Towards a quantitative understanding of the within-host dynamics of influenza A infections

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.

Measles Infection Dose Responses: Insights from Mathematical Modeling

How viral infections develop can change based on the number of viruses initially entering the body. The understanding of the impacts of infection doses remains incomplete, in part due to challenging constraints, and a lack of research. Gaining more insights is crucial regarding the measles virus (MV). The higher the MV infection dose, the earlier the peak of acute viremia, but the magnitude of the peak viremia remains almost constant. Measles is highly contagious, causes immunosuppression such as lymphopenia, and contributes substantially to childhood morbidity and mortality. This work investigated mechanisms underlying the observed wild-type measles infection dose responses in cynomolgus monkeys. We fitted longitudinal data on viremia using maximum likelihood estimation, and used the Akaike Information Criterion (AIC) to evaluate relevant biological hypotheses and their respective model parameterizations. The lowest AIC indicates a linear relationship between the infection dose, the initial viral load, and the initial number of activated MV-specific T cells. Early peak viremia is associated with high initial number of activated MV-specific T cells. Thus, when MV infection dose increases, the initial viremia and associated immune cell stimulation increase, and reduce the time it takes for T cell killing to be sufficient, thereby allowing dose-independent peaks for viremia, MV-specific T cells, and lymphocyte depletion. Together, these results suggest that the development of measles depends on virus-host interactions at the start and the efficiency of viral control by cellular immunity. These relationships are additional motivations for prevention, vaccination, and early treatment for measles.

How robust are estimates of key parameters in standard viral dynamic models?

Mathematical models of viral infection have been developed, fitted to data, and provide insight into disease pathogenesis for multiple agents that cause chronic infection, including HIV, hepatitis C, and B virus. However, for agents that cause acute infections or during the acute stage of agents that cause chronic infections, viral load data are often collected after symptoms develop, usually around or after the peak viral load. Consequently, we frequently lack data in the initial phase of viral growth, i.e., when pre-symptomatic transmission events occur. Missing data may make estimating the time of infection, the infectious period, and parameters in viral dynamic models, such as the cell infection rate, difficult. However, having extra information, such as the average time to peak viral load, may improve the robustness of the estimation. Here, we evaluated the robustness of estimates of key model parameters when viral load data prior to the viral load peak is missing, when we know the values of some parameters and/or the time from infection to peak viral load. Although estimates of the time of infection are sensitive to the quality and amount of available data, particularly pre-peak, other parameters important in understanding disease pathogenesis, such as the loss rate of infected cells, are less sensitive. Viral infectivity and the viral production rate are key parameters affecting the robustness of data fits. Fixing their values to literature values can help estimate the remaining model parameters when pre-peak data is missing or limited. We find a lack of data in the pre-peak growth phase underestimates the time to peak viral load by several days, leading to a shorter predicted growth phase. On the other hand, knowing the time of infection (e.g., from epidemiological data) and fixing it results in good estimates of dynamical parameters even in the absence of early data. While we provide ways to approximate model parameters in the absence of early viral load data, our results also suggest that these data, when available, are needed to estimate model parameters more precisely.

A mathematical model for the within-host (re)infection dynamics of SARS-CoV-2

Interactions between SARS-CoV-2 and the immune system during infection are complex. However, understanding the within-host SARS-CoV-2 dynamics is of enormous importance for clinical and public health outcomes. Current mathematical models focus on describing the within-host SARS-CoV-2 dynamics during the acute infection phase. Thereby they ignore important long-term post-acute infection effects. We present a mathematical model, which not only describes the SARS-CoV-2 infection dynamics during the acute infection phase, but extends current approaches by also recapitulating clinically observed long-term post-acute infection effects, such as the recovery of the number of susceptible epithelial cells to an initial pre-infection homeostatic level, a permanent and full clearance of the infection within the individual, immune waning, and the formation of long-term immune capacity levels after infection. Finally, we used our model and its description of the long-term post-acute infection dynamics to explore reinfection scenarios differentiating between distinct variant-specific properties of the reinfecting virus. Together, the model's ability to describe not only the acute but also the long-term post-acute infection dynamics provides a more realistic description of key outcomes and allows for its application in clinical and public health scenarios.

