Dynamics of influenza virus infection and pathology

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.

Investigating Functional Roles for Positive Feedback and Cellular Heterogeneity in the Type I Interferon Response to Viral Infection

Secretion of type I interferons (IFN) by infected cells mediates protection against many viruses, but prolonged or excessive type I IFN secretion can lead to immune pathology. A proper type I IFN response must therefore maintain a balance between protection and excessive IFN secretion. It has been widely noted that the type I IFN response is driven by positive feedback and is heterogeneous, with only a fraction of infected cells upregulating IFN expression even in clonal cell lines, but the functional roles of feedback and heterogeneity in balancing protection and excessive IFN secretion are not clear. To investigate the functional roles for feedback and heterogeneity, we constructed a mathematical model coupling IFN and viral dynamics that extends existing mathematical models by accounting for feedback and heterogeneity. We fit our model to five existing datasets, reflecting different experimental systems. Fitting across datasets allowed us to compare the IFN response across the systems and suggested different signatures of feedback and heterogeneity in the different systems. Further, through numerical experiments, we generated hypotheses of functional roles for IFN feedback and heterogeneity consistent with our mathematical model. We hypothesize an inherent tradeoff in the IFN response: a positive feedback loop prevents excessive IFN secretion, but also makes the IFN response vulnerable to viral antagonism. We hypothesize that cellular heterogeneity of the IFN response functions to protect the feedback loop from viral antagonism. Verification of our hypotheses will require further experimental studies. Our work provides a basis for analyzing the type I IFN response across systems.

The continual threat of influenza virus infections at the human-animal interface: What is new from a one health perspective?

This year, in 2018, we mark 100 years since the 1918 influenza pandemic. In the last 100 years, we have expanded our knowledge of public health and increased our ability to detect and prevent influenza; however, we still face challenges resulting from these continually evolving viruses. Today, it is clear that influenza viruses have multiple animal reservoirs (domestic and wild), making infection prevention in humans especially difficult to achieve. With this report, we summarize new knowledge regarding influenza A, B, C and D viruses and their control. We also introduce how a multi-disciplinary One Health approach is necessary to mitigate these threats.

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 Systems and Treatment Perspective of Models of Influenza Virus-Induced Host Responses

Severe influenza infections are often characterized as having unique host responses (e.g., early, severe hypercytokinemia). Neuraminidase inhibitors can be effective in controlling the severe symptoms of influenza but are often not administered until late in the infection. Several studies suggest that immune modulation may offer protection to high risk groups. Here, we review the current state of mathematical models of influenza-induced host responses. Selecting three models with conserved immune response components, we determine if the immune system components which most affect virus replication when perturbed are conserved across the models. We also test each model’s response to a pre-induction of interferon before the virus is administered. We find that each model emphasizes the importance of controlling the infected cell population to control viral replication. Moreover, our work shows that the structure of current models does not allow for significant responses to increased interferon concentrations. These results suggest that the current library of available published models of influenza infection does not adequately represent the complex interactions of the virus, interferon, and other aspects of the immune response. Specifically, the method used to model virus-resistant cells may need to be adapted in future work to more realistically represent the immune response to viral infection.

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

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

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.

Complete Genome Sequencing of Two Equine Influenza A(H3N8) Virus Strains Isolated in Kazakhstan

Here, we report the complete genome sequencing of strains A/equine/Kostanay/9/2012(H3N8) and A/equine/LKZ/9/2012(H3N8) of the equine influenza virus belonging to Florida sublineage, clade 2. The strains were isolated in 2012 in the northern and southern regions of Kazakhstan, respectively.

Simulation Model for Dynamics of Dengue with Innate and Humoral Immune Responses

Dengue virus is a mosquito borne Flavivirus and the most prevalent arbovirus in tropical and subtropical regions around the world. The incidence of dengue has increased drastically over the last few years at an alarming rate. The clinical manifestation of dengue ranges from asymptomatic infection to severe dengue. Even though the viral kinetics of dengue infection is lacking, innate immune response and humoral immune response are thought to play a major role in controlling the virus count. Here, we developed a computer simulation mathematical model including both innate and adaptive immune responses to study the within-host dynamics of dengue virus infection. A sensitivity analysis was carried out to identify key parameters that would contribute towards severe dengue. A detailed stability analysis was carried out to identify relevant range of parameters that contributes to different outcomes of the infection. This study provides a qualitative understanding of the biological factors that can explain the viral kinetics during a dengue infection.

What Controls the Acute Viral Infection Following Yellow Fever Vaccination?

Does target cell depletion, innate immunity, or adaptive immunity play the dominant role in controlling primary acute viral infections? Why do some individuals have higher peak virus titers than others? Answering these questions is a basic problem in immunology and can be particularly difficult in humans due to limited data, heterogeneity in responses in different individuals, and limited ability for experimental manipulation. We address these questions for infections following vaccination with the live attenuated yellow fever virus (YFV-17D) by analyzing viral load data from 80 volunteers. Using a mixed effects modeling approach, we find that target cell depletion models do not fit the data as well as innate or adaptive immunity models. Examination of the fits of the innate and adaptive immunity models to the data allows us to select a minimal model that gives improved fits by widely used model selection criteria (AICc and BIC) and explains why it is hard to distinguish between the innate and adaptive immunity models. We then ask why some individuals have over 1000-fold higher virus titers than others and find that most of the variation arises from differences in the initial/maximum growth rate of the virus in different individuals.

