Mathematical model of a three-stage innate immune response to a pneumococcal lung infection

Clonal population expansion of Staphylococcus aureus occurs due to escape from a finite number of intraphagocyte niches

Staphylococcus aureus is a human commensal and also an opportunist pathogen causing life threatening infections. During S. aureus disease, the abscesses that characterise infection can be clonal, whereby a large bacterial population is founded by a single or few organisms. Our previous work has shown that macrophages are responsible for restricting bacterial growth such that a population bottleneck occurs and clonality can emerge. A subset of phagocytes fail to control S. aureus resulting in bacterial division, escape and founding of microabscesses that can seed other host niches. Here we investigate the basis for clonal microabscess formation, using in vitro and in silico models of S. aureus macrophage infection. Macrophages that fail to control S. aureus are characterised by formation of intracellular bacterial masses, followed by cell lysis. High-resolution microscopy reveals that most macrophages had internalised only a single S. aureus, providing a conceptual framework for clonal microabscess generation, which was supported by a stochastic individual-based, mathematical model. Once a threshold of masses was reached, increasing the number of infecting bacteria did not result in greater mass numbers, despite enhanced phagocytosis. This suggests a finite number of permissive, phagocyte niches determined by macrophage associated factors. Increased understanding of the parameters of infection dynamics provides avenues for development of rational control measures.

The multilevel hierarchical data EM-algorithm. Applications to discrete-time Markov chain epidemic models

The theory of multilevel hierarchical data Expectation Maximization (EM)-algorithm is introduced via discrete time Markov chain (DTMC) epidemic models. A general model for a multilevel hierarchical discrete data is derived. The observed sample Y in the system is a stochastic incomplete data, and the missing data Z exhibits a multilevel hierarchical data structure. The EM-algorithm to find ML-estimates for parameters in the stochastic system is derived. Applications of the EM-algorithm are exhibited in the two DTMC models, to find ML-estimates of the system parameters. Numerical results are given for influenza epidemics in the state of Georgia (GA), USA.

A simple model of COVID-19 explains disease severity and the effect of treatments

Considerable effort has been made to better understand why some people suffer from severe COVID-19 while others remain asymptomatic. This has led to important clinical findings; people with severe COVID-19 generally experience persistently high levels of inflammation, slower viral load decay, display a dysregulated type-I interferon response, have less active natural killer cells and increased levels of neutrophil extracellular traps. How these findings are connected to the pathogenesis of COVID-19 remains unclear. We propose a mathematical model that sheds light on this issue by focusing on cells that trigger inflammation through molecular patterns: infected cells carrying pathogen-associated molecular patterns (PAMPs) and damaged cells producing damage-associated molecular patterns (DAMPs). The former signals the presence of pathogens while the latter signals danger such as hypoxia or lack of nutrients. Analyses show that SARS-CoV-2 infections can lead to a self-perpetuating feedback loop between DAMP expressing cells and inflammation, identifying the inability to quickly clear PAMPs and DAMPs as the main contributor to hyperinflammation. The model explains clinical findings and reveal conditions that can increase the likelihood of desired clinical outcome from treatment administration. In particular, the analysis suggest that antivirals need to be administered early during infection to have an impact on disease severity. The simplicity of the model and its high level of consistency with clinical findings motivate its use for the formulation of new treatment strategies.

Combination of in vivo phage therapy data with in silico model highlights key parameters for pneumonia treatment efficacy

The clinical (re)development of bacteriophage (phage) therapy to treat antibiotic-resistant infections faces the challenge of understanding the dynamics of phage-bacteria interactions in the in vivo context. Here, we develop a general strategy coupling in vitro and in vivo experiments with a mathematical model to characterize the interplay between phage and bacteria during pneumonia induced by a pathogenic strain of Escherichia coli. The model allows the estimation of several key parameters for phage therapeutic efficacy. In particular, it quantifies the impact of dose and route of phage administration as well as the synergism of phage and the innate immune response on bacterial clearance. Simulations predict a limited impact of the intrinsic phage characteristics in agreement with the current semi-empirical choices of phages for compassionate treatments. Model-based approaches will foster the deployment of future phage-therapy clinical trials.

A data-driven model of the role of energy in sepsis

Exposure to pathogens elicits a complex immune response involving multiple interdependent pathways. This response may mitigate detrimental effects and restore health but, if imbalanced, can lead to negative outcomes including sepsis. This complexity and need for balance pose a challenge for clinicians and have attracted attention from modelers seeking to apply computational tools to guide therapeutic approaches. In this work, we address a shortcoming of such past efforts by incorporating the dynamics of energy production and consumption into a computational model of the acute immune response. With this addition, we performed fits of model dynamics to data obtained from non-human primates exposed to Escherichia coli. Our analysis identifies parameters that may be crucial in determining survival outcomes and also highlights energy-related factors that modulate the immune response across baseline and altered glucose conditions.

sEH promotes macrophage phagocytosis and lung clearance of Streptococcus pneumoniae

Epoxyeicosatrienoic acids (EETs) have potent antiinflammatory properties. Hydrolysis of EETs by soluble epoxide hydrolase/ epoxide hydrolase 2 (sEH/EPHX2) to less active diols attenuates their antiinflammatory effects. Macrophage activation is critical to many inflammatory responses; however, the role of EETs and sEH in regulating macrophage function remains unknown. Lung bacterial clearance of Streptococcus pneumoniae was impaired in Ephx2-deficient (Ephx2-/-) mice and in mice treated with an sEH inhibitor. The EET receptor antagonist EEZE restored lung clearance of S. pneumoniae in Ephx2-/- mice. Ephx2-/- mice had normal lung Il1b, Il6, and Tnfa expression levels and macrophage recruitment to the lungs during S. pneumoniae infection; however, Ephx2 disruption attenuated proinflammatory cytokine induction, Tlr2 and Pgylrp1 receptor upregulation, and Ras-related C3 botulinum toxin substrates 1 and 2 (Rac1/2) and cell division control protein 42 homolog (Cdc42) activation in PGN-stimulated macrophages. Consistent with these observations, Ephx2-/- macrophages displayed reduced phagocytosis of S. pneumoniae in vivo and in vitro. Heterologous overexpression of TLR2 and peptidoglycan recognition protein 1 (PGLYRP1) in Ephx2-/- macrophages restored macrophage activation and phagocytosis. Human macrophage function was similarly regulated by EETs. Together, these results demonstrate that EETs reduced macrophage activation and phagocytosis of S. pneumoniae through the downregulation of TLR2 and PGLYRP1 expression. Defining the role of EETs and sEH in macrophage function may lead to the development of new therapeutic approaches for bacterial diseases.