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.

Modelling the impact of JNJ-1802, a first-in-class dengue inhibitor blocking the NS3-NS4B interaction, on in-vitro DENV-2 dynamics

Dengue virus (DENV) is a public health challenge across the tropics and subtropics. Currently, there is no licensed prophylactic or antiviral treatment for dengue. The novel DENV inhibitor JNJ-1802 can significantly reduce viral load in mice and non-human primates. Here, using a mechanistic viral kinetic model calibrated against viral RNA data from experimental in-vitro infection studies, we assess the in-vitro inhibitory effect of JNJ-1802 by characterising infection dynamics of two DENV-2 strains in the absence and presence of different JNJ-1802 concentrations. Viral RNA suppression to below the limit of detection was achieved at concentrations of >1.6 nM, with a median concentration exhibiting 50% of maximal inhibitory effect (IC50) of 1.23x10-02 nM and 1.28x10-02 nM for the DENV-2/RL and DENV-2/16681 strains, respectively. This work provides important insight into the in-vitro inhibitory effect of JNJ-1802 and presents a first step towards a modelling framework to support characterization of viral kinetics and drug effect across different host systems.

A cooperativity between virus and bacteria during respiratory infections

Respiratory tract infections remain the leading cause of morbidity and mortality worldwide. The burden is further increased by polymicrobial infection or viral and bacterial co-infection, often exacerbating the existing condition. Way back in 1918, high morbidity due to secondary pneumonia caused by bacterial infection was known, and a similar phenomenon was observed during the recent COVID-19 pandemic in which secondary bacterial infection worsens the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) condition. It has been observed that viruses paved the way for subsequent bacterial infection; similarly, bacteria have also been found to aid in viral infection. Viruses elevate bacterial infection by impairing the host's immune response, disrupting epithelial barrier integrity, expression of surface receptors and adhesion proteins, direct binding of virus to bacteria, altering nutritional immunity, and effecting the bacterial biofilm. Similarly, the bacteria enhance viral infection by altering the host's immune response, up-regulation of adhesion proteins, and activation of viral proteins. During co-infection, respiratory bacterial and viral pathogens were found to adapt and co-exist in the airways of their survival and to benefit from each other, i.e., there is a cooperative existence between the two. This review comprehensively reviews the mechanisms involved in the synergistic/cooperativity relationship between viruses and bacteria and their interaction in clinically relevant respiratory infections.

Mathematical Modeling of Oncolytic Virus Therapy Reveals Role of the Immune Response

Oncolytic adenoviruses (OAds) present a promising path for cancer treatment due to their selectivity in infecting and lysing tumor cells and their ability to stimulate the immune response. In this study, we use an ordinary differential equation (ODE) model of tumor growth inhibited by oncolytic virus activity to parameterize previous research on the effect of genetically re-engineered OAds in A549 lung cancer tumors in murine models. We find that the data are best fit by a model that accounts for an immune response, and that the immune response provides a mechanism for elimination of the tumor. We also find that parameter estimates for the most effective OAds share characteristics, most notably a high infection rate and low viral clearance rate, that might be potential reasons for these viruses' efficacy in delaying tumor growth. Further studies observing E1A and P19 recombined viruses in different tumor environments may further illuminate the extent of the effects of these genetic modifications.

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.

A Novel Mathematical Model That Predicts the Protection Time of SARS-CoV-2 Antibodies

