Modeling Influenza Virus Infection: A Roadmap for Influenza Research

Identifiability investigation of within-host models of acute virus infection

Uncertainty in parameter estimates from fitting within-host models to empirical data limits the model's ability to uncover mechanisms of infection, disease progression, and to guide pharmaceutical interventions. Understanding the effect of model structure and data availability on model predictions is important for informing model development and experimental design. To address sources of uncertainty in parameter estimation, we use four mathematical models of influenza A infection with increased degrees of biological realism. We test the ability of each model to reveal its parameters in the presence of unlimited data by performing structural identifiability analyses. We then refine the results by predicting practical identifiability of parameters under daily influenza A virus titers alone or together with daily adaptive immune cell data. Using these approaches, we present insight into the sources of uncertainty in parameter estimation and provide guidelines for the types of model assumptions, optimal experimental design, and biological information needed for improved predictions.

Author summary

Within-host models of virus infections fitted to data have improved our understanding of mechanisms of infection, disease progression, and allowed us to provide guidelines for pharmaceutical interventions. Given their predictive power, it is essential that we properly uncover and address uncertainty in model predictions and parameter estimation. Here, we focus on the effect of model structure and data availability on our ability to uncover unknown parameters. To address these questions, we use four mathematical models of influenza A infection with increased degrees of biological realism. We test the ability of each model to reveal its parameters in the presence of unlimited data by performing structural identifiability analysis. We then refine the results by predicting practical identifiability of parameters under daily influenza A virus titers alone or together with daily adaptive immune cell data. Using these approaches, we present insights into the sources of uncertainty in parameter estimations and provide guidelines for the types of model assumptions, optimal experimental design, and biological information needed for improved predictions.

Exploring the immune-inflammatory mechanism of Maxing Shigan Decoction in treating influenza virus A-induced pneumonia based on an integrated strategy of single-cell transcriptomics and systems biology

BACKGROUND

Influenza is an acute respiratory infection caused by influenza virus. Maxing Shigan Decoction (MXSGD) is a commonly used traditional Chinese medicine prescription for the prevention and treatment of influenza. However, its mechanism remains unclear.

METHOD

The mice model of influenza A virus pneumonia was established by nasal inoculation. After 3 days of intervention, the lung index was calculated, and the pathological changes of lung tissue were detected by HE staining. Firstly, transcriptomics technology was used to analyze the differential genes and important pathways in mouse lung tissue regulated by MXSGD. Then, real-time fluorescent quantitative PCR (RT-PCR) was used to verify the changes in mRNA expression in lung tissues. Finally, intestinal microbiome and intestinal metabolomics were performed to explore the effect of MXSGD on gut microbiota.

RESULTS

The lung inflammatory cell infiltration in the MXSGD group was significantly reduced (p < 0.05). The results of bioinformatics analysis for transcriptomics results show that these genes are mainly involved in inflammatory factors and inflammation-related signal pathways mediated inflammation biological modules, etc. Intestinal microbiome showed that the intestinal flora Actinobacteriota level and Desulfobacterota level increased in MXSGD group, while Planctomycetota in MXSGD group decreased. Metabolites were mainly involved in primary bile acid biosynthesis, thiamine metabolism, etc. This suggests that MXSGD has a microbial-gut-lung axis regulation effect on mice with influenza A virus pneumonia.

CONCLUSION

MXSGD may play an anti-inflammatory and immunoregulatory role by regulating intestinal microbiome and intestinal metabolic small molecules, and ultimately play a role in the treatment of influenza A virus pneumonia.

Modeling and analysis of the effect of optimal virus control on the spread of HFMD

A within-host and between-host hand, foot and mouth disease (HFMD) mathematical model is established and the affect of optimal control in its within-host part on HFMD transmission is studied. Through define two basic reproduction numbers, by using the fast-slow system analysis method of time scale, the global stabilities of the between-host (slow) system and within-host (fast) system are researched, respectively. An optimal control problem with drug-treatment control on coupled within-host and between-host HFMD model is formulated and analysed theoretically. Finally, the purposed optimal control measures are applied to the actual HFMD epidemic analysis in Zhejiang Province, China from April 1, 2021 to June 30, 2021. The numerical results show that the drug control strategies can reduce the virus load per capita and can effectively prevent large-scale outbreaks of HFMD.

Outlining recent updates on influenza therapeutics and vaccines: A comprehensive review

Influenza virus has presented a considerable healthcare challenge during the past years, particularly in vulnerable groups with compromised immune systems. Therapeutics and vaccination have always been in research annals since the spread of influenza. Efforts have been going on to develop an antiviral therapeutic approach that could assist in better disease management and reduce the overall disease complexity, resistance development, and fatality rates. On the other hand, vaccination presents a chance for effective, long-term, cost-benefit, and preventive response against the morbidity and mortality associated with the influenza. However, the issues of resistance development, strain mutation, antigenic variability, and inability to cure wide-spectrum and large-scale strains of the virus by available vaccines remain there. The article gathers the updated data for the therapeutics and available influenza vaccines, their mechanism of action, shortcomings, and trials under clinical experimentation. A methodological approach has been adopted to identify the prospective therapeutics and available vaccines approved and within the clinical trials against the influenza virus. Review contains influenza therapeutics, including traditional and novel antiviral drugs and inhibitor therapies against influenza virus as well as research trials based on newer drug combinations and latest technologies such as nanotechnology and organic and plant-based natural products. Most recent development of influenza vaccine has been discussed including some updates on traditional vaccination protocols and discussion on next-generation and upgraded novel technologies. This review will help the readers to understand the righteous approach for dealing with influenza virus infection and for deducing futuristic approaches for novel therapeutic and vaccine trials against Influenza.

