A mathematical model of intrahost pneumococcal pneumonia infection dynamics in murine strains

Kinetics, thresholds, and a comparison of mechanisms underlying systemic infection by Listeria monocytogenes

Studies on the system-scale pathogenesis of Listeria monocytogenes infection have classically focused on its ability to colonize in the intestines following an exposure event. However, despite this, many of the most dangerous complications arising from L. monocytogenes infection are observed days, weeks, or months after exposure, resulting indirectly from bacteria escaping this intestinal colonization hub and invading other organs. Over time, findings of various individual phenomena observed during systemic infection have accumulated, including a shift away from the principal route of intestinal dissemination, delays in bacterial colonization of the central nervous system, differing bacterial flux rates across organs, and multi-stability of bacterial population levels. To further our quantitative understanding of foodborne bacterial infection dynamics, a compartmental model of systemic infection that synthesizes these findings is proposed. Under parameterization to infection in BALB/c mice, the model is used to show a substantial decrease in bacterial populations resulting from dissemination through the mesenteric lymph nodes, as compared to the portal vein, when controlling for the number of bacteria passing through each route. Due to the compartmental nature of this model, we anticipate that this result may be paralleled in other microbes which make use of these pathways to escape the intestinal environment. Additionally, we predict thresholds for intestinal dissemination along each of these routes, which must be surpassed to induce systemic infection, and describe how these thresholds change over time. Supplementarily, logistic curves are fitted to synthetic data as a means of robustly quantifying the dose-response relationship beyond the intestinal barrier.

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.

An agent-based model for collaborative learning to combat antimicrobial resistance: proof of concept based on broiler production in Senegal

Antimicrobial resistance (AMR) is a substantial global One Health problem. This paper reports on initial, proof-of-concept development of an agent-based model (ABM) as part of wider modelling efforts to support collaborations between groups interested in policy development for animal health and food systems. The model simulates AMR in poultry production in Senegal. It simultaneously addresses current policy issues, builds on existing modelling in the domain and describes AMR in the broiler chicken production cycle as seen by producers and veterinarians. This enables implementation and assessment of producer antimicrobial use and infection prevention and control strategies in terms of immediate economic incentives, potentially helping to advance conversations by addressing national policy priorities. Our model is presented as a flexible tool with promise for extension as part of AMR policy development in Senegal and West Africa, using participatory approaches. This work indicates that ABM can potentially play a useful role in fostering counter-AMR initiatives driven by food system actor behaviour in lower- and middle-income countries more generally.

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.

Age-Related Changes to the Immune System Exacerbate the Inflammatory Response to Pandemic H1N1 Infection

Age-induced dysregulation of the immune response is a major contributor to the morbidity and mortality related to influenza a virus infections. Experimental data have shown substantial changes to the activation and maintenance of the immune response will occur with age, but it remains unclear which of these many interrelated changes are most critical to controlling the survival of the host during infection. To ascertain which mechanisms are predominantly responsible for the increased morbidity in elderly hosts, we developed an ordinary differential equation model to simulate the immune response to pandemic H1N1 infection. We fit this model to experimental data measured in young and old macaques. We determined that the severity of the infection in the elderly hosts is caused by a dysregulation in the innate immune response. We also simulated CD8+ T cell exhaustion, a common consequence of chronic and extensive infections. Our simulations indicate that while T cell exhaustion is possible in both age groups, its effects are more severe in the elderly population, as their dysregulated immune response cannot easily compensate for the exhausted T cells. Finally, we explore a therapeutic approach to reversing T cell exhaustion through an inflammatory stimulus. A controlled increase in inflammatory signals can lead to a higher chance of surviving the infection, but excess inflammation will likely lead to septic death. These results indicate that our model captures distinctions in the predominant mechanisms controlling the immune response in younger and older hosts and allows for simulations of clinically relevant therapeutic strategies post-infection.