Infectious diseases such as SARS-CoV-2 pose a considerable threat to public health. Constructing a reliable mathematical model helps us quantitatively explain the kinetic characteristics of antibody-virus interactions. A novel and robust model is developed to integrate antibody dynamics with virus dynamics based on a comprehensive understanding of immunology principles. This model explicitly formulizes the pernicious effect of the antibody, together with a positive feedback stimulation of the virus-antibody complex on the antibody regeneration. Besides providing quantitative insights into antibody and virus dynamics, it demonstrates good adaptivity in recapturing the virus-antibody interaction. It is proposed that the environmental antigenic substances help maintain the memory cell level and the corresponding neutralizing antibodies secreted by those memory cells. A broader application is also visualized in predicting the antibody protection time caused by a natural infection. Suitable binding antibodies and the presence of massive environmental antigenic substances would prolong the protection time against breakthrough infection. The model also displays excellent fitness and provides good explanations for antibody selection, antibody interference, and self-reinfection. It helps elucidate how our immune system efficiently develops neutralizing antibodies with good binding kinetics. It provides a reasonable explanation for the lower SARS-CoV-2 mortality in the population that was vaccinated with other vaccines. It is inferred that the best strategy for prolonging the vaccine protection time is not repeated inoculation but a directed induction of fast-binding antibodies. Eventually, this model will inform the future construction of an optimal mathematical model and help us fight against those infectious diseases.

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.

Molecular Communications in Viral Infections Research: Modeling, Experimental Data, and Future Directions

Hundreds of millions of people worldwide are affected by viral infections each year, and yet, several of them neither have vaccines nor effective treatment during and post-infection. This challenge has been highlighted by the COVID-19 pandemic, showing how viruses can quickly spread and impact society as a whole. Novel interdisciplinary techniques must emerge to provide forward-looking strategies to combat viral infections, as well as possible future pandemics. In the past decade, an interdisciplinary area involving bioengineering, nanotechnology and information and communication technology (ICT) has been developed, known as Molecular Communications. This new emerging area uses elements of classical communication systems to molecular signalling and communication found inside and outside biological systems, characterizing the signalling processes between cells and viruses. In this paper, we provide an extensive and detailed discussion on how molecular communications can be integrated into the viral infectious diseases research, and how possible treatment and vaccines can be developed considering molecules as information carriers. We provide a literature review on molecular communications models for viral infection (intra-body and extra-body), a deep analysis on their effects on immune response, how experimental can be used by the molecular communications community, as well as open issues and future directions.

Comparing antiviral strategies against COVID-19 via multiscale within-host modelling

Within-host models of COVID-19 infection dynamics enable the merits of different forms of antiviral therapy to be assessed in individual patients. A stochastic agent-based model of COVID-19 intracellular dynamics is introduced here, that incorporates essential steps of the viral life cycle targeted by treatment options. Integration of model predictions with an intercellular ODE model of within-host infection dynamics, fitted to patient data, generates a generic profile of disease progression in patients that have recovered in the absence of treatment. This is contrasted with the profiles obtained after variation of model parameters pertinent to the immune response, such as effector cell and antibody proliferation rates, mimicking disease progression in immunocompromised patients. These profiles are then compared with disease progression in the presence of antiviral and convalescent plasma therapy against COVID-19 infections. The model reveals that using both therapies in combination can be very effective in reducing the length of infection, but these synergistic effects decline with a delayed treatment start. Conversely, early treatment with either therapy alone can actually increase the duration of infection, with infectious virions still present after the decline of other markers of infection. This suggests that usage of these treatments should remain carefully controlled in a clinical environment.

Data-driven methods for present and future pandemics: Monitoring, modelling and managing

This survey analyses the role of data-driven methodologies for pandemic modelling and control. We provide a roadmap from the access to epidemiological data sources to the control of epidemic phenomena. We review the available methodologies and discuss the challenges in the development of data-driven strategies to combat the spreading of infectious diseases. Our aim is to bring together several different disciplines required to provide a holistic approach to epidemic analysis, such as data science, epidemiology, and systems-and-control theory. A 3M-analysis is presented, whose three pillars are: Monitoring, Modelling and Managing. The focus is on the potential of data-driven schemes to address three different challenges raised by a pandemic: (i) monitoring the epidemic evolution and assessing the effectiveness of the adopted countermeasures; (ii) modelling and forecasting the spread of the epidemic; (iii) making timely decisions to manage, mitigate and suppress the contagion. For each step of this roadmap, we review consolidated theoretical approaches (including data-driven methodologies that have been shown to be successful in other contexts) and discuss their application to past or present epidemics, such as Covid-19, as well as their potential application to future epidemics.