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

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

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

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

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

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

Modeling suggests that virion production cycles within individual cells is key to understanding acute hepatitis B virus infection kinetics

Hepatitis B virus (HBV) infection kinetics in immunodeficient mice reconstituted with humanized livers from inoculation to steady state is highly dynamic despite the absence of an adaptive immune response. To recapitulate the multiphasic viral kinetic patterns, we developed an agent-based model that includes intracellular virion production cycles reflecting the cyclic nature of each individual virus lifecycle. The model fits the data well predicting an increase in production cycles initially starting with a long production cycle of 1 virion per 20 hours that gradually reaches 1 virion per hour after approximately 3-4 days before virion production increases dramatically to reach to a steady state rate of 4 virions per hour per cell. Together, modeling suggests that it is the cyclic nature of the virus lifecycle combined with an initial slow but increasing rate of HBV production from each cell that plays a role in generating the observed multiphasic HBV kinetic patterns in humanized mice.

Antibody Dynamics Simulation-A Mathematical Exploration of Clonal Deletion and Somatic Hypermutation

We have employed mathematical modeling techniques to construct a comprehensive framework for elucidating the intricate response mechanisms of the immune system, facilitating a deeper understanding of B-cell clonal deletion and somatic hypermutation. Our improved model introduces innovative mechanisms that shed light on positive and negative selection processes during T-cell and B-cell development. Notably, clonal deletion is attributed to the attenuated immune stimulation exerted by self-antigens with high binding affinities, rendering them less effective in eliciting subsequent B-cell maturation and differentiation. Secondly, our refined model places particular emphasis on the crucial role played by somatic hypermutation in modulating the immune system's functionality. Through extensive investigation, we have determined that somatic hypermutation not only expedites the production of highly specific antibodies pivotal in combating microbial infections but also serves as a regulatory mechanism to dampen autoimmunity and enhance self-tolerance within the organism. Lastly, our model advances the understanding of the implications of antibody in vivo evolution in the overall process of organismal aging. With the progression of time, the age-associated amplification of autoimmune activity becomes apparent. While somatic hypermutation effectively delays this process, mitigating the levels of autoimmune response, it falls short of reversing this trajectory entirely. In conclusion, our advanced mathematical model offers a comprehensive and scholarly approach to comprehend the intricacies of the immune system. By encompassing novel mechanisms for selection, emphasizing the functional role of somatic hypermutation, and illuminating the consequences of in vivo antibody evolution, our model expands the current understanding of immune responses and their implications in aging.

The race to understand immunopathology in COVID-19: Perspectives on the impact of quantitative approaches to understand within-host interactions

The COVID-19 pandemic has revealed the need for the increased integration of modelling and data analysis to public health, experimental, and clinical studies. Throughout the first two years of the pandemic, there has been a concerted effort to improve our understanding of the within-host immune response to the SARS-CoV-2 virus to provide better predictions of COVID-19 severity, treatment and vaccine development questions, and insights into viral evolution and the impacts of variants on immunopathology. Here we provide perspectives on what has been accomplished using quantitative methods, including predictive modelling, population genetics, machine learning, and dimensionality reduction techniques, in the first 26 months of the COVID-19 pandemic approaches, and where we go from here to improve our responses to this and future pandemics.

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.

Online searches of children’s oseltamivir in public primary and specialized care: Detecting influenza outbreaks in Finland using dedicated databases for health care professionals

Introduction

Health care professionals working in primary and specialized care typically search for medical information from Internet sources. In Finland, Physician’s Databases are online portals aimed at professionals seeking medical information. As dosage errors may occur when prescribing medication to children, professionals’ need for reliable medical information has increased in public health care centers and hospitals. Influenza continues to be a public health threat, with young children at risk of developing severe illness and easily transmitting the virus. Oseltamivir is used to treat children with influenza. The objective of this study was to compare searches for children’s oseltamivir and influenza diagnoses in primary and specialized care, and to determine if the searches could aid detection of influenza outbreaks.

Methods

We compared searches in Physician’s Databases for children’s oral suspension of oseltamivir (6 mg/mL) for influenza diagnoses of children under 7 years and laboratory findings of influenza A and B from the National Infectious Disease Register. Searches and diagnoses were assessed in primary and specialized care across Finland by season from 2012–2016. The Moving Epidemic Method (MEM) calculated seasonal starts and ends, and paired differences in the mean compared two indicators. Correlation was tested to compare seasons.

Results

We found that searches and diagnoses in primary and specialized care showed visually similar patterns annually. The MEM-calculated starting weeks in searches appeared mainly in the same week. Oseltamivir searches in primary care preceded diagnoses by −1.0 weeks (95% CI: −3.0, −0.3; p = 0.132) with very high correlation (τ = 0.913). Specialized care oseltamivir searches and diagnoses correlated moderately (τ = 0.667).

Conclusion

Health care professionals’ searches for children’s oseltamivir in online databases linked with the registers of children’s influenza diagnoses in primary and specialized care. Therefore, database searches should be considered as supplementary information in disease surveillance when detecting influenza epidemics.

Analysis of multi-strain infection of vaccinated and recovered population through epidemic model: Application to COVID-19

In this work, an innovative multi-strain SV EAIR epidemic model is developed for the study of the spread of a multi-strain infectious disease in a population infected by mutations of the disease. The population is assumed to be completely susceptible to n different variants of the disease, and those who are vaccinated and recovered from a specific strain k (k ≤ n) are immune to previous and present strains j = 1, 2, ⋯, k, but can still be infected by newer emerging strains j = k + 1, k + 2, ⋯, n. The model is designed to simulate the emergence and dissemination of viral strains. All the equilibrium points of the system are calculated and the conditions for existence and global stability of these points are investigated and used to answer the question as to whether it is possible for the population to have an endemic with more than one strain. An interesting result that shows that a strain with a reproduction number greater than one can still die out on the long run if a newer emerging strain has a greater reproduction number is verified numerically. The effect of vaccines on the population is also analyzed and a bound for the herd immunity threshold is calculated. The validity of the work done is verified through numerical simulations by applying the proposed model and strategy to analyze the multi-strains of the COVID-19 virus, in particular, the Delta and the Omicron variants, in the United State.