Understanding the within-host dynamics of influenza A virus: from theory to clinical implications

Mathematical models have provided important insights into acute viral dynamics within individual patients. In this paper, we study the simplest target cell-limited models to investigate the within-host dynamics of influenza A virus infection in humans. Despite the biological simplicity of the models, we show how these can be used to understand the severity of the infection and the key attributes of possible immunotherapy and antiviral drugs for the treatment of infection at different times post infection. Through an analytic approach, we derive and estimate simple summary biological quantities that can provide novel insights into the infection dynamics and the definition of clinical endpoints. We focus on nine quantities, including the area under the viral load curve, peak viral load, the time to peak viral load and the level of cell death due to infection. Using Markov chain Monte Carlo methods, we fitted the models to data collected from 12 untreated volunteers who participated in two clinical studies that tested the antiviral drugs oseltamivir and zanamivir. Based on the results, we also discuss various difficulties in deriving precise estimates of the parameters, even in the very simple models considered, when experimental data are limited to viral load measures and/or there is a limited number of viral load measurements post infection.

The Mechanisms for Within-Host Influenza Virus Control Affect Model-Based Assessment and Prediction of Antiviral Treatment

Models of within-host influenza viral dynamics have contributed to an improved understanding of viral dynamics and antiviral effects over the past decade. Existing models can be classified into two broad types based on the mechanism of viral control: models utilising target cell depletion to limit the progress of infection and models which rely on timely activation of innate and adaptive immune responses to control the infection. In this paper, we compare how two exemplar models based on these different mechanisms behave and investigate how the mechanistic difference affects the assessment and prediction of antiviral treatment. We find that the assumed mechanism for viral control strongly influences the predicted outcomes of treatment. Furthermore, we observe that for the target cell-limited model the assumed drug efficacy strongly influences the predicted treatment outcomes. The area under the viral load curve is identified as the most reliable predictor of drug efficacy, and is robust to model selection. Moreover, with support from previous clinical studies, we suggest that the target cell-limited model is more suitable for modelling in vitro assays or infection in some immunocompromised/immunosuppressed patients while the immune response model is preferred for predicting the infection/antiviral effect in immunocompetent animals/patients.

On the Role of CD8+ T Cells in Determining Recovery Time from Influenza Virus Infection

Myriad experiments have identified an important role for CD8⁺ T cell response mechanisms in determining recovery from influenza A virus infection. Animal models of influenza infection further implicate multiple elements of the immune response in defining the dynamical characteristics of viral infection. To date, influenza virus models, while capturing particular aspects of the natural infection history, have been unable to reproduce the full gamut of observed viral kinetic behavior in a single coherent framework. Here, we introduce a mathematical model of influenza viral dynamics incorporating innate, humoral, and cellular immune components and explore its properties with a particular emphasis on the role of cellular immunity. Calibrated against a range of murine data, our model is capable of recapitulating observed viral kinetics from a multitude of experiments. Importantly, the model predicts a robust exponential relationship between the level of effector CD8⁺ T cells and recovery time, whereby recovery time rapidly decreases to a fixed minimum recovery time with an increasing level of effector CD8⁺ T cells. We find support for this relationship in recent clinical data from influenza A (H7N9) hospitalized patients. The exponential relationship implies that people with a lower level of naive CD8⁺ T cells may receive significantly more benefit from induction of additional effector CD8⁺ T cells arising from immunological memory, itself established through either previous viral infection or T cell-based vaccines.

Heterogeneous shedding of influenza by human subjects and its implications for epidemiology and control

Heterogeneity of infectiousness is an important feature of the spread of many infections, with implications for disease dynamics and control, but its relevance to human influenza virus is still unclear. For a transmission event to occur, an infected individual needs to release infectious particles via respiratory symptoms. Key factors to take into account are virus dynamics, particle release in relation to respiratory symptoms, the amount of virus shed and, importantly, how these vary between infected individuals. A quantitative understanding of the process of influenza transmission is relevant to designing effective mitigation measures. Here we develop an influenza infection dynamics model fitted to virological, systemic and respiratory symptoms to investigate how within-host dynamics relates to infectiousness. We show that influenza virus shedding is highly heterogeneous between subjects. From analysis of data on experimental infections, we find that a small proportion (<20%) of influenza infected individuals are responsible for the production of 95% of infectious particles. Our work supports targeting mitigation measures at most infectious subjects to efficiently reduce transmission. The effectiveness of public health interventions targeted at highly infectious individuals would depend on accurate identification of these subjects and on how quickly control measures can be applied.

Hierarchical effects of pro-inflammatory cytokines on the post-influenza susceptibility to pneumococcal coinfection

In the course of influenza A virus (IAV) infections, a secondary bacterial infection frequently leads to serious respiratory conditions provoking high hospitalization and death tolls. Although abundant pro-inflammatory responses have been reported as key contributing factors for these severe dual infections, the relative contributions of cytokines remain largely unclear. In the current study, mathematical modelling based on murine experimental data dissects IFN-γ as a cytokine candidate responsible for impaired bacterial clearance, thereby promoting bacterial growth and systemic dissemination during acute IAV infection. We also found a time-dependent detrimental role of IL-6 in curtailing bacterial outgrowth which was not as distinct as for IFN-γ. Our numerical simulations suggested a detrimental effect of IFN-γ alone and in synergism with IL-6 but no conclusive pathogenic effect of IL-6 and TNF-α alone. This work provides a rationale to understand the potential impact of how to manipulate temporal immune components, facilitating the formulation of hypotheses about potential therapeutic strategies to treat coinfections.