Incorporating Time Delays in the Mathematical Modelling of the Human Immune Response in Viral Infections

Mathematical modelling helps to describe the functional and causal relationships between objects in the physical world. The complexity of these models increases as more components and variables are added to maintain and observe. Differential equations are regularly used in these models, as they are able to display the interactions between several variables and describe non-linear behaviour. Differential equations are commonly used in immune response mathematical models to help describe these complex and dynamic interactions within the immune system of the organism. Time delays in the immune system are common and are often disregarded due to the low-resolution of models, which provide limited description of the specific section of immune system being studied. The few models that incorporate time delays are mostly at the epidemiological level, to track the spread of the virus in the population. In this paper we review the applications of the models based on differential equations and describe their potential utilization for the studies of immune response in SARS-CoV-2.

Independent Decompositions of Chemical Reaction Networks

A chemical reaction network (CRN) is composed of reactions that can be seen as interactions among entities called species, which exist within the system. Endowed with kinetics, CRN has a corresponding set of ordinary differential equations (ODEs). In chemical reaction network theory, we are interested with connections between the structure of the CRN and qualitative properties of the corresponding ODEs. One of the results in decomposition theory of CRNs is that the intersection of the sets of positive steady states of the subsystems is equal to the set of positive steady states of the whole system, if the decomposition is independent. Hence, computational approach using independent decompositions can be used as an efficient tool in studying large systems. In this work, we provide a necessary and sufficient condition for the existence of a nontrivial independent decomposition of a CRN, which leads to a novel step-by-step method to obtain such decomposition, if it exists. We also illustrate these results using real-life examples. In particular, we show that a CRN of a popular model of anaerobic yeast fermentation pathway has a nontrivial independent decomposition, while a particular biological system, which is a metabolic network with one positive feedforward and a negative feedback has none. Finally, we analyze properties of positive steady states of reaction networks of specific influenza virus models.

Impact of Oseltamivir Treatment on Influenza A and B Virus Dynamics in Human Volunteers

Influenza viruses infect millions of humans every year causing an estimated 400,000 deaths globally. Due to continuous virus evolution current vaccines provide only limited protection against the flu. Several antiviral drugs are available to treat influenza infection, and one of the most commonly used drugs is oseltamivir (Tamiflu). While the mechanism of action of oseltamivir as a neuraminidase inhibitor is well-understood, the impact of oseltamivir on influenza virus dynamics in humans has been controversial. Many clinical trials with oseltamivir have been done by pharmaceutical companies such as Roche but the results of these trials until recently have been provided as summary reports or papers. Typically, such reports included median virus shedding curves for placebo and drug-treated influenza virus infected volunteers often indicating high efficacy of the early treatment. However, median shedding curves may be not accurately representing drug impact in individual volunteers. Importantly, due to public pressure clinical trials data testing oseltamivir efficacy has been recently released in the form of redacted PDF documents. We digitized and re-analyzed experimental data on influenza virus shedding in human volunteers from three previously published trials: on influenza A (1 trial) or B viruses (2 trials). Given that not all volunteers exposed to influenza viruses actually start virus shedding we found that impact of oseltamivir on the virus shedding dynamics was dependent on (i) selection of volunteers that were infected with the virus, and (ii) the detection limit in the measurement assay; both of these details were not well-articulated in the published studies. By assuming that any non-zero viral measurement is above the limit of detection we could match previously published data on median influenza A virus (flu A study) shedding but not on influenza B virus shedding (flu B study B) in human volunteers. Additional analyses confirmed that oseltamivir had an impact on the duration of shedding and overall shedding (defined as area under the curve) but this result varied by the trial. Interestingly, treatment had no impact on the rates at which shedding increased or declined with time in individual volunteers. Additional analyses showed that oseltamivir impacted the kinetics of the end of viral shedding, and in about 20-40% of volunteers that shed the virus treatment had no impact on viral shedding duration. Our results suggest an unusual impact of oseltamivir on influenza viruses shedding kinetics and caution about the use of published median data or data from a few individuals for inferences. Furthermore, we call for the need to publish raw data from critical clinical trials that can be independently analyzed.

