune response is necessary for the early suppression of virus production in infected respiratory cells, the different pathways by which the innate immune response can affect cloacal viral shedding have not been studied in chickens. The present study aims to evaluate the sensitivity of H9N2 low pathogenic AIV shedding in chicken gastrointestinal cells to different type-I interferon (IFN) response pathways, and to determine the impact of a cellular eclipse phase (latent period) on the time to peak virus shedding using a mathematical model describing within host viral kinetics. Our model results demonstrate that a mechanistic model that incorporates 1) the intracellular antiviral effects of type-I IFN on virus production, 2) destruction of infected cells by type-I IFN activated Natural Killer cells, and 3) an eclipse phase is most consistent with experimental cloacal virus shedding data. These results provide a potential mechanistic explanation for the delay to peak cloacal virus shedding observed in experimental studies conducted in chickens, as well as an improved understanding of the primary type-I IFN pathways involved in the control of cloacal virus shedding, which may lead to the development of more targeted vaccine candidates.

Dynamic Perspectives on the Search for a Universal Influenza Vaccine

A universal influenza vaccine (UIV) could considerably alleviate the public health burden of both seasonal and pandemic influenza. Although significant progress has been achieved in clarifying basic immunology and virology relating to UIV, several important questions relating to the dynamics of infection, immunity, and pathogen evolution remain unsolved. In this study, we review these gaps, which span integrative levels, from cellular to global and timescales from molecular events to decades. We argue that they can be best addressed by a tight integration of empirical (laboratory, epidemiological) research and theory and suggest fruitful areas for this synthesis. In particular, quantifying natural and vaccinal limitations on viral transmission are central to this effort.

Modeling Favipiravir Antiviral Efficacy Against Emerging Viruses: From Animal Studies to Clinical Trials

In 2014, our research network was involved in the evaluation of favipiravir, an anti-influenza polymerase inhibitor, against Ebola virus. In this review, we discuss how mathematical modeling was used, first to propose a relevant dosing regimen in humans, and then to optimize its antiviral efficacy in a nonhuman primate (NHP) model. The data collected in NHPs were finally used to develop a model of Ebola pathogenesis integrating the interactions among the virus, the innate and adaptive immune response, and the action of favipiravir. We conclude the review of this work by discussing how these results are of relevance for future human studies in the context of Ebola virus, but also for other emerging viral diseases for which no therapeutics are available.

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.

Varying Inoculum Dose to Assess the Roles of the Immune Response and Target Cell Depletion by the Pathogen in Control of Acute Viral Infections

It is difficult to determine whether an immune response or target cell depletion by the infectious agent is most responsible for the control of acute primary infection. Both mechanisms can explain the basic dynamics of an acute infection-exponential growth of the pathogen followed by control and clearance-and can also be represented by many different differential equation models. Consequently, traditional model comparison techniques using time series data can be ambiguous or inconclusive. We propose that varying the inoculum dose and measuring the subsequent infectious load can rule out target cell depletion by the pathogen as the main control mechanism. Infectious load can be any measure that is proportional to the number of infected cells, such as viraemia. We show that a twofold or greater change in infectious load is unlikely when target cell depletion controls infection, regardless of the model details. Analyzing previously published data from mice infected with influenza, we find the proportion of lung epithelial cells infected was 21-fold greater (95% confidence interval 14-32) in the highest dose group than in the lowest. This provides evidence in favor of an alternative to target cell depletion, such as innate immunity, in controlling influenza infections in this experimental system. Data from other experimental animal models of acute primary infection have a similar pattern.