Advances in Parameter Estimation and Learning from Data for Mathematical Models of Hepatitis C Viral Kinetics

Mathematical models, some of which incorporate both intracellular and extracellular hepatitis C viral kinetics, have been advanced in recent years for studying HCV–host dynamics, antivirals mode of action, and their efficacy. The standard ordinary differential equation (ODE) hepatitis C virus (HCV) kinetic model keeps track of uninfected cells, infected cells, and free virus. In multiscale models, a fourth partial differential equation (PDE) accounts for the intracellular viral RNA (vRNA) kinetics in an infected cell. The PDE multiscale model is substantially more difficult to solve compared to the standard ODE model, with governing differential equations that are stiff. In previous contributions, we developed and implemented stable and efficient numerical methods for the multiscale model for both the solution of the model equations and parameter estimation. In this contribution, we perform sensitivity analysis on model parameters to gain insight into important properties and to ensure our numerical methods can be safely used for HCV viral dynamic simulations. Furthermore, we generate in-silico patients using the multiscale models to perform machine learning from the data, which enables us to remove HCV measurements on certain days and still be able to estimate meaningful observations with a sufficiently small error.

The Contribution of Viral Proteins to the Synergy of Influenza and Bacterial Co-Infection

A severe course of acute respiratory disease caused by influenza A virus (IAV) infection is often linked with subsequent bacterial superinfection, which is difficult to cure. Thus, synergistic influenza-bacterial co-infection represents a serious medical problem. The pathogenic changes in the infected host are accelerated as a consequence of IAV infection, reflecting its impact on the host immune response. IAV infection triggers a complex process linked with the blocking of innate and adaptive immune mechanisms required for effective antiviral defense. Such disbalance of the immune system allows for easier initiation of bacterial superinfection. Therefore, many new studies have emerged that aim to explain why viral-bacterial co-infection can lead to severe respiratory disease with possible fatal outcomes. In this review, we discuss the key role of several IAV proteins-namely, PB1-F2, hemagglutinin (HA), neuraminidase (NA), and NS1-known to play a role in modulating the immune defense of the host, which consequently escalates the development of secondary bacterial infection, most often caused by Streptococcus pneumoniae. Understanding the mechanisms leading to pathological disorders caused by bacterial superinfection after the previous viral infection is important for the development of more effective means of prevention; for example, by vaccination or through therapy using antiviral drugs targeted at critical viral proteins.

Optimizing antiviral therapy for COVID-19 with learned pathogenic model

COVID-19 together with variants have caused an unprecedented amount of mental and economic turmoil with ever increasing fatality and no proven therapies in sight. The healthcare industry is racing to find a cure with multitude of clinical trials underway to access the efficacy of repurposed antivirals, however the much needed insights into the dynamics of pathogenesis of SARS-CoV-2 and corresponding pharmacology of antivirals are lacking. This paper introduces systematic pathological model learning of COVID-19 dynamics followed by derivative free optimization based multi objective drug rescheduling. The pathological model learnt from clinical data of severe COVID-19 patients treated with remdesivir could additionally predict immune T cells response and resulted in a dramatic reduction in remdesivir dose and schedule leading to lower toxicities, however maintaining a high virological efficacy.

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

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

Towards a Mathematical Model for the Viral Progression in the Pharynx

In this work, a comprehensive model for the viral progression in the pharynx has been developed. This one-dimension model considers both Fickian diffusion and convective flow coupled with chemical reactions, such as virus population growth, infected and uninfected cell accumulation as well as virus clearance. The effect of a sterilizing agent such as an alcoholic solution on the viral progression in the pharynx was taken into account and a parametric analysis for the effect of kinetic rate parameters on virus propagation was made. Moreover, different conditions caused by further medical treatment, such as a decrease in virus yield per infected cell, were examined. It is shown that the infection fails to establish by decreasing the virus yield per infected cell. It is believed that this work could be used to further investigate the medical treatment of viral progression in the pharynx.

Prevalence and Determinants of Vaccine Hesitancy in Aseer Region, Saudi Arabia

Objectives

This study aimed to assess the awareness of the general population regarding vaccines to determine the prevalence of vaccine hesitancy in Aseer Region in the southern part of Saudi Arabia.

Methods

A descriptive cross-sectional approach was used, targeting all parents in Aseer Region. The study was carried out from January to April 2020. The data for this study were collected using a structured questionnaire, which was developed by the researchers after an intensive literature review and consultation with experts. The questionnaire covered aspects such as parents’ sociodemographic data, their awareness regarding vaccine safety and efficacy for children and their attitude and adherence to children’s vaccination, including their hesitancy towards vaccines.

Results

The survey included 796 participants (response rate: 100%) whose ages ranged from 18 to 55 years. Two-thirds (63.4%) of the participants were female. Regarding vaccination adherence and hesitancy among participants, more than three-quarters completely adhered to the vaccination schedule for their children, and only 3.9% were non-adherent. With regards to participants’ awareness regarding vaccine safety and efficacy for children, 89.3% agreed that vaccination keeps children healthy, 84.2% reported that vaccines are safe and effective for children and 83.4% reported that all scheduled vaccines in Saudi Arabia are effective.