Combining laboratory and mathematical models to infer mechanisms underlying kinetic changes in macrophage susceptibility to an RNA virus

Background

Macrophages are essential to innate immunity against many pathogens, but some pathogens also target macrophages as routes to infection. The Porcine Reproductive and Respiratory Syndrome virus (PRRSV) is an RNA virus that infects porcine alveolar macrophages (PAMs) causing devastating impact on global pig production. Identifying the cellular mechanisms that mediate PAM susceptibility to the virus is crucial for developing effective interventions. Previous evidence suggests that the scavenger receptor CD163 is essential for productive infection of PAMs with PRRSV. Here we use an integrative in-vitro–in-silico modelling approach to determine whether and how PAM susceptibility to PRRSV changes over time, to assess the role of CD163 expression on such changes, and to infer other potential causative mechanisms altering cell susceptibility.

Results

Our in-vitro experiment showed that PAM susceptibility to PRRSV changed considerably over incubation time. Moreover, an increasing proportion of PAMs apparently lacking CD163 were found susceptible to PRRSV at the later incubation stages, thus conflicting with current understanding that CD163 is essential for productive infection of PAMs with PRRSV. We developed process based dynamic mathematical models and fitted these to the data to assess alternative hypotheses regarding potential underlying mechanisms for the observed susceptibility and biomarker trends. The models informed by our data support the hypothesis that although CD163 may have enhanced cell susceptibility, it was not essential for productive infection in our study. Instead the models promote the existence of a reversible cellular state, such as macrophage polarization, mediated in a density dependent manner by autocrine factors, to be responsible for the observed kinetics in cell susceptibility.

Conclusions

Our dynamic model–inference approach provides strong support that PAM susceptibility to the PRRS virus is transient, reversible and can be mediated by compounds produced by the target cells themselves, and that these can render PAMs lacking the CD163 receptor susceptible to PRRSV. The results have implications for the development of therapeutics aiming to boost target cell resistance and prompt future investigation of dynamic changes in macrophage susceptibility to PRRSV and other viruses.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0345-5) contains supplementary material, which is available to authorized users.

Mathematical Models for Immunology: Current State of the Art and Future Research Directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.

Maternally-derived antibodies do not prevent transmission of swine influenza A virus between pigs

A transmission experiment involving 5-week-old specific-pathogen-free (SPF) piglets, with (MDA(+)) or without maternally-derived antibodies (MDA(-)), was carried out to evaluate the impact of passive immunity on the transmission of a swine influenza A virus (swIAV). In each group (MDA(+)/MDA(-)), 2 seeders were placed with 4 piglets in direct contact and 5 in indirect contact (3 replicates per group). Serological kinetics (ELISA) and individual viral shedding (RT-PCR) were monitored for 28 days after infection. MDA waning was estimated using a nonlinear mixed-effects model and survival analysis. Differential transmission rates were estimated depending on the piglets' initial serological status and contact structure (direct contact with pen-mates or indirect airborne contact). The time to MDA waning was 71.3 [52.8-92.1] days on average. The airborne transmission rate was 1.41 [0.64-2.63] per day. The compared shedding pattern between groups showed that MDA(+) piglets had mainly a reduced susceptibility to infection compared to MDA(-) piglets. The resulting reproduction number estimated in MDA(+) piglets (5.8 [1.4-18.9]), although 3 times lower than in MDA(-) piglets (14.8 [6.4-27.1]), was significantly higher than 1. Such an efficient and extended spread of swIAV at the population scale in the presence of MDAs could contribute to swIAV persistence on farms, given the fact that the period when transmission is expected to be impacted by the presence of MDAs can last up to 10 weeks.

Models of Viral Population Dynamics

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

Multi-epitope Models Explain How Pre-existing Antibodies Affect the Generation of Broadly Protective Responses to Influenza

The development of next-generation influenza vaccines that elicit strain-transcendent immunity against both seasonal and pandemic viruses is a key public health goal. Targeting the evolutionarily conserved epitopes on the stem of influenza’s major surface molecule, hemagglutinin, is an appealing prospect, and novel vaccine formulations show promising results in animal model systems. However, studies in humans indicate that natural infection and vaccination result in limited boosting of antibodies to the stem of HA, and the level of stem-specific antibody elicited is insufficient to provide broad strain-transcendent immunity. Here, we use mathematical models of the humoral immune response to explore how pre-existing immunity affects the ability of vaccines to boost antibodies to the head and stem of HA in humans, and, in particular, how it leads to the apparent lack of boosting of broadly cross-reactive antibodies to the stem epitopes. We consider hypotheses where binding of antibody to an epitope: (i) results in more rapid clearance of the antigen; (ii) leads to the formation of antigen-antibody complexes which inhibit B cell activation through Fcγ receptor-mediated mechanism; and (iii) masks the epitope and prevents the stimulation and proliferation of specific B cells. We find that only epitope masking but not the former two mechanisms to be key in recapitulating patterns in data. We discuss the ramifications of our findings for the development of vaccines against both seasonal and pandemic influenza.

The current influenza vaccine requires frequent updating in order to protect against small changes in the virus from one year to the next as well as larger changes associated with the emergence of new influenza strains from zoonotic reservoirs that cause pandemics. There is a considerable interest in developing “universal” vaccines that will boost immune responses to the conserved regions of the virus, in particular, to the stem region of the major virus surface molecule hemagglutinin (HA). However, recent data reveals that vaccination results in very limited boosting of antibodies to the stem of HA. We use mathematical models to explore different hypotheses that may explain why vaccination does not boost antibodies to the conserved parts of the virus. By confronting our models with the data from the human vaccination trials we found that the key mechanism preventing effective boosting of the responses to the stem of HA is masking of the stem by pre-existing antibodies developed during previous infections and vaccinations. We discuss how this masking effect could be overcome in a “universal” influenza vaccine.