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.

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.

Integrating mathematical models with experimental data to investigate the within-host dynamics of bacterial infections

Bacterial infections still constitute a major cause of mortality and morbidity worldwide. The unavailability of therapeutics, antimicrobial resistance and the chronicity of infections due to incomplete clearance contribute to this phenomenon. Despite the progress in antimicrobial and vaccine development, knowledge about the effect that therapeutics have on the host–bacteria interactions remains incomplete. Insights into the characteristics of bacterial colonization and migration between tissues and the relationship between replication and host- or therapeutically induced killing can enable efficient design of treatment approaches. Recently, innovative experimental techniques have generated data enabling the qualitative characterization of aspects of bacterial dynamics. Here, we argue that mathematical modeling as an adjunct to experimental data can enrich the biological insight that these data provide. However, due to limited interdisciplinary training, efforts to combine the two remain limited. To promote this dialogue, we provide a categorization of modeling approaches highlighting their relationship to data generated by a range of experimental techniques in the area of in vivo bacterial dynamics. We outline common biological themes explored using mathematical models with case studies across all pathogen classes. Finally, this review advocates multidisciplinary integration to improve our mechanistic understanding of bacterial infections and guide the use of existing or new therapies.

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.

Modelling the impact of antibody-dependent enhancement on disease severity of Zika virus and dengue virus sequential and co-infection

Human infections with viruses of the genus Flavivirus, including dengue virus (DENV) and Zika virus (ZIKV), are of increasing global importance. Owing to antibody-dependent enhancement (ADE), secondary infection with one Flavivirus following primary infection with another Flavivirus can result in a significantly larger peak viral load with a much higher risk of severe disease. Although several mathematical models have been developed to quantify the virus dynamics in the primary and secondary infections of DENV, little progress has been made regarding secondary infection of DENV after a primary infection of ZIKV, or DENV-ZIKV co-infection. Here, we address this critical gap by developing compartmental models of virus dynamics. We first fitted the models to published data on dengue viral loads of the primary and secondary infections with the observation that the primary infection reaches its peak much more gradually than the secondary infection. We then quantitatively show that ADE is the key factor determining a sharp increase/decrease of viral load near the peak time in the secondary infection. In comparison, our simulations of DENV and ZIKV co-infection (simultaneous rather than sequential) show that ADE has very limited influence on the peak DENV viral load. This indicates pre-existing immunity to ZIKV is the determinant of a high level of ADE effect. Our numerical simulations show that (i) in the absence of ADE effect, a subsequent co-infection is beneficial to the second virus; and (ii) if ADE is feasible, then a subsequent co-infection can induce greater damage to the host with a higher peak viral load and a much earlier peak time for the second virus, and for the second peak for the first virus.

Modeling the Effects of Resource-Driven Immune Defense on Parasite Transmission in Heterogeneous Host Populations

Individuals experience heterogeneous environmental conditions that can affect within-host processes such as immune defense against parasite infection. Variation among individuals in parasite shedding can cause some hosts to contribute disproportionately to population-level transmission, but we currently lack mechanistic theory that predicts when environmental conditions can result in large disease outbreaks through the formation of immunocompromised superspreading individuals. Here, I present a within-host model of a microparasite's interaction with the immune system that links an individual host's resource intake to its infectious period. For environmental scenarios driving population-level heterogeneity in resource intake (resource scarcity and resource subsidy relative to baseline availability), I generate a distribution of infectious periods and simulate epidemics on these heterogeneous populations. I find that resource scarcity can result in large epidemics through creation of superspreading individuals, while resource subsidies can reduce or prevent transmission of parasites close to their invasion threshold by homogenizing resource allocation to immune defense. Importantly, failure to account for heterogeneity in competence can result in under-prediction of outbreak size, especially when parasites are close to their invasion threshold. More generally, this framework suggests that differences in conditions experienced by individual hosts can lead to superspreading via differences in resource allocation to immune defense alone, even in the absence of other heterogeneites such as host contacts.