Iterative community-driven development of a SARS-CoV-2 tissue simulator

The 2019 novel coronavirus, SARS-CoV-2, is a pathogen of critical significance to international public health. Knowledge of the interplay between molecular-scale virus-receptor interactions, single-cell viral replication, intracellular-scale viral transport, and emergent tissue-scale viral propagation is limited. Moreover, little is known about immune system-virus-tissue interactions and how these can result in low-level (asymptomatic) infections in some cases and acute respiratory distress syndrome (ARDS) in others, particularly with respect to presentation in different age groups or pre-existing inflammatory risk factors. Given the nonlinear interactions within and among each of these processes, multiscale simulation models can shed light on the emergent dynamics that lead to divergent outcomes, identify actionable "choke points" for pharmacologic interventions, screen potential therapies, and identify potential biomarkers that differentiate patient outcomes. Given the complexity of the problem and the acute need for an actionable model to guide therapy discovery and optimization, we introduce and iteratively refine a prototype of a multiscale model of SARS-CoV-2 dynamics in lung tissue. The first prototype model was built and shared internationally as open source code and an online interactive model in under 12 hours, and community domain expertise is driving regular refinements. In a sustained community effort, this consortium is integrating data and expertise across virology, immunology, mathematical biology, quantitative systems physiology, cloud and high performance computing, and other domains to accelerate our response to this critical threat to international health. More broadly, this effort is creating a reusable, modular framework for studying viral replication and immune response in tissues, which can also potentially be adapted to related problems in immunology and immunotherapy.

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 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.

Mathematical modeling of ventilator-induced lung inflammation

Respiratory infections, such as the novel coronavirus (SARS-COV-2) and other lung injuries, damage the pulmonary epithelium. In the most severe cases this leads to acute respiratory distress syndrome (ARDS). Due to respiratory failure associated with ARDS, the clinical intervention is the use of mechanical ventilation. Despite the benefits of mechanical ventilators, prolonged or misuse of these ventilators may lead to ventilation-associated/ventilation-induced lung injury (VILI). Damage caused to epithelial cells within the alveoli can lead to various types of complications and increased mortality rates. A key component of the immune response is recruitment of macrophages, immune cells that differentiate into phenotypes with unique pro- and/or anti-inflammatory roles based on the surrounding environment. An imbalance in pro- and anti-inflammatory responses can have deleterious effects on the individual's health. To gain a greater understanding of the mechanisms of the immune response to VILI and post-ventilation outcomes, we develop a mathematical model of interactions between the immune system and site of damage while accounting for macrophage polarization. Through Latin hypercube sampling we generate a virtual cohort of patients with biologically feasible dynamics. We use a variety of methods to analyze the results, 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 and de-activation best predicted outcome. Using this new information, we hypothesize inter-ventions and use these treatment strategies to modulate damage in select virtual cases.

Within-host mechanisms of immune regulation explain the contrasting dynamics of two helminth species in both single and dual infections

Variation in the intensity and duration of infections is often driven by variation in the network and strength of host immune responses. While many of the immune mechanisms and components are known for parasitic helminths, how these relationships change from single to multiple infections and impact helminth dynamics remains largely unclear. Here, we used laboratory data from a rabbit-helminth system and developed a within-host model of infection to investigate different scenarios of immune regulation in rabbits infected with one or two helminth species. Model selection suggests that the immunological pathways activated against Trichostrongylus retortaeformis and Graphidium strigosum are similar. However, differences in the strength of these immune signals lead to the contrasting dynamics of infections, where the first parasite is rapidly cleared and the latter persists with high intensities. In addition to the reactions identified in single infections, rabbits with both helminths also activate new pathways that asymmetrically affect the dynamics of the two species. These new signals alter the intensities but not the general trend of the infections. The type of interactions described can be expected in many other host-helminth systems. Our immune framework is flexible enough to capture different mechanisms and their complexity, and provides essential insights to the understanding of multi-helminth infections.

Modified kinetics of generation of reactive species in peripheral blood of patients with type 2 diabetes

Level of reactive species in blood is an important pathogenic factor in diabetes mellitus leading to dysfunctions of vascular endothelial and smooth muscle cells and coagulation system abnormality. A massive release of reactive species (respiratory burst), catalyzed by NADPH oxidase in blood phagocytes, is not well understood in diabetes. The work aimed to study kinetics of response to microbial particles in blood to specify changes in regulatory mechanisms of generation of reactive species in patients with type 2 diabetes. Production of reactive species in blood and isolated granulocytes was measured by luminol-dependent chemiluminescence. Respiratory burst was initiated by serum opsonized zymosan in blood samples and phorbol ester in cell samples. Kinetic parameters were calculated from experimental kinetic curves of chemiluminescence intensity. ROC curve analysis and mathematical modeling were used to reveal the most significant predictors and clarify specific mechanisms of NADPH oxidase activation. It was shown that kinetic parameters of response to opsonized zymosan (lag-time, response rate, amplitude, production of reactive species) were higher in blood of patients than controls. Amplitude and response rate were the most statistically significant predictors for distinguishing patients and controls at high glucose. It indicated NADPH oxidase activation was the target of hyperglycemia. Mathematical modeling showed hyperglycemia increased stability of NADPH oxidase complex, decreased synchronization of its assembling and elevated neutrophil capacity to phagocytosis in patients. Weak or no dependence of response kinetics on ionomycin concentration was shown in patients indicating changed Ca²⁺-dependent mechanism of NADPH oxidase activation. Hyperglycemia in type 2 diabetes causes disturbances in mechanisms of NADPH oxidase activation associated with both phagocytosis and the state of intracellular signaling systems, including Ca²⁺-dependent. We suggest that NADPH oxidase in blood granulocytes can be a promising target for clinical intervention improving management of diabetic complications associated with inflammation.