Conclusion

Vaccine hesitancy among participants was not low, and this should be taken into account notwithstanding their high awareness levels. The recorded antivaccine action was mostly related to vaccine safety and not its efficacy.

Antiviral Gene Expression in Young and Aged Murine Lung during H1N1 and H3N2

Influenza is a respiratory virus that alone or in combination with secondary bacterial pathogens can contribute to the development of acute pneumonia in persons >65 years of age. Host innate immune antiviral signaling early in response to influenza is essential to inhibit early viral replication and guide the initiation of adaptive immune responses. Using young adult (3 months) and aged adult mice infected with mouse adapted H1N1 or H3N2, the results of our study illustrate dysregulated and/or diminished activation of key signaling pathways in aged lung contribute to increased lung inflammation and morbidity. Specifically, within the first seven days of infection, there were significant changes in genes associated with TLR and RIG-I signaling detected in aged murine lung in response to H1N1 or H3N2. Taken together, the results of our study expand our current understanding of age-associated changes in antiviral signaling in the lung.

Optimal Allocation of Vaccine and Antiviral Drugs for Influenza Containment over Delayed Multiscale Epidemic Model considering Time-Dependent Transmission Rate

In this study, two types of epidemiological models called "within host" and "between hosts" have been studied. The within-host model represents the innate immune response, and the between-hosts model signifies the SEIR (susceptible, exposed, infected, and recovered) epidemic model. The major contribution of this paper is to break the chain of infectious disease transmission by reducing the number of susceptible and infected people via transferring them to the recovered people group with vaccination and antiviral treatment, respectively. Both transfers are considered with time delay. In the first step, optimal control theory is applied to calculate the optimal final time to control the disease within a host's body with a cost function. To this end, the vaccination that represents the effort that converts healthy cells into resistant-to-infection cells in the susceptible individual's body is used as the first control input to vaccinate the susceptible individual against the disease. Moreover, the next control input (antiviral treatment) is applied to eradicate the concentrations of the virus and convert healthy cells into resistant-to-infection cells simultaneously in the infected person's body to treat the infected individual. The calculated optimal time in the first step is considered as the delay of vaccination and antiviral treatment in the SEIR dynamic model. Using Pontryagin's maximum principle in the second step, an optimal control strategy is also applied to an SEIR mathematical model with a nonlinear transmission rate and time delay, which is computed as optimal time in the first step. Numerical results are consistent with the analytical ones and corroborate our theoretical results.

Intra- and Inter-cellular Modeling of Dynamic Interaction between Zika Virus and Its Naturally Occurring Defective Viral Genomes

Here, we examine in silico the infection dynamics and interactions of two Zika virus (ZIKV) genomes: one is the full-length ZIKV genome (wild type [WT]), and the other is one of the naturally occurring defective viral genomes (DVGs), which can replicate in the presence of the WT genome, appears under high-MOI (multiplicity of infection) passaging conditions, and carries a deletion encompassing part of the structural and NS1 protein-coding region. Ordinary differential equations (ODEs) were used to simulate the infection of cells by virus particles and the intracellular replication of the WT and DVG genomes that produce these particles. For each virus passage in Vero and C6/36 cell cultures, the rates of the simulated processes were fitted to two types of observations: virus titer data and the assembled haplotypes of the replicate passage samples. We studied the consistency of the model with the experimental data across all passages of infection in each cell type separately as well as the sensitivity of the model's parameters. We also determined which simulated processes of virus evolution are the most important for the adaptation of the WT and DVG interplay in these two disparate cell culture environments. Our results demonstrate that in the majority of passages, the rates of DVG production are higher inC6/36 cells than in Vero cells, which might result in tolerance and therefore drive the persistence of the mosquito vector in the context of ZIKV infection. Additionally, the model simulations showed a slower accumulation of infected cells under higher activation of the DVG-associated processes, which indicates a potential role of DVGs in virus attenuation. IMPORTANCE One of the ideas for lessening Zika pathogenicity is the addition of its natural or engineered defective virus genomes (DVGs) (have no pathogenicity) to the infection pool: a DVG is redirecting the wild-type (WT)-associated virus development resources toward its own maturation. The mathematical model presented here, attuned to the data from interplays between WT Zika viruses and their natural DVGs in mammalian and mosquito cells, provides evidence that the loss of uninfected cells is attenuated by the DVG development processes. This model enabled us to estimate the rates of virus development processes in the WT/DVG interplay, determine the key processes, and show that the key processes are faster in mosquito cells than in mammalian ones. In general, the presented model and its detailed study suggest in what important virus development processes the therapeutically efficient DVG might compete with the WT; this may help in assembling engineered DVGs for ZIKV and other flaviviruses.

Dynamically linking influenza virus infection kinetics, lung injury, inflammation, and disease severity

Influenza viruses cause a significant amount of morbidity and mortality. Understanding host immune control efficacy and how different factors influence lung injury and disease severity are critical. We established and validated dynamical connections between viral loads, infected cells, CD8⁺ T cells, lung injury, inflammation, and disease severity using an integrative mathematical model-experiment exchange. Our results showed that the dynamics of inflammation and virus-inflicted lung injury are distinct and nonlinearly related to disease severity, and that these two pathologic measurements can be independently predicted using the model-derived infected cell dynamics. Our findings further indicated that the relative CD8⁺ T cell dynamics paralleled the percent of the lung that had resolved with the rate of CD8⁺ T cell-mediated clearance rapidly accelerating by over 48,000 times in 2 days. This complimented our analyses showing a negative correlation between the efficacy of innate and adaptive immune-mediated infected cell clearance, and that infection duration was driven by CD8⁺ T cell magnitude rather than efficacy and could be significantly prolonged if the ratio of CD8⁺ T cells to infected cells was sufficiently low. These links between important pathogen kinetics and host pathology enhance our ability to forecast disease progression, potential complications, and therapeutic efficacy.