Mathematical Model Reveals the Role of Memory CD8 T Cell Populations in Recall Responses to Influenza

The current influenza vaccine provides narrow protection against the strains included in the vaccine, and needs to be reformulated every few years in response to the constantly evolving new strains. Novel approaches are directed toward developing vaccines that provide broader protection by targeting B and T cell epitopes that are conserved between different strains of the virus. In this paper, we focus on developing mathematical models to explore the CD8 T cell responses to influenza, how they can be boosted, and the conditions under which they contribute to protection. Our models suggest that the interplay between spatial heterogeneity (with the virus infecting the respiratory tract and the immune response being generated in the secondary lymphoid organs) and T cell differentiation (with proliferation occurring in the lymphoid organs giving rise to a subpopulation of resident T cells in the respiratory tract) is the key to understand the dynamics of protection afforded by the CD8 T cell response to influenza. Our results suggest that the time lag for the generation of resident T cells in the respiratory tract and their rate of decay following infection are the key factors that limit the efficacy of CD8 T cell responses. The models predict that an increase in the level of central memory T cells leads to a gradual decrease in the viral load, and, in contrast, there is a sharper protection threshold for the relationship between the size of the population of resident T cells and protection. The models also suggest that repeated natural influenza infections cause the number of central memory CD8 T cells and the peak number of resident memory CD8 T cells to reach their plateaus, and while the former is maintained, the latter decays with time since the most recent infection.

Forsythoside A Controls Influenza A Virus Infection and Improves the Prognosis by Inhibiting Virus Replication in Mice

OBJECTIVE

The objective of this study was to observe the effects of forsythoside A on controlling influenza A virus (IAV) infection and improving the prognosis of IAV infection.

METHODS

Forty-eight SPF C57BL/6j mice were randomly divided into the following four groups: Group A: normal control group (normal con); Group B: IAV control group (V con); Group C: IAV+ oseltamivir treatment group (V oseltamivir; 0.78 mg/mL, 0.2 mL/mouse/day); Group D: IAV+ forsythoside A treatment group (V FTA; 2 μg/mL, 0.2 mL/mouse/day). Real-time fluorescence quantitative PCR (RT-qPCR) was used to measure mRNA expression of the TLR7, MyD88, TRAF6, IRAK4 and NF-κB p65 mRNA in TLR7 signaling pathway and the virus replication level in lung. Western blot was used to measure TLR7, MyD88 and NF-κB p65 protein. Flow cytometry was used to detect the proportion of the T cell subsets Th1/Th2 and Th17/Treg.

RESULTS

The body weight began to decrease after IAV infection, while FTA and oseltamivir could reduce the rate of body weight loss. The pathological damages in the FTA and oseltamivir group were less serious. TLR7, MyD88, TRAF6, IRAK4 and NF-κB p65 mRNA were up-regulated after virus infection (p < 0.01) while down-regulated after oseltamivir and FTA treatment (p < 0.01). The results of TLR7, MyD88 and NF-κB p65 protein consisted with correlative mRNA. Flow cytometry showed the Th1/Th2 differentiated towards Th2, and the Th17/Treg cells differentiated towards Treg after FTA treatment.

CONCLUSIONS

Our study suggests forsythoside A can control influenza A virus infection and improve the prognosis of IAV infection by inhibiting influenza A virus replication.

Crossing the scale from within-host infection dynamics to between-host transmission fitness: a discussion of current assumptions and knowledge

The progression of an infection within a host determines the ability of a pathogen to transmit to new hosts and to maintain itself in the population. While the general connection between the infection dynamics within a host and the population-level transmission dynamics of pathogens is widely acknowledged, a comprehensive and quantitative understanding that would allow full integration of the two scales is still lacking. Here, we provide a brief discussion of both models and data that have attempted to provide quantitative mappings from within-host infection dynamics to transmission fitness. We present a conceptual framework and provide examples of studies that have taken first steps towards development of a quantitative framework that scales from within-host infections to population-level fitness of different pathogens. We hope to illustrate some general themes, summarize some of the recent advances and-maybe most importantly-discuss gaps in our ability to bridge these scales, and to stimulate future research on this important topic.

Masking of antigenic epitopes by antibodies shapes the humoral immune response to influenza

The immune responses to influenza, a virus that exhibits strain variation, show complex dynamics where prior immunity shapes the response to the subsequent infecting strains. Original antigenic sin (OAS) describes the observation that antibodies to the first encountered influenza strain, specifically antibodies to the epitopes on the head of influenza's main surface glycoprotein, haemagglutinin (HA), dominate following infection with new drifted strains. OAS suggests that responses to the original strain are preferentially boosted. Recent studies also show limited boosting of the antibodies to conserved epitopes on the stem of HA, which are attractive targets for a 'universal vaccine'. We develop multi-epitope models to explore how pre-existing immunity modulates the immune response to new strains following immunization. Our models suggest that the masking of antigenic epitopes by antibodies may play an important role in describing the complex dynamics of OAS and limited boosting of antibodies to the stem of HA. Analysis of recently published data confirms model predictions for how pre-existing antibodies to an epitope on HA decrease the magnitude of boosting of the antibody response to this epitope following immunization. We explore strategies for boosting of antibodies to conserved epitopes and generating broadly protective immunity to multiple strains.