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.

Mathematical modelling identifies the role of adaptive immunity as a key controller of respiratory syncytial virus in cotton rats

Respiratory syncytial virus (RSV) is a common virus that can have varying effects ranging from mild cold-like symptoms to mortality depending on the age and immune status of the individual. We combined mathematical modelling using ordinary differential equations (ODEs) with measurement of RSV infection kinetics in primary well-differentiated human bronchial epithelial cultures in vitro and in immunocompetent and immunosuppressed cotton rats to glean mechanistic details that underlie RSV infection kinetics in the lung. Quantitative analysis of viral titre kinetics in our mathematical model showed that the elimination of infected cells by the adaptive immune response generates unique RSV titre kinetic features including a faster timescale of viral titre clearance than viral production, and a monotonic decrease in the peak RSV titre with decreasing inoculum dose. Parameter estimation in the ODE model using a nonlinear mixed effects approach revealed a very low rate (average single-cell lifetime > 10 days) of cell lysis by RSV before the adaptive immune response is initiated. Our model predicted negligible changes in the RSV titre kinetics at early times post-infection (less than 5 dpi) but a slower decay in RSV titre in immunosuppressed cotton rats compared to that in non-suppressed cotton rats at later times (greater than 5 dpi) in silico. These predictions were in excellent agreement with the experimental results. Our combined approach quantified the importance of the adaptive immune response in suppressing RSV infection in cotton rats, which could be useful in testing RSV vaccine candidates.

In vivo Neutralization of Pro-inflammatory Cytokines During Secondary Streptococcus pneumoniae Infection Post Influenza A Virus Infection

An overt pro-inflammatory immune response is a key factor contributing to lethal pneumococcal infection in an influenza pre-infected host and represents a potential target for therapeutic intervention. However, there is a paucity of knowledge about the level of contribution of individual cytokines. Based on the predictions of our previous mathematical modeling approach, the potential benefit of IFN-γ- and/or IL-6-specific antibody-mediated cytokine neutralization was explored in C57BL/6 mice infected with the influenza A/PR/8/34 strain, which were subsequently infected with the Streptococcus pneumoniae strain TIGR4 on day 7 post influenza. While single IL-6 neutralization had no effect on respiratory bacterial clearance, single IFN-γ neutralization enhanced local bacterial clearance in the lungs. Concomitant neutralization of IFN-γ and IL-6 significantly reduced the degree of pneumonia as well as bacteremia compared to the control group, indicating a positive effect for the host during secondary bacterial infection. The results of our model-driven experimental study reveal that the predicted therapeutic value of IFN-γ and IL-6 neutralization in secondary pneumococcal infection following influenza infection is tightly dependent on the experimental protocol while at the same time paving the way toward the development of effective immune therapies.

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.

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.

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.

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.

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.

Early HIV infection predictions: role of viral replication errors

In order to prevent and/or control infections it is necessary to understand their early-time dynamics. However this is precisely the phase of HIV about which the least is known. To investigate the initial stages of HIV infection within a host we have developed a multi-type, continuous-time branching process model. This model is a stochastic extension of the standard viral dynamics model, under the assumption that the number of cell targets for viral infection is constant, biologically reasonable since, during the earliest stages of HIV infection, very few cells are infected relative to their total population size. We use our model to investigate three important clinical characteristics of early HIV infection following intravenous challenge: risk of infection, time to infection clearance (assuming failed infection), and time to infection detection. Our focus is on the impact of errors in viral replication that result in non-infectious virus production on these characteristics. Only a small fraction of circulating virus in any chronically infected individual is capable of infecting susceptible cells: estimates range from 1/10⁴ - 1/10³. Characterization and quantification of the processes by which virus becomes defective remains incomplete. We consider two mechanisms that result in defective virus: (1) Copying errors, i.e., lethal errors in reverse transcription, which introduce mutations into the HIV-1 proviral genome, some of which may cripple the viral genome produced, and (2) Packaging errors, i.e., errors during viral packaging, at the end of the viral replication cycle, which cause defective virus by packaging new virions without, for example, viral RNA or key proteins required for infectivity. We show that assumptions on mechanisms of defective virus production can significantly impact early HIV infection model predictions. For example, the risk of infection is orders of magnitude higher if all defective virus is associated with packaging errors, but infection is predicted to be detectable sooner following HIV exposure if all defective virus is associated with copying errors. Thus, in order to make reliable predictions of risk, clearance time, and detection time, better characterization of viral replication is required.