A near analytic solution of a stochastic immune response model considering variability in virus and T-cell dynamics

Biological processes at the cellular level are stochastic in nature, and the immune response system is no different. Therefore, models that attempt to explain this system need to also incorporate noise or fluctuations that can account for the observed variability. In this work, a stochastic model of the immune response system is presented in terms of the dynamics of T cells and virus particles. Making use of the Green's function and the Wilemski-Fixman approximation, this model is then solved to obtain the analytical expression for the joint probability density function of these variables in the early and late stages of infection. This is then also used to calculate the average level of virus particles in the system. Upon comparing the theoretically predicted average virus levels to those of COVID-19 patients, it is hypothesized that the long-lived dynamics that are characteristics of such viral infections are due to the long range correlations in the temporal fluctuations of the virions. This model, therefore, provides an insight into the effects of noise on viral dynamics.

Homogenization of a reaction diffusion equation can explain influenza A virus load data

We study the influence of spatial heterogeneity on the antiviral activity of mouse embryonic fibroblasts (MEF) infected with influenza A. MEF of type Ube1L^-/- are composed of two distinct sub-populations, the strong type that sustains a strong viral infection and the weak type, sustaining a weak viral load. We present new data on the virus load infection of Ube1L^-/-, which have been micro-printed in a checker board pattern of different sizes of the inner squares. Surprisingly, the total viral load at one day after inoculation significantly depends on the sizes of the inner squares. We explain this observation by using a reaction diffusion model and we show that mathematical homogenization can explain the observed inhomogeneities. If the individual patches are large, then the growth rate and the carrying capacity will be the arithmetic means of the patches. For finer and finer patches the average growth rate is still the arithmetic mean, however, the carrying capacity uses the harmonic mean. While fitting the PDE to the experimental data, we also predict that a discrepancy in virus load would be unobservable after only half a day. Furthermore, we predict the viral load in different inner squares that had not been measured in our experiment and the travelling distance the virions can reach after one day.

Mathematical modeling of ventilator-induced lung inflammation

Despite the benefits of mechanical ventilators, prolonged or misuse of ventilators may lead to ventilation-associated/ventilation-induced lung injury (VILI). Lung insults, such as respiratory infections and lung injuries, can damage the pulmonary epithelium, with the most severe cases needing mechanical ventilation for effective breathing and survival. Damaged epithelial cells within the alveoli trigger a local immune response. A key immune cell is the macrophage, which can differentiate into a spectrum of phenotypes ranging from pro- to anti-inflammatory. To gain a greater understanding of the mechanisms of the immune response to VILI and post-ventilation outcomes, we developed a mathematical model of interactions between the immune system and site of damage while accounting for macrophage phenotype. Through Latin hypercube sampling we generated a collection of parameter sets that are associated with a numerical steady state. We then simulated ventilation-induced damage using these steady state values as the initial conditions in order to evaluate how baseline immune state and lung health affect outcomes. We used a variety of methods to analyze the resulting parameter sets, transients, and outcomes, including a random forest decision tree algorithm and parameter sensitivity with eFAST. Analysis shows that parameters and properties of transients related to epithelial repair and M1 activation are important factors. Using the results of this analysis, we hypothesized interventions and used these treatment strategies to modulate the response to ventilation for particular parameters sets.

Stability analysis in COVID-19 within-host model with immune response

The 2019 coronavirus disease (COVID-19) is now a global pandemic. Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) is the causative pathogen of COVID-19. Here, we study an in-host model that highlights the effector T cell response to SARS-CoV-2. The stability of a unique positive equilibrium point, with viral load V * , suggests that the virus may replicate fast enough to overcome T cell response and cause infection. This overcoming is the bifurcation point, near which the orders of magnitude for V * can be sensitive to numerical changes in the parameter values. Our work offers a mathematical insight into how SARS-CoV-2 causes the disease.

Protective efficacy of mucosal and subcutaneous immunization with DnaJ-ΔA146Ply against influenza and Streptococcus pneumoniae co-infection in mice

Respiratory tract coinfections, specifically involving influenza A virus (IAV) and Streptococcus pneumoniae (S. pneumoniae), remain a major health problem worldwide. Secondary bacterial pneumonia is a common complication and an important cause of mortality related to seasonal and pandemic influenza infections. Vaccination is a basic control strategy against influenza and S. pneumoniae. The fusion protein DnaJ-ΔA146Ply is a vaccine candidate which can induce immune responses against pneumococcal infections via mucosal and subcutaneous immunization in mice. In the present study, we established a co-infection model using mouse-adapted laboratory strains of IAV (PR8) and S. pneumoniae (19F) in mice intranasally and subcutaneously immunized with DnaJ-ΔA146Ply. Our results showed that vaccinated mice suffered decreased weight loss compared with control mice. The survival rates were higher in intranasally and subcutaneously immunized mice than in control mice. In addition, the bacterial loads in nasal washes and lung homogenates were lower in vaccinated mice than in control mice. Furthermore, lung damage was alleviated in vaccinated mice compared with control mice, with less broken alveoli and less proinflammatory cytokine production. Taken together, these results indicate that vaccination with DnaJ-ΔA146Ply shows protective potential against influenza and S. pneumoniae co-infection in mice.