Modelling within-host macrophage dynamics in influenza virus infection

Human respiratory disease associated with influenza virus infection is of significant public health concern. Macrophages, as part of the front line of host innate cellular defence, have been shown to play an important role in controlling viral replication. However, fatal outcomes of infection, as evidenced in patients infected with highly pathogenic viral strains, are often associated with prompt activation and excessive accumulation of macrophages. Activated macrophages can produce a large amount of pro-inflammatory cytokines, which leads to severe symptoms and at times death. However, the mechanism for rapid activation and excessive accumulation of macrophages during infection remains unclear. It has been suggested that the phenomena may arise from complex interactions between macrophages and influenza virus. In this work, we develop a novel mathematical model to study the relationship between the level of macrophage activation and the level of viral load in influenza infection. Our model combines a dynamic model of viral infection, a dynamic model of macrophages and the essential interactions between the virus and macrophages. Our model predicts that the level of macrophage activation can be negatively correlated with the level of viral load when viral infectivity is sufficiently high. We further identify that temporary depletion of resting macrophages in response to viral infection is a major driver in our model for the negative relationship between the level of macrophage activation and viral load, providing new insight into the mechanisms that regulate macrophage activation. Our model serves as a framework to study the complex dynamics of virus-macrophage interactions and provides a mechanistic explanation for existing experimental observations, contributing to an enhanced understanding of the role of macrophages in influenza viral infection.

A mathematical model shows macrophages delay Staphylococcus aureus replication, but limitations in microbicidal capacity restrict bacterial clearance

S. aureus is a leading cause of bacterial infection. Macrophages, the first line of defence in the human immune response, phagocytose and kill S. aureus but the pathogen can evade these responses. Therefore, the exact role of macrophages is incompletely defined. We develop a mathematical model of macrophage - S. aureus dynamics, built on recent experimental data. We demonstrate that, while macrophages may not clear infection, they significantly delay its growth and potentially buy time for recruitment of further cells. We find that macrophage killing is a major obstacle to controlling infection and ingestion capacity also limits the response. We find bistability such that the infection can be limited at low doses. Our combination of experimental data, mathematical analysis and model fitting provide important insights in to the early stages of S. aureus infections, showing macrophages play an important role limiting bacterial replication but can be overwhelmed with large inocula.

Topological data analysis to model the shape of immune responses during co-infections

Co-infections by multiple pathogens have important implications in many aspects of health, epidemiology and evolution. However, how to disentangle the non-linear dynamics of the immune response when two infections take place at the same time is largely unexplored. Using data sets of the immune response during influenza-pneumococcal co-infection in mice, we employ here topological data analysis to simplify and visualise high dimensional data sets. We identified persistent shapes of the simplicial complexes of the data in the three infection scenarios: single viral infection, single bacterial infection, and co-infection. The immune response was found to be distinct for each of the infection scenarios and we uncovered that the immune response during the co-infection has three phases and two transition points. During the first phase, its dynamics is inherited from its response to the primary (viral) infection. The immune response has an early shift (few hours post co-infection) and then modulates its response to react against the secondary (bacterial) infection. Between 18 and 26 h post co-infection the nature of the immune response changes again and does no longer resembles either of the single infection scenarios.

Quantifying the Role of Stochasticity in the Development of Autoimmune Disease

In this paper, we propose and analyse a mathematical model for the onset and development of autoimmune disease, with particular attention to stochastic effects in the dynamics. Stability analysis yields parameter regions associated with normal cell homeostasis, or sustained periodic oscillations. Variance of these oscillations and the effects of stochastic amplification are also explored. Theoretical results are complemented by experiments, in which experimental autoimmune uveoretinitis (EAU) was induced in B10.RIII and C57BL/6 mice. For both cases, we discuss peculiarities of disease development, the levels of variation in T cell populations in a population of genetically identical organisms, as well as a comparison with model outputs.

Mechanisms and Points of Control in the Spread of Inflammation: A Mathematical Investigation

Understanding the mechanisms that control the body’s response to inflammation is of key importance, due to its involvement in myriad medical conditions, including cancer, arthritis, Alzheimer’s disease and asthma. While resolving inflammation has historically been considered a passive process, since the turn of the century the hunt for novel therapeutic interventions has begun to focus upon active manipulation of constituent mechanisms, particularly involving the roles of apoptosing neutrophils, phagocytosing macrophages and anti-inflammatory mediators. Moreover, there is growing interest in how inflammatory damage can spread spatially due to the motility of inflammatory mediators and immune cells. For example, impaired neutrophil chemotaxis is implicated in causing chronic inflammation under trauma and in ageing, while neutrophil migration is an attractive therapeutic target in ailments such as chronic obstructive pulmonary disease. We extend an existing homogeneous model that captures interactions between inflammatory mediators, neutrophils and macrophages to incorporate spatial behaviour. Through bifurcation analysis and numerical simulation, we show that spatially inhomogeneous outcomes can present close to the switch from bistability to guaranteed resolution in the corresponding homogeneous model. Finally, we show how aberrant spatial mechanisms can play a role in the failure of inflammation to resolve and discuss our results within the broader context of seeking novel inflammatory treatments.

Modeling Early Stages of Bone and Joint Infections Dynamics in Humans: A Multi-Agent, Multi-System Based Model

Diagnosis and management of bone and joint infections (BJI) is a challenging task. The high intra and inter patient's variability in terms of clinical presentation makes it impossible to rely on a systematic description or classical statistical analysis for its diagnosis. Advances can be achieved through a better understanding of the system behavior that results from the interactions between the components at a micro-scale level, which is difficult to mastered using traditional methods. Multiple studies from the literature report factors and interactions that affect the dynamics of the BJI system. The objectives of this study were (i) to perform a systematic review to identify relevant interactions between agents (cells, pathogens) and parameters values that characterize agents and interactions, and (ii) to develop a two dimensional computational model of the BJI system based on the results of the systematic review. The model would simulate the behavior resulting from the interactions on the cellular and molecular levels to explore the BJI dynamics, using an agent-based modeling approach. The BJI system's response to different microbial inoculum levels was simulated. The model succeeded in mimicking the dynamics of bacteria, the innate immune cells, and the bone mass during the first stage of infection and for different inoculum levels in a consistent manner. The simulation displayed the destruction in bone tissue as a result of the alteration in bone remodeling process during the infection. The model was used to generate different patterns of system behaviors that could be analyzed in further steps. Simulations results suggested evidence for the existence of latent infections. Finally, we presented a way to analyze and synthesize massive simulated data in a concise and comprehensive manner based on the semi-supervised identification of ordinary differential equations (ODE) systems. It allows to use the known framework for temporal and structural ODE analyses and therefore summarize the whole simulated system dynamical behavior. This first model is intended to be validated by in vivo or in vitro data and expected to generate hypotheses to be challenged by real data. Step by step, it can be modified and complexified based on the test/validation iteration cycles.