Transmission-clearance trade-offs indicate that dengue virulence evolution depends on epidemiological context

An extensive body of theory addresses the topic of pathogen virulence evolution, yet few studies have empirically demonstrated the presence of fitness trade-offs that would select for intermediate virulence. Here we show the presence of transmission-clearance trade-offs in dengue virus using viremia measurements. By fitting a within-host model to these data, we further find that the interaction between dengue and the host immune response can account for the observed trade-offs. Finally, we consider dengue virulence evolution when selection acts on the virus’s production rate. By combining within-host model simulations with empirical findings on how host viral load affects human-to-mosquito transmission success, we show that the virus’s transmission potential is maximized at production rates associated with intermediate virulence and that the optimal production rate critically depends on dengue’s epidemiological context. These results indicate that long-term changes in dengue’s global distribution impact the invasion and spread of virulent dengue virus genotypes.

Theory predicts that pathogens will evolve towards intermediate virulence, yet the necessary trade-offs invoked by this theory have rarely been demonstrated empirically. Here, the authors show that dengue virus dynamics exhibit a trade-off between transmission and clearance rates.

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.

Understanding Immunity through the Lens of Disease Ecology

As we describe the immune system in ever more exquisite detail, we might find that no matter how successful, this approach will not be sufficient to understand the spread of infectious agents, their susceptibility to vaccine therapy, and human disease resistance. Compared with the strict reductionism practiced as a means of characterizing most biological processes, I propose that the progression and outcome of disease-causing host-parasite interactions will be more clearly understood through a focus on disease ecology.

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.

The impact of cell regeneration on the dynamics of viral coinfection

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

In-host modeling

Understanding the mechanisms governing host-pathogen kinetics is important and can guide human interventions. In-host mathematical models, together with biological data, have been used in this endeavor. In this review, we present basic models used to describe acute and chronic pathogenic infections. We highlight the power of model predictions, the role of drug therapy, and advantage of considering the dynamics of immune responses. We also present the limitations of these models due in part to the trade-off between the complexity of the model and their predictive power, and the challenges a modeler faces in determining the appropriate formulation for a given problem.

Analysis of Practical Identifiability of a Viral Infection Model

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

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.

Estimating biologically relevant parameters under uncertainty for experimental within-host murine West Nile virus infection

West Nile virus (WNV) is an emerging pathogen that has decimated bird populations and caused severe outbreaks of viral encephalitis in humans. Currently, little is known about the within-host viral kinetics of WNV during infection. We developed mathematical models to describe viral replication, spread and host immune response in wild-type and immunocompromised mice. Our approach fits a target cell-limited model to viremia data from immunocompromised knockout mice and an adaptive immune response model to data from wild-type mice. Using this approach, we first estimate parameters governing viral production and viral spread in the host using simple models without immune responses. We then use these parameters in a more complex immune response model to characterize the dynamics of the humoral immune response. Despite substantial uncertainty in input parameters, our analysis generates relatively precise estimates of important viral characteristics that are composed of nonlinear combinations of model parameters: we estimate the mean within-host basic reproductive number,R0, to be 2.3 (95% of values in the range 1.7-2.9); the mean infectious virion burst size to be 2.9 plaque-forming units (95% of values in the range 1.7-4.7); and the average number of cells infected per infectious virion to be between 0.3 and 0.99. Our analysis gives mechanistic insights into the dynamics of WNV infection and produces estimates of viral characteristics that are difficult to measure experimentally. These models are a first step towards a quantitative understanding of the timing and effectiveness of the humoral immune response in reducing host viremia and consequently the epidemic spread of WNV.