The value of infectious disease modeling and trend assessment: a public health perspective

INTRODUCTION

Disease outbreaks of acquired immunodeficiency syndrome, severe acute respiratory syndrome, pandemic H1N1, H7N9, H5N1, Ebola, Zika, Middle East respiratory syndrome, and recently COVID-19 have raised the attention of the public over the past half-century. Revealing the characteristics and epidemic trends are important parts of disease control. The biological scenarios including transmission characteristics can be constructed and translated into mathematical models, which can help to predict and gain a deeper understanding of diseases.

AREAS COVERED

This review discusses the models for infectious diseases and highlights their values in the field of public health. This information will be of interest to mathematicians and clinicians, and make a significant contribution toward the development of more specific and effective models. Literature searches were performed using the online database of PubMed (inception to August 2020).

EXPERT OPINION

Modeling could contribute to infectious disease control by means of predicting the scales of disease epidemics, indicating the characteristics of disease transmission, evaluating the effectiveness of interventions or policies, and warning or forecasting during the pre-outbreak of diseases. With the development of theories and the ability of calculations, infectious disease modeling would play a much more important role in disease prevention and control of public health.

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.

A biomathematical model of immune response and barrier function in mice with pneumococcal lung infection

Pneumonia is one of the leading causes of death worldwide. The course of the disease is often highly dynamic with unforeseen critical deterioration within hours in a relevant proportion of patients. Besides antibiotic treatment, novel adjunctive therapies are under development. Their additive value needs to be explored in preclinical and clinical studies and corresponding therapy schedules require optimization prior to introduction into clinical practice. Biomathematical modeling of the underlying disease and therapy processes might be a useful aid to support these processes. We here propose a biomathematical model of murine immune response during infection with Streptococcus pneumoniae aiming at predicting the outcome of different treatment schedules. The model consists of a number of non-linear ordinary differential equations describing the dynamics and interactions of the pulmonal pneumococcal population and relevant cells of the innate immune response, namely alveolar- and inflammatory macrophages and neutrophils. The cytokines IL-6 and IL-10 and the chemokines CCL2, CXCL1 and CXCL5 are considered as major mediators of the immune response. We also model the invasion of peripheral blood monocytes, their differentiation into macrophages and bacterial penetration through the epithelial barrier causing blood stream infections. We impose therapy effects on this system by modelling antibiotic therapy and treatment with the novel C5a-inactivator NOX-D19. All equations are derived by translating known biological mechanisms into equations and assuming appropriate response kinetics. Unknown model parameters were determined by fitting the predictions of the model to time series data derived from mice experiments with close-meshed time series of state parameters. Parameter fittings resulted in a good agreement of model and data for the experimental scenarios. The model can be used to predict the performance of alternative schedules of combined antibiotic and NOX-D19 treatment. We conclude that we established a comprehensive biomathematical model of pneumococcal lung infection, immune response and barrier function in mice allowing simulations of new treatment schedules. We aim to validate the model on the basis of further experimental data. We also plan the inclusion of further novel therapy principles and the translation of the model to the human situation in the near future.

Targeting TMPRSS2 and Cathepsin B/L together may be synergistic against SARS-CoV-2 infection

The entry of SARS-CoV-2 into target cells requires the activation of its surface spike protein, S, by host proteases. The host serine protease TMPRSS2 and cysteine proteases Cathepsin B/L can activate S, making two independent entry pathways accessible to SARS-CoV-2. Blocking the proteases prevents SARS-CoV-2 entry in vitro. This blockade may be achieved in vivo through 'repurposing' drugs, a potential treatment option for COVID-19 that is now in clinical trials. Here, we found, surprisingly, that drugs targeting the two pathways, although independent, could display strong synergy in blocking virus entry. We predicted this synergy first using a mathematical model of SARS-CoV-2 entry and dynamics in vitro. The model considered the two pathways explicitly, let the entry efficiency through a pathway depend on the corresponding protease expression level, which varied across cells, and let inhibitors compromise the efficiency in a dose-dependent manner. The synergy predicted was novel and arose from effects of the drugs at both the single cell and the cell population levels. Validating our predictions, available in vitro data on SARS-CoV-2 and SARS-CoV entry displayed this synergy. Further, analysing the data using our model, we estimated the relative usage of the two pathways and found it to vary widely across cell lines, suggesting that targeting both pathways in vivo may be important and synergistic given the broad tissue tropism of SARS-CoV-2. Our findings provide insights into SARS-CoV-2 entry into target cells and may help improve the deployability of drug combinations targeting host proteases required for the entry.

Mathematical modeling of hepatitis C RNA replication, exosome secretion and virus release

Hepatitis C virus (HCV) causes acute hepatitis C and can lead to life-threatening complications if it becomes chronic. The HCV genome is a single plus strand of RNA. Its intracellular replication is a spatiotemporally coordinated process of RNA translation upon cell infection, RNA synthesis within a replication compartment, and virus particle production. While HCV is mainly transmitted via mature infectious virus particles, it has also been suggested that HCV-infected cells can secrete HCV RNA carrying exosomes that can infect cells in a receptor independent manner. In order to gain insight into these two routes of transmission, we developed a series of intracellular HCV replication models that include HCV RNA secretion and/or virus assembly and release. Fitting our models to in vitro data, in which cells were infected with HCV, suggests that initially most secreted HCV RNA derives from intracellular cytosolic plus-strand RNA, but subsequently secreted HCV RNA derives equally from the cytoplasm and the replication compartments. Furthermore, our model fits to the data suggest that the rate of virus assembly and release is limited by host cell resources. Including the effects of direct acting antivirals in our models, we found that in spite of decreasing intracellular HCV RNA and extracellular virus concentration, low level HCV RNA secretion may continue as long as intracellular RNA is available. This may possibly explain the presence of detectable levels of plasma HCV RNA at the end of treatment even in patients that ultimately attain a sustained virologic response.