Model Averaging in Viral Dynamic Models

The paucity of experimental data makes both inference and prediction particularly challenging in viral dynamic models. In the presence of several candidate models, a common strategy is model selection (MS), in which models are fitted to the data but only results obtained with the "best model" are presented. However, this approach ignores model uncertainty, which may lead to inaccurate predictions. When several models provide a good fit to the data, another approach is model averaging (MA) that weights the predictions of each model according to its consistency to the data. Here, we evaluated by simulations in a nonlinear mixed-effect model framework the performances of MS and MA in two realistic cases of acute viral infection, i.e., (1) inference in the presence of poorly identifiable parameters, namely, initial viral inoculum and eclipse phase duration, (2) uncertainty on the mechanisms of action of the immune response. MS was associated in some scenarios with a large rate of false selection. This led to a coverage rate lower than the nominal coverage rate of 0.95 in the majority of cases and below 0.50 in some scenarios. In contrast, MA provided better estimation of parameter uncertainty, with coverage rates ranging from 0.72 to 0.98 and mostly comprised within the nominal coverage rate. Finally, MA provided similar predictions than those obtained with MS. In conclusion, parameter estimates obtained with MS should be taken with caution, especially when several models well describe the data. In this situation, MA has better performances and could be performed to account for model uncertainty.

Accelerated viral dynamics in bat cell lines, with implications for zoonotic emergence

Bats host virulent zoonotic viruses without experiencing disease. A mechanistic understanding of the impact of bats’ virus hosting capacities, including uniquely constitutive immune pathways, on cellular-scale viral dynamics is needed to elucidate zoonotic emergence. We carried out virus infectivity assays on bat cell lines expressing induced and constitutive immune phenotypes, then developed a theoretical model of our in vitro system, which we fit to empirical data. Best fit models recapitulated expected immune phenotypes for representative cell lines, supporting robust antiviral defenses in bat cells that correlated with higher estimates for within-host viral propagation rates. In general, heightened immune responses limit pathogen-induced cellular morbidity, which can facilitate the establishment of rapidly-propagating persistent infections within-host. Rapidly-transmitting viruses that have evolved with bat immune systems will likely cause enhanced virulence following emergence into secondary hosts with immune systems that diverge from those unique to bats.

Bats can carry viruses that are deadly to other mammals without themselves showing serious symptoms. In fact, bats are natural reservoirs for viruses that have some of the highest fatality rates of any viruses that people acquire from wild animals – including rabies, Ebola and the SARS coronavirus.

Bats have a suite of antiviral defenses that keep the amount of virus in check. For example, some bats have an antiviral immune response called the interferon pathway perpetually switched on. In most other mammals, having such a hyper-vigilant immune response would cause harmful inflammation. Bats, however, have adapted anti-inflammatory traits that protect them from such harm, include the loss of certain genes that normally promote inflammation. However, no one has previously explored how these unique antiviral defenses of bats impact the viruses themselves.

Now, Brook et al. have studied this exact question using bat cells grown in the laboratory. The experiments made use of cells from one bat species – the black flying fox – in which the interferon pathway is always on, and another – the Egyptian fruit bat – in which this pathway is only activated during an infection. The bat cells were infected with three different viruses, and then Brook et al. observed how the interferon pathway helped keep the infections in check, before creating a computer model of this response.

The experiments and model helped reveal that the bats’ defenses may have a potential downside for other animals, including humans. In both bat species, the strongest antiviral responses were countered by the virus spreading more quickly from cell to cell. This suggests that bat immune defenses may drive the evolution of faster transmitting viruses, and while bats are well protected from the harmful effects of their own prolific viruses, other creatures like humans are not.

The findings may help to explain why bats are often the source for viruses that are deadly in humans. Learning more about bats' antiviral defenses and how they drive virus evolution may help scientists develop better ways to predict, prevent or limit the spread of viruses from bats to humans. More studies are needed in bats to help these efforts. In the meantime, the experiments highlight the importance of warning people to avoid direct contact with wild bats.

Recombinant vector vaccine evolution

Replicating recombinant vector vaccines consist of a fully competent viral vector backbone engineered to express an antigen from a foreign transgene. From the perspective of viral replication, the transgene is not only dispensable but may even be detrimental. Thus vaccine revertants that delete or inactivate the transgene may evolve to dominate the vaccine virus population both during the process of manufacture of the vaccine as well as during the course of host infection. A particular concern is that this vaccine evolution could reduce its antigenicity—the immunity elicited to the transgene. We use mathematical and computational models to study vaccine evolution and immunity. These models include evolution arising during the process of manufacture, the dynamics of vaccine and revertant growth, plus innate and adaptive immunity elicited during the course of infection. Although the selective basis of vaccine evolution is easy to comprehend, the immunological consequences are not. One complication is that the opportunity for vaccine evolution is limited by the short period of within-host growth before the viral population is cleared. Even less obvious, revertant growth may only weakly interfere with vaccine growth in the host and thus have a limited effect on immunity to vaccine. Overall, we find that within-host vaccine evolution can sometimes compromise vaccine immunity, but only when the extent of evolution during vaccine manufacture is severe, and this evolution can be easily avoided or mitigated.