A Computational Model of Inhibition of HIV-1 by Interferon-Alpha

Type 1 interferons such as interferon-alpha (IFNα) inhibit replication of Human immunodeficiency virus (HIV-1) by upregulating the expression of genes that interfere with specific steps in the viral life cycle. This pathway thus represents a potential target for immune-based therapies that can alter the dynamics of host-virus interactions to benefit the host. To obtain a deeper mechanistic understanding of how IFNα impacts spreading HIV-1 infection, we modeled the interaction of HIV-1 with CD4 T cells and IFNα as a dynamical system. This model was then tested using experimental data from a cell culture model of spreading HIV-1 infection. We found that a model in which IFNα induces reversible cellular states that block both early and late stages of HIV-1 infection, combined with a saturating rate of conversion to these states, was able to successfully fit the experimental dataset. Sensitivity analysis showed that the potency of inhibition by IFNα was particularly dependent on specific network parameters and rate constants. This model will be useful for designing new therapies targeting the IFNα network in HIV-1-infected individuals, as well as potentially serving as a template for understanding the interaction of IFNα with other viruses.

Within-Host Models of High and Low Pathogenic Influenza Virus Infections: The Role of Macrophages

The World Health Organization identifies influenza as a major public health problem. While the strains commonly circulating in humans usually do not cause severe pathogenicity in healthy adults, some strains that have infected humans, such as H5N1, can cause high morbidity and mortality. Based on the severity of the disease, influenza viruses are sometimes categorized as either being highly pathogenic (HP) or having low pathogenicity (LP). The reasons why some strains are LP and others HP are not fully understood. While there are likely multiple mechanisms of interaction between the virus and the immune response that determine LP versus HP outcomes, we focus here on one component, namely macrophages (MP). There is some evidence that MP may both help fight the infection and become productively infected with HP influenza viruses. We developed mathematical models for influenza infections which explicitly included the dynamics and action of MP. We fit these models to viral load and macrophage count data from experimental infections of mice with LP and HP strains. Our results suggest that MP may not only help fight an influenza infection but may contribute to virus production in infections with HP viruses. We also explored the impact of combination therapies with antivirals and anti-inflammatory drugs on HP infections. Our study suggests a possible mechanism of MP in determining HP versus LP outcomes, and how different interventions might affect infection dynamics.

A spatial model of the efficiency of T cell search in the influenza-infected lung

Emerging strains of influenza, such as avian H5N1 and 2009 pandemic H1N1, are more virulent than seasonal H1N1 influenza, yet the underlying mechanisms for these differences are not well understood. Subtle differences in how a given strain interacts with the immune system are likely a key factor in determining virulence. One aspect of the interaction is the ability of T cells to locate the foci of the infection in time to prevent uncontrolled expansion. Here, we develop an agent based spatial model to focus on T cell migration from lymph nodes through the vascular system to sites of infection. We use our model to investigate whether different strains of influenza modulate this process. We calibrate the model using viral and chemokine secretion rates we measure in vitro together with values taken from literature. The spatial nature of the model reveals unique challenges for T cell recruitment that are not apparent in standard differential equation models. In this model comparing three influenza viruses, plaque expansion is governed primarily by the replication rate of the virus strain, and the efficiency of the T cell search-and-kill is limited by the density of infected epithelial cells in each plaque. Thus for each virus there is a different threshold of T cell search time above which recruited T cells are unable to control further expansion. Future models could use this relationship to more accurately predict control of the infection.

On the extinction probability in models of within-host infection: the role of latency and immunity

Not every exposure to virus establishes infection in the host; instead, the small amount of initial virus could become extinct due to stochastic events. Different diseases and routes of transmission have a different average number of exposures required to establish an infection. Furthermore, the host immune response and antiviral treatment affect not only the time course of the viral load provided infection occurs, but can prevent infection altogether by increasing the extinction probability. We show that the extinction probability when there is a time-dependent immune response depends on the chosen form of the model-specifically, on the presence or absence of a delay between infection of a cell and production of virus, and the distribution of latent and infectious periods of an infected cell. We hypothesise that experimentally measuring the extinction probability when the virus is introduced at different stages of the immune response, alongside the viral load which is usually measured, will improve parameter estimates and determine the most suitable mathematical form of the model.

Opportunities and challenges of Integral Projection Models for modelling host-parasite dynamics

Epidemiological dynamics are shaped by and may in turn shape host demography. These feedbacks can result in hard to predict patterns of disease incidence. Mathematical models that integrate infection and demography are consequently a key tool for informing expectations for disease burden and identifying effective measures for control.

A major challenge is capturing the details of infection within individuals and quantifying their downstream impacts to understand population‐scale outcomes. For example, parasite loads and antibody titres may vary over the course of an infection and contribute to differences in transmission at the scale of the population. To date, to capture these subtleties, models have mostly relied on complex mechanistic frameworks, discrete categorization and/or agent‐based approaches.

Integral Projection Models (IPMs) allow variance in individual trajectories of quantitative traits and their population‐level outcomes to be captured in ways that directly reflect statistical models of trait–fate relationships. Given increasing data availability, and advances in modelling, there is considerable potential for extending this framework to traits of relevance for infectious disease dynamics.

Here, we provide an overview of host and parasite natural history contexts where IPMs could strengthen inference of population dynamics, with examples of host species ranging from mice to sheep to humans, and parasites ranging from viruses to worms. We discuss models of both parasite and host traits, provide two case studies and conclude by reviewing potential for both ecological and evolutionary research.

Modeling Influenza Virus Infection: A Roadmap for Influenza Research

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

Connecting within and between-hosts dynamics in the influenza infection-staged epidemiological models with behavior change

Influenza viruses are a major public health problem worldwide. Although influenza has been extensively researched, there are still many aspects that are not fully understood such as the effects of within and between-hosts dynamics and their impact on behavior change. Here, we develop mathematical models with multiple infection stages and estimate parameters based on within-host data to investigate the impact of behavior change on influenza dynamics. We divide the infected population into three and four groups based on the age of the infection, which corresponds to viral load shedding. We consider within-host data on viral shedding to estimate the length and force of infection of the different infectivity stages. Our results show that behavior changes, due to exogenous events (e.g., media coverage) and disease symptoms, are effective in delaying and lowering an epidemic peak. We show that the dynamics of viral shedding and symptoms, during the infection, are key features when considering epidemic prevention strategies. This study improves our understanding of the spread of influenza virus infection in the population and provides information about the impact of emergent behavior and its connection to the within and between-hosts dynamics.