Approximately 70 million people are chronically infected with hepatitis C virus (HCV), which if left untreated may lead to cirrhosis and liver cancer. However, modern drug therapy is highly effective and hepatitis C is the first chronic virus infection that can be cured with short-term therapy in almost all infected individuals. The within-host transmission of HCV occurs mainly via infectious virus particles, but experimental studies suggest that there may be additional receptor-independent cell-to-cell transmission by exosomes that carry the HCV genome. In order to understand the intracellular HCV lifecycle and HCV RNA spread, we developed a series of mathematical models that take both exosomal secretion and viral secretion into account. By fitting these models to in vitro data, we found that secretion of both HCV RNA as well as virus probably occurs and that the rate of virus assembly is likely limited by cellular co-factors on which the virus strongly depends for its own replication. Furthermore, our modeling predicted that the parameters governing the processes in the viral lifecycle that are targeted by direct acting antivirals are the most sensitive to perturbations, which may help explain their ability to cure this infection.

In-host Mathematical Modelling of COVID-19 in Humans

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

Modelling the linkage between influenza infection and cardiovascular events via thrombosis

There is a heavy burden associated with influenza including all-cause hospitalization as well as severe cardiovascular and cardiorespiratory events. Influenza associated cardiac events have been linked to multiple biological pathways in a human host. To study the contribution of influenza virus infection to cardiovascular thrombotic events, we develop a dynamic model which incorporates some key elements of the host immune response, inflammatory response, and blood coagulation. We formulate these biological systems and integrate them into a cohesive modelling framework to show how blood clotting may be connected to influenza virus infection. With blood clot formation inside an artery resulting from influenza virus infection as the primary outcome of this integrated model, we demonstrate how blood clot severity may depend on circulating prothrombin levels. We also utilize our model to leverage clinical data to inform the threshold level of the inflammatory cytokine TNFα which initiates tissue factor induction and subsequent blood clotting. Our model provides a tool to explore how individual biological components contribute to blood clotting events in the presence of influenza infection, to identify individuals at risk of clotting based on their circulating prothrombin levels, and to guide the development of future vaccines to optimally interact with the immune system.

Chemical kinetics of the development of coronaviral infection in the human body: Critical conditions, toxicity mechanisms, "thermoheliox", and "thermovaccination"

Kinetic modeling of the behavior of complex chemical and biochemical systems is an effective approach to study of the mechanisms of the process. A kinetic model of coronaviral infection development with a description of the dynamic behavior of the main variables, including the concentration of viral particles, affected cells, and pathogenic microflora, is proposed. Changes in the concentration of hydrogen ions in the lungs and the pH -dependence of carbonic anhydrase activity (a key breathing enzyme) are critical. A significant result is the demonstration of an acute bifurcation transition that determines life or system collapse. This transition is connected with exponential growth of concentrations of the process participants and with functioning of the key enzyme carbonic anhydrase in development of toxic effects. Physical and chemical interpretations of the therapeutic effects of the body temperature rise and the potential therapeutic effect of “thermoheliox” (respiration with a thermolized mixture of helium and oxygen) are given. The phenomenon of “thermovaccination” is predicted, which involves stimulation of the immune response by “thermoheliox”.

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The proposed kinetic model describes the dynamics of coronaviral infection development.

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Acidification and pH dependence of key enzymes is discussed as a basis of viral toxicity.

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An acute bifurcation transition of the system to collapse is demonstrated.

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The theory and experimental facts of “thermoheliox” therapy are discussed.

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“Thermovaccination” by “thermoheliox” is predicted.

Influencing public health policy with data-informed mathematical models of infectious diseases: Recent developments and new challenges

Modern data and computational resources, coupled with algorithmic and theoretical advances to exploit these, allow disease dynamic models to be parameterised with increasing detail and accuracy. While this enhances models' usefulness in prediction and policy, major challenges remain. In particular, lack of identifiability of a model's parameters may limit the usefulness of the model. While lack of parameter identifiability may be resolved through incorporation into an inference procedure of prior knowledge, formulating such knowledge is often difficult. Furthermore, there are practical challenges associated with acquiring data of sufficient quantity and quality. Here, we discuss recent progress on these issues.

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

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

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

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

Trends in mathematical modeling of host-pathogen interactions

Pathogenic microorganisms entail enormous problems for humans, livestock, and crop plants. A better understanding of the different infection strategies of the pathogens enables us to derive optimal treatments to mitigate infectious diseases or develop vaccinations preventing the occurrence of infections altogether. In this review, we highlight the current trends in mathematical modeling approaches and related methods used for understanding host-pathogen interactions. Since these interactions can be described on vastly different temporal and spatial scales as well as abstraction levels, a variety of computational and mathematical approaches are presented. Particular emphasis is placed on dynamic optimization, game theory, and spatial modeling, as they are attracting more and more interest in systems biology. Furthermore, these approaches are often combined to illuminate the complexities of the interactions between pathogens and their host. We also discuss the phenomena of molecular mimicry and crypsis as well as the interplay between defense and counter defense. As a conclusion, we provide an overview of method characteristics to assist non-experts in their decision for modeling approaches and interdisciplinary understanding.

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.