Recombinant vector vaccines are live replicating viruses that are engineered to carry extra genes derived from a pathogen—and these extra genes produce proteins against which we want to generate immunity. These vaccine genomes may evolve to lose the extra genes during the process of manufacture of the vaccine or during replication within an individual, and there is a concern that this evolution might severely limit the vaccine’s efficacy. The dynamics of this process are studied here with mathematical models. The potential for vaccine evolution within the host is somewhat limited by the short-term growth of the vaccine population before it is suppressed by the immune response. We find that evolution is a problem only when the process of manufacture results in the majority of the vaccine virus being revertant. We show that increasing the vaccine inoculum size or reducing the level of revertant in the vaccine inoculum can largely avoid the loss of immunity arising from evolution.

Within-host infectious disease models accommodating cellular coinfection, with an application to influenza

Within-host models are useful tools for understanding the processes regulating viral load dynamics. While existing models have considered a wide range of within-host processes, at their core these models have shown remarkable structural similarity. Specifically, the structure of these models generally consider target cells to be either uninfected or infected, with the possibility of accommodating further resolution (e.g. cells that are in an eclipse phase). Recent findings, however, indicate that cellular coinfection is the norm rather than the exception for many viral infectious diseases, and that cells with high multiplicity of infection are present over at least some duration of an infection. The reality of these cellular coinfection dynamics is not accommodated in current within-host models although it may be critical for understanding within-host dynamics. This is particularly the case if multiplicity of infection impacts infected cell phenotypes such as their death rate and their viral production rates. Here, we present a new class of within-host disease models that allow for cellular coinfection in a scalable manner by retaining the low-dimensionality that is a desirable feature of many current within-host models. The models we propose adopt the general structure of epidemiological ‘macroparasite’ models that allow hosts to be variably infected by parasites such as nematodes and host phenotypes to flexibly depend on parasite burden. Specifically, our within-host models consider target cells as ‘hosts’ and viral particles as ‘macroparasites’, and allow viral output and infected cell lifespans, among other phenotypes, to depend on a cell’s multiplicity of infection. We show with an application to influenza that these models can be statistically fit to viral load and other within-host data, and demonstrate using model selection approaches that they have the ability to outperform traditional within-host viral dynamic models. Important in vivo quantities such as the mean multiplicity of cellular infection and time-evolving reassortant frequencies can also be quantified in a straightforward manner once these macroparasite models have been parameterized. The within-host model structure we develop here provides a mathematical way forward to address questions related to the roles of cellular coinfection, collective viral interactions, and viral complementation in within-host viral dynamics and evolution.

Structure and Hierarchy of Influenza Virus Models Revealed by Reaction Network Analysis

Influenza A virus is recognized today as one of the most challenging viruses that threatens both human and animal health worldwide. Understanding the control mechanisms of influenza infection and dynamics is crucial and could result in effective future treatment strategies. Many kinetic models based on differential equations have been developed in recent decades to capture viral dynamics within a host. These models differ in their complexity in terms of number of species elements and number of reactions. Here, we present a new approach to understanding the overall structure of twelve influenza A virus infection models and their relationship to each other. To this end, we apply chemical organization theory to obtain a hierarchical decomposition of the models into chemical organizations. The decomposition is based on the model structure (reaction rules) but is independent of kinetic details such as rate constants. We found different types of model structures ranging from two to eight organizations. Furthermore, the model's organizations imply a partial order among models entailing a hierarchy of model, revealing a high model diversity with respect to their long-term behavior. Our methods and results can be helpful in model development and model integration, also beyond the influenza area.