Complex Stability and an Irrevertible Transition Reverted by Peptide and Fibroblasts in a Dynamic Model of Innate Immunity

We here apply a control analysis and various types of stability analysis to an in silico model of innate immunity that addresses the management of inflammation by a therapeutic peptide. Motivation is the observation, both in silico and in experiments, that this therapy is not robust. Our modeling results demonstrate how (1) the biological phenomena of acute and chronic modes of inflammation may reflect an inherently complex bistability with an irrevertible flip between the two modes, (2) the chronic mode of the model has stable, sometimes unique, steady states, while its acute-mode steady states are stable but not unique, (3) as witnessed by TNF levels, acute inflammation is controlled by multiple processes, whereas its chronic-mode inflammation is only controlled by TNF synthesis and washout, (4) only when the antigen load is close to the acute mode's flipping point, many processes impact very strongly on cells and cytokines, (5) there is no antigen exposure level below which reduction of the antigen load alone initiates a flip back to the acute mode, and (6) adding healthy fibroblasts makes the transition from acute to chronic inflammation revertible, although (7) there is a window of antigen load where such a therapy cannot be effective. This suggests that triple therapies may be essential to overcome chronic inflammation. These may comprise (1) anti-immunoglobulin light chain peptides, (2) a temporarily reduced antigen load, and (3a) fibroblast repopulation or (3b) stem cell strategies.

A Whole-Body Mathematical Model of Sepsis Progression and Treatment Designed in the BioGears Physiology Engine

Sepsis is a debilitating condition associated with a high mortality rate that greatly strains hospital resources. Though advances have been made in improving sepsis diagnosis and treatment, our understanding of the disease is far from complete. Mathematical modeling of sepsis has the potential to explore underlying biological mechanisms and patient phenotypes that contribute to variability in septic patient outcomes. We developed a comprehensive, whole-body mathematical model of sepsis pathophysiology using the BioGears Engine, a robust open-source virtual human modeling project. We describe the development of a sepsis model and the physiologic response within the BioGears framework. We then define and simulate scenarios that compare sepsis treatment regimens. As such, we demonstrate the utility of this model as a tool to augment sepsis research and as a training platform to educate medical staff.

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.

Modelling the in-host dynamics of Neisseria gonorrhoeae infection

The bacterial species Neisseria gonorrhoeae (NG) has evolved to replicate effectively and exclusively in human epithelia, with its survival dependent on complex interactions between bacteria, host cells and antimicrobial agents. A better understanding of these interactions is needed to inform development of new approaches to gonorrhoea treatment and prevention but empirical studies have proven difficult, suggesting a role for mathematical modelling. Here, we describe an in-host model of progression of untreated male symptomatic urethral infection, including NG growth and interactions with epithelial cells and neutrophils, informed by in vivo and in vitro studies. The model reproduces key observations on bacterial load and clearance and we use multivariate sensitivity analysis to refine plausible ranges for model parameters. Model variants are also shown to describe mouse infection dynamics with altered parameter ranges that correspond to observed differences between human and mouse infection. Our results highlight the importance of NG internalisation, particularly within neutrophils, in sustaining infection in the human model, with ∼80% of the total NG population internalised from day 25 on. This new mechanistic model of in-host NG infection dynamics should also provide a platform for future studies relating to antimicrobial treatment and resistance and infection at other anatomical sites.

A mathematical model of the use of supplemental oxygen to combat surgical site infection

Infections are a common complication of any surgery, often requiring a recovery period in hospital. Supplemental oxygen therapy administered during and immediately after surgery is thought to enhance the immune response to bacterial contamination. However, aerobic bacteria thrive in oxygen-rich environments, and so it is unclear whether oxygen has a net positive effect on recovery. Here, we develop a mathematical model of post-surgery infection to investigate the efficacy of supplemental oxygen therapy on surgical-site infections. A 4-species, coupled, set of non-linear partial differential equations that describes the space-time dependence of neutrophils, bacteria, chemoattractant and oxygen is developed and analysed to determine its underlying properties. Through numerical solutions, we quantify the efficacy of different supplemental oxygen regimes on the treatment of surgical site infections in wounds of different initial bacterial load. A sensitivity analysis is performed to investigate the robustness of the predictions to changes in the model parameters. The numerical results are in good agreement with analyses of the associated well-mixed model. Our model findings provide insight into how the nature of the contaminant and its initial density influence bacterial infection dynamics in the surgical wound.

Risk Analysis Implications of Dose-Response Thresholds for NLRP3 Inflammasome-Mediated Diseases: Respirable Crystalline Silica and Lung Cancer as an Example

Chronic inflammation mediates an extraordinarily wide range of diseases. Recent progress in understanding intracellular inflammasome assembly, priming, activation, cytokine signaling, and interactions with mitochondrial reactive oxygen species, lysosome disruption, cell death, and prion-like polymerization and spread of inflammasomes among cells, has potentially profound implications for dose-response modeling. This article discusses mechanisms of exposure concentration and duration thresholds for NOD-like receptor protein 3 (NLRP3)-mediated inflammatory responses and develops a simple biomathematical model of the onset of exposure-related tissue-level chronic inflammation and resulting disease risks, focusing on respirable crystalline silica (RCS) and lung cancer risk as an example. An inflammation-mediated 2-stage clonal expansion model of RCS-induced lung cancer is proposed that explains why relatively low estimated concentrations of RCS (eg, <1 mg/m³) do not increase lung cancer risk and why even high occupational concentrations increase risk only modestly (typically relative risk <2). The model of chronic inflammation implies a dose-response threshold for excess cancer risk, in contrast to traditional linear-no-threshold assumptions. If this implication is correct, then concentrations of crystalline silica (or amphibole asbestos fibers, or other environmental challenges that act via the NLRP3 inflammasome) below the threshold do not cause chronic inflammation and resulting elevated risks of inflammation-mediated diseases.