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

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

Chandipura Virus Utilizes the Prosurvival Function of RelA NF-κB for Its Propagation

Chandipura virus (CHPV), a cytoplasmic RNA virus, has been implicated in several outbreaks of acute encephalitis in India. Despite the relevance of CHPV to human health, how the virus interacts with the host signaling machinery remains obscure. In response to viral infections, mammalian cells activate RelA/NF-κB heterodimers, which induce genes encoding interferon beta (IFN-β) and other immune mediators. Therefore, RelA is generally considered to be an antiviral transcription factor. However, RelA activates a wide spectrum of genes in physiological settings, and there is a paucity of direct genetic evidence substantiating antiviral RelA functions. Using mouse embryonic fibroblasts, we genetically dissected the role of RelA in CHPV pathogenesis. We found that CHPV indeed activated RelA and that RelA deficiency abrogated the expression of IFN-β in response to virus infections. Unexpectedly, infection of Rela ^-/- fibroblasts led to a decreased CHPV yield. Our investigation clarified that RelA-dependent synthesis of prosurvival factors restrained infection-inflicted cell death and that exacerbated cell death processes prevented multiplication of CHPV in RelA-deficient cells. Chikungunya virus, a cytopathic RNA virus associated also with epidemics, required RelA, and Japanese encephalitis virus, which produced relatively minor cytopathic effects in fibroblasts, circumvented the need of RelA for their propagation. In sum, we documented a proviral function of the pleiotropic factor RelA linked to its prosurvival properties. RelA promoted the growth of cytopathic RNA viruses by extending the life span of infected cells, which serve as the replicative niche of intracellular pathogens. We argue that our finding bears significance for understanding host-virus interactions and may have implications for antiviral therapeutic regimes.IMPORTANCE RelA/NF-κB participates in a wide spectrum of physiological processes, including shaping immune responses against invading pathogens. In virus-infected cells, RelA typically induces the expression of IFN-β, which restrains viral propagation in neighboring cells involving paracrine mechanisms. Our study suggested that RelA might also play a proviral role. A cell-autonomous RelA activity amplified the yield of Chandipura virus, a cytopathic RNA virus associated with human epidemics, by extending the life span of infected cells. Our finding necessitates a substantial revision of our understanding of host-virus interactions and indicates a dual role of NF-κB signaling during the course of RNA virus infections. Our study also bears significance for therapeutic regimes which alter NF-κB activities while alleviating the viral load.

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.

Healthcare professionals' queries on oseltamivir and influenza in Finland 2011-2016-Can we detect influenza epidemics with specific online searches?

BACKGROUND

Healthcare professionals (HCPs) search medical information during their clinical work using Internet sources. In Finland, Physician's Databases (PD) serve as an Internet medical portal aimed at HCPs. Influenza epidemics appear seasonal outbreaks causing public health concern. Oseltamivir can be used to treat influenza. Little is known about HCPs' queries on oseltamivir and influenza from dedicated online medical portals and whether queries could be used as an additional source of information for disease surveillance when detecting influenza epidemics.

METHODS

We compared HCPs' queries on oseltamivir and influenza from PD to influenza diagnoses from the primary healthcare register in Finland 2011-2016. The Moving Epidemic Method (MEM) calculated the starts of influenza epidemics. Laboratory reports of influenza A and influenza B were assessed. Paired differences compared queries, diagnoses, and laboratory reports by using starting weeks. Kendall's correlation test assessed the season-to-season similarity.

RESULTS

We found that PD and the primary healthcare register showed visually similar patterns annually. Paired differences in the mean showed that influenza epidemics based on queries on oseltamivir started earlier than epidemics based on diagnoses by -0.80 weeks (95% CI: -1.0, 0.0) with high correlation (τ = 0.943). Queries on influenza preceded queries on oseltamivir by -0.80 weeks (95% CI: -1.2, 0.0) and diagnoses by -1.60 weeks (95% CI: -1.8, -1.0).

CONCLUSIONS

HCPs' queries on oseltamivir and influenza from Internet medical databases correlated with register diagnoses of influenza. Therefore, they should be considered as a supplementary source of information for disease surveillance when detecting influenza epidemics.

Coupling multiscale within-host dynamics and between-host transmission with recovery (SIR) dynamics

Multiscale models that link within-host infection to between-host transmission are valuable tools to progress understanding of viral infectious diseases. In this paper, we present two multiscale models that couple within-host infection to a susceptible-infected-recovered (SIR) model. A disease-induced transmission rate bridges the scales from within to between-host. Our stability analysis on the first model (influenza infection) reveals two equilibrium points for the SIR model that describe endemic scenarios where both susceptible and infected cases maintain nonzero population sizes. Consequently, the between-host system has two bifurcations determined by the corresponding basic reproduction number of the within-host and the size of the infected population at the interior equilibrium point. Analysis on the second model (Ebola infection) reveals the limited transient inhibitory effect of antibodies on viral replication, which influences the time window from infection to a potential outbreak. Simulations numerically illustrate our results.

Adjuvanted influenza vaccine dynamics

Adjuvanted influenza vaccines constitute a key element towards inducing neutralizing antibody responses in populations with reduced responsiveness, such as infants and elderly subjects, as well as in devising antigen-sparing strategies. In particular, squalene-containing adjuvants have been observed to induce enhanced antibody responses, as well as having an influence on cross-reactive immunity. To explore the effects of adjuvanted vaccine formulations on antibody response and their relation to protein-specific immunity, we propose different mathematical models of antibody production dynamics in response to influenza vaccination. Data from ferrets immunized with commercial H1N1pdm09 vaccine antigen alone or formulated with different adjuvants was instrumental to adjust model parameters. While the affinity maturation process complexity is abridged, the proposed model is able to recapitulate the essential features of the observed dynamics. Our numerical results suggest that there exists a qualitative shift in protein-specific antibody response, with enhanced production of antibodies targeting the NA protein in adjuvanted versus non-adjuvanted formulations, in conjunction with a protein-independent boost that is over one order of magnitude larger for squalene-containing adjuvants. Furthermore, simulations predict that vaccines formulated with squalene-containing adjuvants are able to induce sustained antibody titers in a robust way, with little impact of the time interval between immunizations.