Innate Immunity and the Inter-exposure Interval Determine the Dynamics of Secondary Influenza Virus Infection and Explain Observed Viral Hierarchies

Influenza is an infectious disease that primarily attacks the respiratory system. Innate immunity provides both a very early defense to influenza virus invasion and an effective control of viral growth. Previous modelling studies of virus–innate immune response interactions have focused on infection with a single virus and, while improving our understanding of viral and immune dynamics, have been unable to effectively evaluate the relative feasibility of different hypothesised mechanisms of antiviral immunity. In recent experiments, we have applied consecutive exposures to different virus strains in a ferret model, and demonstrated that viruses differed in their ability to induce a state of temporary immunity or viral interference capable of modifying the infection kinetics of the subsequent exposure. These results imply that virus-induced early immune responses may be responsible for the observed viral hierarchy. Here we introduce and analyse a family of within-host models of re-infection viral kinetics which allow for different viruses to stimulate the innate immune response to different degrees. The proposed models differ in their hypothesised mechanisms of action of the non-specific innate immune response. We compare these alternative models in terms of their abilities to reproduce the re-exposure data. Our results show that 1) a model with viral control mediated solely by a virus-resistant state, as commonly considered in the literature, is not able to reproduce the observed viral hierarchy; 2) the synchronised and desynchronised behaviour of consecutive virus infections is highly dependent upon the interval between primary virus and challenge virus exposures and is consistent with virus-dependent stimulation of the innate immune response. Our study provides the first mechanistic explanation for the recently observed influenza viral hierarchies and demonstrates the importance of understanding the host response to multi-strain viral infections. Re-exposure experiments provide a new paradigm in which to study the immune response to influenza and its role in viral control.

Infection with the influenza virus is responsible for serious morbidity and mortality. In otherwise-healthy individuals, infection is usually acute, lasting between 5 to 10 days. Over this time, the virus initially replicates rapidly, before peaking and then being cleared from the body. Despite extensive study, we do not yet fully understand the processes which lead to viral control and viral clearance from the host. Experimental and modelling studies of single infections have previously indicated that both the innate and adaptive immune responses play an important role in combating infection. Here we study a novel dataset on how the host responds to sequential exposure to two different strains of influenza. We introduce a family of mathematical models of the within-host dynamics of influenza infection which allow for re-infection. Our models allow us, for the first time, to differentiate between alternative hypothesised mechanisms by which the innate immune response acts to control viral replication. This study improves our understanding of the innate immune response to influenza and demonstrates that re-exposure studies provide a new paradigm for further experimental research. Our findings may contribute to the development of next-generation treatment and vaccination strategies which rely upon an understanding of the host’s immunological response to influenza infection.

Minimal within-host dengue models highlight the specific roles of the immune response in primary and secondary dengue infections

In recent years, the within-host viral dynamics of dengue infections have been increasingly characterized, and the relationship between aspects of these dynamics and the manifestation of severe disease has been increasingly probed. Despite this progress, there are few mathematical models of within-host dengue dynamics, and the ones that exist focus primarily on the general role of immune cells in the clearance of infected cells, while neglecting other components of the immune response in limiting viraemia. Here, by considering a suite of mathematical within-host dengue models of increasing complexity, we aim to isolate the critical components of the innate and the adaptive immune response that suffice in the reproduction of several well-characterized features of primary and secondary dengue infections. By building up from a simple target cell limited model, we show that only the innate immune response is needed to recover the characteristic features of a primary symptomatic dengue infection, while a higher rate of viral infectivity (indicative of antibody-dependent enhancement) and infected cell clearance by T cells are further needed to recover the characteristic features of a secondary dengue infection. We show that these minimal models can reproduce the increased risk of disease associated with secondary heterologous infections that arises as a result of a cytokine storm, and, further, that they are consistent with virological indicators that predict the onset of severe disease, such as the magnitude of peak viraemia, time to peak viral load, and viral clearance rate. Finally, we show that the effectiveness of these virological indicators to predict the onset of severe disease depends on the contribution of T cells in fuelling the cytokine storm.

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

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

Quantifying Immune Response to Influenza Virus Infection via Multivariate Nonlinear ODE Models with Partially Observed State Variables and Time-Varying Parameters

Influenza A virus (IAV) infection continues to be a global health threat, as evidenced by the outbreak of the novel A/California/7/2009 IAV strain. Previous flu vaccines have proven less effective than hoped for emerging IAV strains, indicating a more thorough understanding of immune responses to primary infection is needed. One issue is the difficulty in directly measuring many key parameters and variables of the immune response. To address these issues, we considered a comprehensive workflow for statistical inference for ordinary differential question (ODE) models with partially observed variables and time-varying parameters, including identifiability analysis, two-stage and NLS estimation, and model selection etc‥ In particular, we proposed a novel one-step method to verify parameter identifiability and formulate estimating equations simultaneously. Thus, the pseudo-LS method can now deal with general ODE models with partially observed state variables for the first time. Using this workflow, we verified the relative significance of various immune factors to virus control, including target epithelial cells, cytotoxic T-lymphocyte (CD8+) cells and IAV specific antibodies (IgG and IgM). Factors other than cytotoxic T-lymphocyte (CTL) killing contributed the most to the loss of infected epithelial cells, though the effects of CTL are still significant. IgM antibody was found to be the major contributor to neutralization of free infectious viral particles. Also, the maximum viral load, which correlates well with mortality, was found to depend more on viral replication rates than infectivity. In contrast to current hypotheses, the results obtained via our methods suggest that IgM antibody and viral replication rates may be worth of further explorations in vaccine development.