A non-linear mixed effect model for innate immune response: In vivo kinetics of endotoxin and its induction of the cytokines tumor necrosis factor alpha and interleukin-6

Endotoxin, a component of the outer membrane of Gram-negative bacteria, has been extensively studied as a stimulator of the innate immune response. However, the temporal aspects and exposure-response relationship of endotoxin and resulting cytokine induction and tolerance development is less well defined. The aim of this work was to establish an in silico model that simultaneously captures and connects the in vivo time-courses of endotoxin, tumor necrosis factor alpha (TNF-α), interleukin-6 (IL-6), and associated tolerance development. Data from six studies of porcine endotoxemia in anesthetized piglets (n = 116) were combined and used in the analysis, with purified endotoxin (Escherichia coli O111:B4) being infused intravenously for 1–30 h in rates of 0.063–16.0 μg/kg/h across studies. All data were modelled simultaneously by means of importance sampling in the non-linear mixed effects modelling software NONMEM. The infused endotoxin followed one-compartment disposition and non-linear elimination, and stimulated the production of TNF-α to describe the rapid increase in plasma concentration. Tolerance development, observed as declining TNF-α concentration with continued infusion of endotoxin, was also driven by endotoxin as a concentration-dependent increase in the potency parameter related to TNF-α production (EC₅₀). Production of IL-6 was stimulated by both endotoxin and TNF-α, and four consecutive transit compartments described delayed increase in plasma IL-6. A model which simultaneously account for the time-courses of endotoxin and two immune response markers, the cytokines TNF-α and IL-6, as well as the development of endotoxin tolerance, was successfully established. This model-based approach is unique in its description of the time-courses and their interrelation and may be applied within research on immune response to bacterial endotoxin, or in pre-clinical pharmaceutical research when dealing with study design or translational aspects.

A review of inflammatory mechanism in airway diseases

BACKGROUND

Inflammation in the lung is the body's natural response to injury. It acts to remove harmful stimuli such as pathogens, irritants, and damaged cells and initiate the healing process. Acute and chronic pulmonary inflammation are seen in different respiratory diseases such as; acute respiratory distress syndrome, chronic obstructive pulmonary disease (COPD), asthma, and cystic fibrosis (CF).

FINDINGS

In this review, we found that inflammatory response in COPD is determined by the activation of epithelial cells and macrophages in the respiratory tract. Epithelial cells and macrophages discharge transforming growth factor-β (TGF-β), which trigger fibroblast proliferation and tissue remodeling. Asthma leads to airway hyper-responsiveness, obstruction, mucus hyper-production, and airway-wall remodeling. Cytokines, allergens, chemokines, and infectious agents are the main stimuli that activate signaling pathways in epithelial cells in asthma. Mutation of the CF transmembrane conductance regulator (CFTR) gene results in CF. Mutations in CFTR influence the lung epithelial innate immune function that leads to exaggerated and ineffective airway inflammation that fails to abolish pulmonary pathogens. We present mechanistic computational models (based on ordinary differential equations, partial differential equations and agent-based models) that have been applied in studying the complex physiological and pathological mechanisms of chronic inflammation in different airway diseases.

CONCLUSION

The scope of the present review is to explore the inflammatory mechanism in airway diseases and highlight the influence of aging on airways' inflammation mechanism. The main goal of this review is to encourage research collaborations between experimentalist and modelers to promote our understanding of the physiological and pathological mechanisms that control inflammation in different airway diseases.

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.

Mechanism-Based Disease Progression Model Describing Host-Pathogen Interactions During the Pathogenesis of Acinetobacter baumannii Pneumonia

The emergence of highly resistant bacteria is a serious threat to global public health. The host immune response is vital for clearing bacteria from the infected host; however, the current drug development paradigm does not take host‐pathogen interactions into consideration. Here, we used a systems‐based approach to develop a quantitative, mechanism‐based disease progression model to describe bacterial dynamics, host immune response, and lung injury in an immunocompetent rat pneumonia model. Previously, Long‐Evans rats were infected with Acinetobacter baumannii (A. baumannii) strain 307‐0294 at five different inocula and total lung bacteria, interleukin‐1beta (IL‐1β), tumor necrosis factor‐α (TNF‐α), cytokine‐induced neutrophil chemoattractant 1 (CINC‐1), neutrophil counts, and albumin were quantified. Model development was conducted in ADAPT5 version 5.0.54 using a pooled approach with maximum likelihood estimation; all data were co‐modeled. The final model characterized host‐pathogen interactions during the natural time course of bacterial pneumonia. Parameters were estimated with good precision. Our expandable model will integrate drug effects to aid in the design of optimized antibiotic regimens.

Influenza Virus Infection Model With Density Dependence Supports Biphasic Viral Decay

Mathematical models that describe infection kinetics help elucidate the time scales, effectiveness, and mechanisms underlying viral growth and infection resolution. For influenza A virus (IAV) infections, the standard viral kinetic model has been used to investigate the effect of different IAV proteins, immune mechanisms, antiviral actions, and bacterial coinfection, among others. We sought to further define the kinetics of IAV infections by infecting mice with influenza A/PR8 and measuring viral loads with high frequency and precision over the course of infection. The data highlighted dynamics that were not previously noted, including viral titers that remain elevated for several days during mid-infection and a sharp 4–5 log₁₀ decline in virus within 1 day as the infection resolves. The standard viral kinetic model, which has been widely used within the field, could not capture these dynamics. Thus, we developed a new model that could simultaneously quantify the different phases of viral growth and decay with high accuracy. The model suggests that the slow and fast phases of virus decay are due to the infected cell clearance rate changing as the density of infected cells changes. To characterize this model, we fit the model to the viral load data, examined the parameter behavior, and connected the results and parameters to linear regression estimates. The resulting parameters and model dynamics revealed that the rate of viral clearance during resolution occurs 25 times faster than the clearance during mid-infection and that small decreases to this rate can significantly prolong the infection. This likely reflects the high efficiency of the adaptive immune response. The new model provides a well-characterized representation of IAV infection dynamics, is useful for analyzing and interpreting viral load dynamics in the absence of immunological data, and gives further insight into the regulation of viral control.