How to prevent viremia rebound? Evidence from a PRRSv data-supported model of immune response

Background

Understanding what determines the between-host variability in infection dynamics is a key issue to better control the infection spread. In particular, pathogen clearance is desirable over rebounds for the health of the infected individual and its contact group. In this context, the Porcine Respiratory and Reproductive Syndrome virus (PRRSv) is of particular interest. Numerous studies have shown that pigs similarly infected with this highly ubiquitous virus elicit diverse response profiles. Whilst some manage to clear the virus within a few weeks, others experience prolonged infection with a rebound. Despite much speculation, the underlying mechanisms responsible for this undesirable rebound phenomenon remain unclear.

Results

We aimed at identifying immune mechanisms that can reproduce and explain the rebound patterns observed in PRRSv infection using a mathematical modelling approach of the within-host dynamics. As diverse mechanisms were found to influence PRRSv infection, we established a model that details the major mechanisms and their regulations at the between-cell scale. We developed an ABC-like optimisation method to fit our model to an extensive set of experimental data, consisting of non-rebounder and rebounder viremia profiles. We compared, between both profiles, the estimated parameter values, the resulting immune dynamics and the efficacies of the underlying immune mechanisms. Exploring the influence of these mechanisms, we showed that rebound was promoted by high apoptosis, high cell infection and low cytolysis by Cytotoxic T Lymphocytes, while increasing neutralisation was very efficient to prevent rebounds.

Conclusions

Our paper provides an original model of the immune response and an appropriate systematic fitting method, whose interest extends beyond PRRS infection. It gives the first mechanistic explanation for emergence of rebounds during PRRSv infection. Moreover, results suggest that vaccines or genetic selection promoting strong neutralising and cytolytic responses, ideally associated with low apoptotic activity and cell permissiveness, would prevent rebound.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0666-7) contains supplementary material, which is available to authorized users.

Mutational load causes stochastic evolutionary outcomes in acute RNA viral infection

Mutational load is known to be of importance for the evolution of RNA viruses, the combination of a high mutation rate and large population size leading to an accumulation of deleterious mutations. However, while the effects of mutational load on global viral populations have been considered, its quantitative effects at the within-host scale of infection are less well understood. We here show that even on the rapid timescale of acute disease, mutational load has an effect on within-host viral adaptation, reducing the effective selection acting upon beneficial variants by ∼10 per cent. Furthermore, mutational load induces considerable stochasticity in the pattern of evolution, causing a more than five-fold uncertainty in the effective fitness of a transmitted beneficial variant. Our work aims to bridge the gap between classic models from population genetic theory and the biology of viral infection. In an advance on some previous models of mutational load, we replace the assumption of a constant variant fitness cost with an experimentally-derived distribution of fitness effects. Expanding previous frameworks for evolutionary simulation, we introduce the Wright-Fisher model with continuous mutation, which describes a continuum of possible modes of replication within a cell. Our results advance our understanding of adaptation in the context of strong selection and a high mutation rate. Despite viral populations having large absolute sizes, critical events in viral adaptation, including antigenic drift and the onset of drug resistance, arise through stochastic evolutionary processes.

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.

Modeling the measles paradox reveals the importance of cellular immunity in regulating viral clearance

Measles virus (MV) is a highly contagious member of the Morbillivirus genus that remains a major cause of childhood mortality worldwide. Although infection induces a strong MV-specific immune response that clears viral load and confers lifelong immunity, transient immunosuppression can also occur, leaving the host vulnerable to colonization from secondary pathogens. This apparent contradiction of viral clearance in the face of immunosuppression underlies what is often referred to as the 'measles paradox', and remains poorly understood. To explore the mechanistic basis underlying the measles paradox, and identify key factors driving viral clearance, we return to a previously published dataset of MV infection in rhesus macaques. These data include virological and immunological information that enable us to fit a mathematical model describing how the virus interacts with the host immune system. In particular, our model incorporates target cell depletion through infection of host immune cells-a hallmark of MV pathology that has been neglected from previous models. We find the model captures the data well, and that both target cell depletion and immune activation are required to explain the overall dynamics. Furthermore, by simulating conditions of increased target cell availability and suppressed cellular immunity, we show that the latter causes greater increases in viral load and delays to MV clearance. Overall, this signals a more dominant role for cellular immunity in resolving acute MV infection. Interestingly, we find contrasting dynamics dominated by target cell depletion when viral fitness is increased. This may have wider implications for animal morbilliviruses, such as canine distemper virus (CDV), that cause fatal target cell depletion in their natural hosts. To our knowledge this work represents the first fully calibrated within-host model of MV dynamics and, more broadly, provides a new platform from which to explore the complex mechanisms underlying Morbillivirus infection.