A review on computational systems biology of pathogen-host interactions

Pathogens manipulate the cellular mechanisms of host organisms via pathogen-host interactions (PHIs) in order to take advantage of the capabilities of host cells, leading to infections. The crucial role of these interspecies molecular interactions in initiating and sustaining infections necessitates a thorough understanding of the corresponding mechanisms. Unlike the traditional approach of considering the host or pathogen separately, a systems-level approach, considering the PHI system as a whole is indispensable to elucidate the mechanisms of infection. Following the technological advances in the post-genomic era, PHI data have been produced in large-scale within the last decade. Systems biology-based methods for the inference and analysis of PHI regulatory, metabolic, and protein-protein networks to shed light on infection mechanisms are gaining increasing demand thanks to the availability of omics data. The knowledge derived from the PHIs may largely contribute to the identification of new and more efficient therapeutics to prevent or cure infections. There are recent efforts for the detailed documentation of these experimentally verified PHI data through Web-based databases. Despite these advances in data archiving, there are still large amounts of PHI data in the biomedical literature yet to be discovered, and novel text mining methods are in development to unearth such hidden data. Here, we review a collection of recent studies on computational systems biology of PHIs with a special focus on the methods for the inference and analysis of PHI networks, covering also the Web-based databases and text-mining efforts to unravel the data hidden in the literature.

Predicting pathogen-specific CD8 T cell immune responses from a modeling approach

The primary CD8 T cell immune response constitutes a major mechanism to fight an infection by intra-cellular pathogens. We aim at assessing whether pathogen-specific dynamical parameters of the CD8 T cell response can be identified, based on measurements of CD8 T cell counts, using a modeling approach. We generated experimental data consisting in CD8 T cell counts kinetics during the response to three different live intra-cellular pathogens: two viruses (influenza, vaccinia) injected intranasally, and one bacteria (Listeria monocytogenes) injected intravenously. All pathogens harbor the same antigen (NP68), but differ in their interaction with the host. In parallel, we developed a mathematical model describing the evolution of CD8 T cell counts and pathogen amount during an immune response. This model is characterized by 9 parameters and includes relevant feedback controls. The model outputs were compared with the three data series and an exhaustive estimation of the parameter values was performed. By focusing on the ability of the model to fit experimental data and to produce a CD8 T cell population mainly composed of memory cells at the end of the response, critical parameters were identified. We show that a small number of parameters (2-4) define the main features of the CD8 T cell immune response and are characteristic of a given pathogen. Among these parameters, two are related to the effector CD8 T cell mediated control of cell and pathogen death. The parameter associated with memory cell death is shown to play no relevant role during the main phases of the CD8 T cell response, yet it becomes essential when looking at the predictions of the model several months after the infection.

The inflammatory response to influenza A virus (H1N1): An experimental and mathematical study

Mortality from influenza infections continues as a global public health issue, with the host inflammatory response contributing to fatalities related to the primary infection. Based on Ordinary Differential Equation (ODE) formalism, a computational model was developed for the in-host response to influenza A virus, merging inflammatory, innate, adaptive and humoral responses to virus and linking severity of infection, the inflammatory response, and mortality. The model was calibrated using dense cytokine and cell data from adult BALB/c mice infected with the H1N1 influenza strain A/PR/8/34 in sublethal and lethal doses. Uncertainty in model parameters and disease mechanisms was quantified using Bayesian inference and ensemble model methodology that generates probabilistic predictions of survival, defined as viral clearance and recovery of the respiratory epithelium. The ensemble recovers the expected relationship between magnitude of viral exposure and the duration of survival, and suggests mechanisms primarily responsible for survival, which could guide the development of immuno-modulatory interventions as adjuncts to current anti-viral treatments. The model is employed to extrapolate from available data survival curves for the population and their dependence on initial viral aliquot. In addition, the model allows us to illustrate the positive effect of controlled inflammation on influenza survival.

Within-host viral dynamics of dengue serotype 1 infection

Dengue, the most common mosquito-borne viral infection of humans, is endemic across much of the world, including much of tropical Asia and is increasing in its geographical range. Here, we present a mathematical model of dengue virus dynamics within infected individuals, detailing the interaction between virus and a simple immune response. We fit this model to measurements of plasma viral titre from cases of primary and secondary DENV 1 infection in Vietnam. We show that variation in model parameters governing the immune response is sufficient to create the observed variation in virus dynamics between individuals. Estimating model parameter values, we find parameter differences between primary and secondary cases consistent with the theory of antibody-dependent enhancement (namely enhanced rates of viral entry to target cells in secondary cases). Finally, we use our model to examine the potential impact of an antiviral drug on the within-host dynamics of dengue. We conclude that the impact of antiviral therapy on virus dynamics is likely to be limited if therapy is only started at the onset of symptoms, owing to the typically late stage of viral pathogenesis reached by the time symptoms are manifested and thus treatment is started.

Seven challenges in modeling pathogen dynamics within-host and across scales

The population dynamics of infectious disease is a mature field in terms of theory and to some extent, application. However for microparasites, the theory and application of models of the dynamics within a single infected host is still an open field. Further, connecting across the scales--from cellular to host level, to population level--has potential to vastly improve our understanding of pathogen dynamics and evolution. Here, we highlight seven challenges in the following areas: transmission bottlenecks, heterogeneity within host, dynamic fitness landscapes within hosts, making use of next-generation sequencing data, capturing superinfection and when and how to model more than two scales.