Development of a Computational Model of Abscess Formation

In some bacterial infections, the immune system cannot eliminate the invading pathogen. In these cases, the invading pathogen is successful in establishing a favorable environment to survive and persist in the host organism. For example, S. aureus bacteria survive in organ tissues employing a set of mechanisms that work in a coordinated and highly regulated way allowing: (1) efficient impairment of the immune response; and (2) protection from the immune cells and molecules. S. aureus secretes several proteins including coagulases and toxins that drive abscess formation and persistence. Unless staphylococcal abscesses are surgically drained and treated with antibiotics, disseminated infection and septicemia produce a lethal outcome. Within this context, this paper develops a simple mathematical model of abscess formation incorporating characteristics that we judge important for an abscess to be formed. Our aim is to build a mathematical model that reproduces some characteristics and behaviors that are observed in the process of abscess formation.

THE MATHEMATICAL ANALYSIS OF THE MODEL OF ANTIBIOTIC-RESISTANT BACTERIA AND THE IMMUNE CELLS

Currently, World Health Organization (WHO) report confirms that the antibiotic-resistant infections are the greatest threat to health. Despite the new therapeutic strategies, the bacteria develop mechanisms to defend themselves against antibiotics. In this paper, we propose a mathematical model describing the dynamics of resistant bacteria, non-resistant bacteria and immune cells exposed to an antibiotic. The global stability of equilibria is performed by using Lyapunov functions.

A model for the optimization of anti-inflammatory treatment with chemerin

Routine treatment of mild to moderate pain with a combination of non-steroidal anti-inflammatory drugs such as paracetamol in combination with corticoid opioids can lead to severe complications including death from gastrointestinal injury or to drug dependence. There is a need for the development of new safer drugs. Chemerin is a mediator promoting resolution of inflammation and it is then a promising candidate for a new treatment. A pilot experimental work using the zymosan-induced peritonitis model has found that injecting extra chemerin resulted in an approximately 1% reduction in the total number of inflammatory cells recruited. This paper combines and adapts existing mathematical models of inflammation to reproduce these results and to explore the therapeutic potential of chemerin through simulations. Analysis of the model predicts that the injection of chemerin at a concentration of 2000 ng ml^-1 within the first 5 min of inflammation onset leads to maximal inflammation inhibition. The degree of inhibition is shown to be sensitive to data used for the fit with a mean inhibition of 22 ± 3.7% for a series of remove-one bootstrap tests, whereas optimal chemerin injection parameters were not. Overall sensitivity analysis identifies parameters of the model that need to be measured more accurately or with increased sampling rate to improve model robustness and confirm chemerin's therapeutic potential.

Multiplicity of Mathematical Modeling Strategies to Search for Molecular and Cellular Insights into Bacteria Lung Infection

Even today two bacterial lung infections, namely pneumonia and tuberculosis, are among the 10 most frequent causes of death worldwide. These infections still lack effective treatments in many developing countries and in immunocompromised populations like infants, elderly people and transplanted patients. The interaction between bacteria and the host is a complex system of interlinked intercellular and the intracellular processes, enriched in regulatory structures like positive and negative feedback loops. Severe pathological condition can emerge when the immune system of the host fails to neutralize the infection. This failure can result in systemic spreading of pathogens or overwhelming immune response followed by a systemic inflammatory response. Mathematical modeling is a promising tool to dissect the complexity underlying pathogenesis of bacterial lung infection at the molecular, cellular and tissue levels, and also at the interfaces among levels. In this article, we introduce mathematical and computational modeling frameworks that can be used for investigating molecular and cellular mechanisms underlying bacterial lung infection. Then, we compile and discuss published results on the modeling of regulatory pathways and cell populations relevant for lung infection and inflammation. Finally, we discuss how to make use of this multiplicity of modeling approaches to open new avenues in the search of the molecular and cellular mechanisms underlying bacterial infection in the lung.

Mathematical modeling of postcoinfection with influenza A virus and Streptococcus pneumoniae, with implications for pneumonia and COPD-risk assessment

Background

The interaction between influenza and pneumococcus is important for understanding how coinfection may exacerbate pneumonia. Secondary pneumococcal pneumonia associated with influenza infection is more likely to increase respiratory morbidity and mortality. This study aimed to assess exacerbated inflammatory effects posed by secondary pneumococcal pneumonia, given prior influenza infection.

Materials and methods

A well-derived mathematical within-host dynamic model of coinfection with influenza A virus and Streptococcus pneumoniae (SP) integrated with dose–response relationships composed of previously published mouse experimental data and clinical studies was implemented to study potentially exacerbated inflammatory responses in pneumonia based on a probabilistic approach.

Results

We found that TNFα is likely to be the most sensitive biomarker reflecting inflammatory response during coinfection among three explored cytokines. We showed that the worst inflammatory effects would occur at day 7 SP coinfection, with risk probability of 50% (likely) to develop severe inflammatory responses. Our model also showed that the day of secondary SP infection had much more impact on the severity of inflammatory responses in pneumonia compared to the effects caused by initial virus titers and bacteria loads.

Conclusion

People and health care workers should be wary of secondary SP infection on day 7 post-influenza infection for prompt and proper control-measure implementation. Our quantitative risk-assessment framework can provide new insights into improvements in respiratory health especially, predominantly due to chronic obstructive pulmonary disease (COPD).