Causes and Consequences of Spatial Within-Host Viral Spread

The spread of viral pathogens both between and within hosts is inherently a spatial process. While the spatial aspects of viral spread at the epidemiological level have been increasingly well characterized, the spatial aspects of viral spread within infected hosts are still understudied. Here, with a focus on influenza A viruses (IAVs), we first review experimental studies that have shed light on the mechanisms and spatial dynamics of viral spread within hosts. These studies provide strong empirical evidence for highly localized IAV spread within hosts. Since mathematical and computational within-host models have been increasingly used to gain a quantitative understanding of observed viral dynamic patterns, we then review the (relatively few) computational modeling studies that have shed light on possible factors that structure the dynamics of spatial within-host IAV spread. These factors include the dispersal distance of virions, the localization of the immune response, and heterogeneity in host cell phenotypes across the respiratory tract. While informative, we find in these studies a striking absence of theoretical expectations of how spatial dynamics may impact the dynamics of viral populations. To mitigate this, we turn to the extensive ecological and evolutionary literature on range expansions to provide informed theoretical expectations. We find that factors such as the type of density dependence, the frequency of long-distance dispersal, specific life history characteristics, and the extent of spatial heterogeneity are critical factors affecting the speed of population spread and the genetic composition of spatially expanding populations. For each factor that we identified in the theoretical literature, we draw parallels to its analog in viral populations. We end by discussing current knowledge gaps related to the spatial component of within-host IAV spread and the potential for within-host spatial considerations to inform the development of disease control strategies.

Exploring the impact of inoculum dose on host immunity and morbidity to inform model-based vaccine design

Vaccination is an effective method to protect against infectious diseases. An important consideration in any vaccine formulation is the inoculum dose, i.e., amount of antigen or live attenuated pathogen that is used. Higher levels generally lead to better stimulation of the immune response but might cause more severe side effects and allow for less population coverage in the presence of vaccine shortages. Determining the optimal amount of inoculum dose is an important component of rational vaccine design. A combination of mathematical models with experimental data can help determine the impact of the inoculum dose. We illustrate the concept of using data and models to inform inoculum dose determination for vaccines, wby fitting a mathematical model to data from influenza A virus (IAV) infection of mice and human parainfluenza virus (HPIV) infection of cotton rats at different inoculum doses. We use the model to map inoculum dose to the level of immune protection and morbidity and to explore how such a framework might be used to determine an optimal inoculum dose. We show how a framework that combines mathematical models with experimental data can be used to study the impact of inoculum dose on important outcomes such as immune protection and morbidity. Our findings illustrate that the impact of inoculum dose on immune protection and morbidity can depend on the specific pathogen and that both protection and morbidity do not necessarily increase monotonically with increasing inoculum dose. Once vaccine design goals are specified with required levels of protection and acceptable levels of morbidity, our proposed framework can help in the rational design of vaccines and determination of the optimal amount of inoculum.

An important component of vaccines is the amount of pathogen inoculum, dead or alive, that is included in the vaccine. This inoculum dose, sometimes also referred to as antigen dose, needs to be large enough to induce good protective immunity. However, one usually also wants to keep the dose low to reduce costs, maximize the number of vaccine doses available, and minimize potential vaccine side effects. The inoculum dose is currently chosen based on limited data from clinical trials. In this study, we set up a framework that combines data with mathematical models to illustrate how such a combination could lead to better and more efficient determination of an optimal inoculum dose for vaccines.