A Critical Role for Immune System Response in Mediating Anti-influenza Drug Synergies Assessed by Mechanistic Modeling

Influenza virus infections represent a serious public health problem worldwide, due to the rapid emergence of drug resistance. One strategy to improve treatment efficacy is to combine drugs that act synergistically. Potentially useful drug combinations are typically identified through empirical testing using in vitro and animal models, but the complexity of the clinical situation warrants the use of more careful analysis and sophisticated approaches. To explore new approaches, we constructed a mechanistic model representing the interaction of antiviral drugs with the viral replication pathway and human immune responses. Simulation of combination therapy using oseltamivir and amantadine predicted significant therapeutic synergy only when immune response was included, in agreement with previous in vitro and in vivo studies using amantadine-resistant strains. Our model can be used to predict the optimal doses for combination therapy, and also raises questions about current drug evaluation methods that do not account for immune system interactions.

Eight challenges in modelling infectious livestock diseases

The transmission of infectious diseases of livestock does not differ in principle from disease transmission in any other animals, apart from that the aim of control is ultimately economic, with the influence of social, political and welfare constraints often poorly defined. Modelling of livestock diseases suffers simultaneously from a wealth and a lack of data. On the one hand, the ability to conduct transmission experiments, detailed within-host studies and track individual animals between geocoded locations make livestock diseases a particularly rich potential source of realistic data for illuminating biological mechanisms of transmission and conducting explicit analyses of contact networks. On the other hand, scarcity of funding, as compared to human diseases, often results in incomplete and partial data for many livestock diseases and regions of the world. In this overview of challenges in livestock disease modelling, we highlight eight areas unique to livestock that, if addressed, would mark major progress in the area.

Identifying selection in the within-host evolution of influenza using viral sequence data

The within-host evolution of influenza is a vital component of its epidemiology. A question of particular interest is the role that selection plays in shaping the viral population over the course of a single infection. We here describe a method to measure selection acting upon the influenza virus within an individual host, based upon time-resolved genome sequence data from an infection. Analysing sequence data from a transmission study conducted in pigs, describing part of the haemagglutinin gene (HA1) of an influenza virus, we find signatures of non-neutrality in six of a total of sixteen infections. We find evidence for both positive and negative selection acting upon specific alleles, while in three cases, the data suggest the presence of time-dependent selection. In one infection we observe what is potentially a specific immune response against the virus; a non-synonymous mutation in an epitope region of the virus is found to be under initially positive, then strongly negative selection. Crucially, given the lack of homologous recombination in influenza, our method accounts for linkage disequilibrium between nucleotides at different positions in the haemagglutinin gene, allowing for the analysis of populations in which multiple mutations are present at any given time. Our approach offers a new insight into the dynamics of influenza infection, providing a detailed characterisation of the forces that underlie viral evolution.

The evolution of the influenza virus is of great importance for human health. Through evolution, current influenza viruses develop the ability to infect people who have been vaccinated against earlier strains. New strains of influenza that infect birds and pigs could evolve to infect and spread between people, causing a global pandemic. The influenza virus lives within a human or animal host, so that viral evolution happens within, or in the spread between, individuals. As such, what happens to the virus during the course of an infection is a question of great interest. We here describe a statistical method that uses viral genome sequence data to measure how evolution affects the influenza virus within a single host. Studying data from infections transmitted between pigs, we find evidence for evolutionary adaptation in six of sixteen animals for which data were available. In one case, an immune response mounted by a pig against the virus is apparent. Our method provides a statistical framework for using sequence data to study viral evolution on very short timescales, enabling new research into within-host viral evolution.

Secondary bacterial infections in influenza virus infection pathogenesis

Influenza is often complicated by bacterial pathogens that colonize the nasopharynx and invade the middle ear and/or lung epithelium. Incidence and pathogenicity of influenza-bacterial coinfections are multifactorial processes that involve various pathogenic virulence factors and host responses with distinct site- and strain-specific differences. Animal models and kinetic models have improved our understanding of how influenza viruses interact with their bacterial co-pathogens and the accompanying immune responses. Data from these models indicate that considerable alterations in epithelial surfaces and aberrant immune responses lead to severe inflammation, a key driver of bacterial acquisition and infection severity following influenza. However, further experimental and analytical studies are essential to determining the full mechanistic spectrum of different viral and bacterial strains and species and to finding new ways to prevent and treat influenza-associated bacterial coinfections. Here, we review recent advances regarding transmission and disease potential of influenza-associated bacterial infections and discuss the current gaps in knowledge.

Viral kinetic modeling: state of the art

Viral kinetic (VK) modeling has led to increased understanding of the within host dynamics of viral infections and the effects of therapy. Here we review recent developments in the modeling of viral infection kinetics with emphasis on two infectious diseases: hepatitis C and influenza. We review how VK modeling has evolved from simple models of viral infections treated with a drug or drug cocktail with an assumed constant effectiveness to models that incorporate drug pharmacokinetics and pharmacodynamics, as well as phenomenological models that simply assume drugs have time varying-effectiveness. We also discuss multiscale models that include intracellular events in viral replication, models of drug-resistance, models that include innate and adaptive immune responses and models that incorporate cell-to-cell spread of infection. Overall, VK modeling has provided new insights into the understanding of the disease progression and the modes of action of several drugs. We expect that VK modeling will be increasingly used in the coming years to optimize drug regimens in order to improve therapeutic outcomes and treatment tolerability for infectious diseases.