Mathematical Modeling of Streptococcus pneumoniae Colonization, Invasive Infection and Treatment

Streptococcus pneumoniae (Sp) is a commensal bacterium that normally resides on the upper airway epithelium without causing infection. However, factors such as co-infection with influenza virus can impair the complex Sp-host interactions and the subsequent development of many life-threatening infectious and inflammatory diseases, including pneumonia, meningitis or even sepsis. With the increased threat of Sp infection due to the emergence of new antibiotic resistant Sp strains, there is an urgent need for better treatment strategies that effectively prevent progression of disease triggered by Sp infection, minimizing the use of antibiotics. The complexity of the host-pathogen interactions has left the full understanding of underlying mechanisms of Sp-triggered pathogenesis as a challenge, despite its critical importance in the identification of effective treatments. To achieve a systems-level and quantitative understanding of the complex and dynamically-changing host-Sp interactions, here we developed a mechanistic mathematical model describing dynamic interplays between Sp, immune cells, and epithelial tissues, where the host-pathogen interactions initiate. The model serves as a mathematical framework that coherently explains various in vitro and in vitro studies, to which the model parameters were fitted. Our model simulations reproduced the robust homeostatic Sp-host interaction, as well as three qualitatively different pathogenic behaviors: immunological scarring, invasive infection and their combination. Parameter sensitivity and bifurcation analyses of the model identified the processes that are responsible for qualitative transitions from healthy to such pathological behaviors. Our model also predicted that the onset of invasive infection occurs within less than 2 days from transient Sp challenges. This prediction provides arguments in favor of the use of vaccinations, since adaptive immune responses cannot be developed de novo in such a short time. We further designed optimal treatment strategies, with minimal strengths and minimal durations of antibiotics, for each of the three pathogenic behaviors distinguished by our model. The proposed mathematical framework will help to design better disease management strategies and new diagnostic markers that can be used to inform the most appropriate patient-specific treatment options.

A Critical, Nonlinear Threshold Dictates Bacterial Invasion and Initial Kinetics During Influenza

Secondary bacterial infections increase morbidity and mortality of influenza A virus (IAV) infections. Bacteria are able to invade due to virus-induced depletion of alveolar macrophages (AMs), but this is not the only contributing factor. By analyzing a kinetic model, we uncovered a nonlinear initial dose threshold that is dependent on the amount of virus-induced AM depletion. The threshold separates the growth and clearance phenotypes such that bacteria decline for dose-AM depletion combinations below the threshold, stay constant near the threshold, and increase above the threshold. In addition, the distance from the threshold correlates to the growth rate. Because AM depletion changes throughout an IAV infection, the dose requirement for bacterial invasion also changes accordingly. Using the threshold, we found that the dose requirement drops dramatically during the first 7d of IAV infection. We then validated these analytical predictions by infecting mice with doses below or above the predicted threshold over the course of IAV infection. These results identify the nonlinear way in which two independent factors work together to support successful post-influenza bacterial invasion. They provide insight into coinfection timing, the heterogeneity in outcome, the probability of acquiring a coinfection, and the use of new therapeutic strategies to combat viral-bacterial coinfections.

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

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

Systems Medicine for Lung Diseases: Phenotypes and Precision Medicine in Cancer, Infection, and Allergy

Lung diseases cause an enormous socioeconomic burden. Four of them are among the ten most important causes of deaths worldwide: Pneumonia has the highest death toll of all infectious diseases, lung cancer kills the most people of all malignant proliferative disorders, chronic obstructive pulmonary disease (COPD) ranks third in mortality among the chronic noncommunicable diseases, and tuberculosis is still one of the most important chronic infectious diseases. Despite all efforts, for example, by the World Health Organization and clinical and experimental researchers, these diseases are still highly prevalent and harmful. This is in part due to the specific organization of tissue homeostasis, architecture, and immunity of the lung. Recently, several consortia have formed and aim to bring together clinical and molecular data from big cohorts of patients with lung diseases with novel experimental setups, biostatistics, bioinformatics, and mathematical modeling. This "systems medicine" concept will help to match the different disease modalities with adequate therapeutic and possibly preventive strategies for individual patients in the sense of precision medicine.

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

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

Quantifying the therapeutic requirements and potential for combination therapy to prevent bacterial coinfection during influenza

Secondary bacterial infections (SBIs) exacerbate influenza-associated disease and mortality. Antimicrobial agents can reduce the severity of SBIs, but many have limited efficacy or cause adverse effects. Thus, new treatment strategies are needed. Kinetic models describing the infection process can help determine optimal therapeutic targets, the time scale on which a drug will be most effective, and how infection dynamics will change under therapy. To understand how different therapies perturb the dynamics of influenza infection and bacterial coinfection and to quantify the benefit of increasing a drug's efficacy or targeting a different infection process, I analyzed data from mice treated with an antiviral, an antibiotic, or an immune modulatory agent with kinetic models. The results suggest that antivirals targeting the viral life cycle are most efficacious in the first 2 days of infection, potentially because of an improved immune response, and that increasing the clearance of infected cells is important for treatment later in the infection. For a coinfection, immunotherapy could control low bacterial loads with as little as 20 % efficacy, but more effective drugs would be necessary for high bacterial loads. Antibiotics targeting bacterial replication and administered 10 h after infection would require 100 % efficacy, which could be reduced to 40 % with prophylaxis. Combining immunotherapy with antibiotics could substantially increase treatment success. Taken together, the results suggest when and why some therapies fail, determine the efficacy needed for successful treatment, identify potential immune effects, and show how the regulation of underlying mechanisms can be used to design new therapeutic strategies.

Mathematical Model of an Innate Immune Response to Cutaneous Wound in the Presence of Local Hypoxia

We developed a 2D multi-agent stochastic model of interaction between cellular debris, bacteria and neutrophils in the surface cutaneous wound with local hypoxia. Bacteria, which grow logistically with a maximum carrying capacity, and debris are phagocytosed by neutrophils with probability determined by the partial pressure of oxygen in the tissue, pO 2  = 4-400 mmHg, according to the Michaelis-Menten equation with K m  = 40 mmHg. The influx of new neutrophils depends linearly (k = 0.05-0.2) on the amount of (a) platelets and (b) neutrophils, which are in contact with bacteria or debris. Each activated neutrophil can accomplish a certain amount of phagocytosis, n max  = 5-20, during its lifespan, T = 1-5 days. The universe of outcomes consists of (a) bacteria clearance (high k and n max ), (b) infection is not cleared by neutrophils (low k and nmax), and (c) intermittent (quasiperiodic) bursts of inflammation. In the absence of infection, phagocytosis stops within 48 h. We found that pO 2 alone did not change the type of outcome, but affects the number of recruited neutrophils and inflammation duration (in the absence of infection by up to 10 and 5 %, respectively).

A Biomathematical Model of Pneumococcal Lung Infection and Antibiotic Treatment in Mice

Pneumonia is considered to be one of the leading causes of death worldwide. The outcome depends on both, proper antibiotic treatment and the effectivity of the immune response of the host. However, due to the complexity of the immunologic cascade initiated during infection, the latter cannot be predicted easily. We construct a biomathematical model of the murine immune response during infection with pneumococcus aiming at predicting the outcome of antibiotic treatment. The model consists of a number of non-linear ordinary differential equations describing dynamics of pneumococcal population, the inflammatory cytokine IL-6, neutrophils and macrophages fighting the infection and destruction of alveolar tissue due to pneumococcus. Equations were derived by translating known biological mechanisms and assuming certain response kinetics. Antibiotic therapy is modelled by a transient depletion of bacteria. Unknown model parameters were determined by fitting the predictions of the model to data sets derived from mice experiments of pneumococcal lung infection with and without antibiotic treatment. Time series of pneumococcal population, debris, neutrophils, activated epithelial cells, macrophages, monocytes and IL-6 serum concentrations were available for this purpose. The antibiotics Ampicillin and Moxifloxacin were considered. Parameter fittings resulted in a good agreement of model and data for all experimental scenarios. Identifiability of parameters is also estimated. The model can be used to predict the performance of alternative schedules of antibiotic treatment. We conclude that we established a biomathematical model of pneumococcal lung infection in mice allowing predictions regarding the outcome of different schedules of antibiotic treatment. We aim at translating the model to the human situation in the near future.

A computational model of invasive aspergillosis in the lung and the role of iron

Background

Invasive aspergillosis is a severe infection of immunocompromised hosts, caused by the inhalation of the spores of the ubiquitous environmental molds of the Aspergillus genus. The innate immune response in this infection entails a series of complex and inter-related interactions between multiple recruited and resident cell populations with each other and with the fungal cell; in particular, iron is critical for fungal growth.

Results

A computational model of invasive aspergillosis is presented here; the model can be used as a rational hypothesis-generating tool to investigate host responses to this infection. Using a combination of laboratory data and published literature, an in silico model of a section of lung tissue was generated that includes an alveolar duct, adjacent capillaries, and surrounding lung parenchyma. The three-dimensional agent-based model integrates temporal events in fungal cells, epithelial cells, monocytes, and neutrophils after inhalation of spores with cellular dynamics at the tissue level, comprising part of the innate immune response. Iron levels in the blood and tissue play a key role in the fungus’ ability to grow, and the model includes iron recruitment and consumption by the different types of cells included. Parameter sensitivity analysis suggests the model is robust with respect to unvalidated parameters, and thus is a viable tool for an in silico investigation of invasive aspergillosis.

Conclusions

Using laboratory data from a mouse model of invasive aspergillosis in the context of transient neutropenia as validation, the model predicted qualitatively similar time course changes in fungal burden, monocyte and neutrophil populations, and tissue iron levels. This model lays the groundwork for a multi-scale dynamic mathematical model of the immune response to Aspergillus species.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0275-2) contains supplementary material, which is available to authorized users.

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

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

The role of respiratory viruses in the etiology of bacterial pneumonia: An ecological perspective

Pneumonia is the leading cause of death among children less than 5 years old worldwide. A wide range of viral, bacterial and fungal agents can cause pneumonia: although viruses are the most common etiologic agent, the severity of clinical symptoms associated with bacterial pneumonia and increasing antibiotic resistance makes bacterial pneumonia a major public health concern. Bacterial pneumonia can follow upper respiratory viral infection and complicate lower respiratory viral infection. Secondary bacterial pneumonia is a major cause of influenza-related deaths. In this review, we evaluate the following hypotheses: (i) respiratory viruses influence the etiology of pneumonia by altering bacterial community structure in the upper respiratory tract (URT) and (ii) respiratory viruses promote or inhibit colonization of the lower respiratory tract (LRT) by certain bacterial species residing in the URT. We conducted a systematic review of the literature to examine temporal associations between respiratory viruses and bacteria and a targeted review to identify potential mechanisms of interactions. We conclude that viruses both alter the bacterial community in the URT and promote bacterial colonization of the LRT. However, it is uncertain whether changes in the URT bacterial community play a substantial role in pneumonia etiology. The exception is Streptococcus pneumoniae where a strong link between viral co-infection, increased carriage and pneumococcal pneumonia has been established.

Computational Identification of Mechanistic Factors That Determine the Timing and Intensity of the Inflammatory Response

Timely resolution of inflammation is critical for the restoration of homeostasis in injured or infected tissue. Chronic inflammation is often characterized by a persistent increase in the concentrations of inflammatory cells and molecular mediators, whose distinct amount and timing characteristics offer an opportunity to identify effective therapeutic regulatory targets. Here, we used our recently developed computational model of local inflammation to identify potential targets for molecular interventions and to investigate the effects of individual and combined inhibition of such targets. This was accomplished via the development and application of computational strategies involving the simulation and analysis of thousands of inflammatory scenarios. We found that modulation of macrophage influx and efflux is an effective potential strategy to regulate the amount of inflammatory cells and molecular mediators in both normal and chronic inflammatory scenarios. We identified three molecular mediators − tumor necrosis factor-α (TNF-α), transforming growth factor-β (TGF-β), and the chemokine CXCL8 − as potential molecular targets whose individual or combined inhibition may robustly regulate both the amount and timing properties of the kinetic trajectories for neutrophils and macrophages in chronic inflammation. Modulation of macrophage flux, as well as of the abundance of TNF-α, TGF-β, and CXCL8, may improve the resolution of chronic inflammation.

A recent approach to quantitatively characterize the timing and intensity of the inflammatory response relies on the use of four quantities termed inflammation indices. The values of the inflammation indices may reflect the differences between normal and pathological inflammation, and may be used to gauge the effects of therapeutic interventions aimed to control inflammation. Yet, the specific inflammatory mechanisms that can be targeted to selectively control these indices remain unknown. Here, we developed and applied a computational strategy to identify potential target mechanisms to regulate such indices. We used our recently developed model of local inflammation to simulate thousands of inflammatory scenarios. We then subjected the corresponding inflammation index values to sensitivity and correlation analysis. We found that the inflammation indices may be significantly influenced by the macrophage influx and efflux rates, as well as by the degradation rates of three specific molecular mediators. These results suggested that the indices can be effectively regulated by individual or combined inhibition of those molecular mediators, which we confirmed by computational experiments. Taken together, our results highlight possible targets of therapeutic intervention that can be used to control both the timing and the intensity of the inflammatory response.