Modeling the transmission dynamics of delayed pneumonia-like diseases with a sensitivity of parameters

Pneumonia is a highly transmitted disease in children. According to the World Health Organization (WHO), the most affected regions include South Asia and sub-Saharan Africa. 15% deaths of children are due to pneumonia. In 2017, 0.88 million children were killed under the age of five years. An analysis of pneumonia disease is performed with the help of a delayed mathematical modelling technique. The epidemiological system contemplates subpopulations of susceptible, carriers, infected and recovered individuals, along with nonlinear interactions between the members of those subpopulations. The positivity and the boundedness of the ongoing problem for nonnegative initial data are thoroughly proved. The system possesses pneumonia-free and pneumonia existing equilibrium points, whose stability is studied rigorously. Moreover, the numerical simulations confirm the validity of these theoretical results.

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

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

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.

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.

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.

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 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.

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.

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 Neutrophil Phenotype Model for Extracorporeal Treatment of Sepsis

Neutrophils play a central role in eliminating bacterial pathogens, but may also contribute to end-organ damage in sepsis. Interleukin-8 (IL-8), a key modulator of neutrophil function, signals through neutrophil specific surface receptors CXCR-1 and CXCR-2. In this study a mechanistic computational model was used to evaluate and deploy an extracorporeal sepsis treatment which modulates CXCR-1/2 levels. First, a simplified mechanistic computational model of IL-8 mediated activation of CXCR-1/2 receptors was developed, containing 16 ODEs and 43 parameters. Receptor level dynamics and systemic parameters were coupled with multiple neutrophil phenotypes to generate dynamic populations of activated neutrophils which reduce pathogen load, and/or primed neutrophils which cause adverse tissue damage when misdirected. The mathematical model was calibrated using experimental data from baboons administered a two-hour infusion of E coli and followed for a maximum of 28 days. Ensembles of parameters were generated using a Bayesian parallel tempering approach to produce model fits that could recreate experimental outcomes. Stepwise logistic regression identified seven model parameters as key determinants of mortality. Sensitivity analysis showed that parameters controlling the level of killer cell neutrophils affected the overall systemic damage of individuals. To evaluate rescue strategies and provide probabilistic predictions of their impact on mortality, time of onset, duration, and capture efficacy of an extracorporeal device that modulated neutrophil phenotype were explored. Our findings suggest that interventions aiming to modulate phenotypic composition are time sensitive. When introduced between 3–6 hours of infection for a 72 hour duration, the survivor population increased from 31% to 40–80%. Treatment efficacy quickly diminishes if not introduced within 15 hours of infection. Significant harm is possible with treatment durations ranging from 5–24 hours, which may reduce survival to 13%. In severe sepsis, an extracorporeal treatment which modulates CXCR-1/2 levels has therapeutic potential, but also potential for harm. Further development of the computational model will help guide optimal device development and determine which patient populations should be targeted by treatment.

Sepsis occurs when a patient develops a whole body immune response due to infection. In this condition, white blood cells called neutrophils circulate in an active state, seeking and eliminating invading bacteria. However, when neutrophils are activated, healthy tissue is inadvertently targeted, leading to organ damage and potentially death. Even though sepsis kills millions worldwide, there are still no specific treatments approved in the United States. This may be due to the complexity and diversity of the body’s immune response, which can be managed well using computational modeling. We have developed a computational model to predict how different levels of neutrophil activation impact survival in an overactive inflammatory conditions. The model was utilized to assess the effectiveness of a simulated experimental sepsis treatment which modulates neutrophil populations and activity. This evaluation determined that treatment timing plays a critical role in therapeutic effectiveness. When utilized properly the treatment drastically improves survival, but there is also risk of causing patient harm when introduced at the wrong time. We intend for this computational model to support and guide further development of sepsis treatments and help translate these preliminary results from bench to bedside.

A Three-Tiered Study of Differences in Murine Intrahost Immune Response to Multiple Pneumococcal Strains

We apply a previously developed 4-variable ordinary differential equation model of in-host immune response to pneumococcal pneumonia to study the variability of the immune response of MF1 mice and to explore bacteria-driven differences in disease progression and outcome. In particular, we study the immune response to D39 strain of bacteria missing portions of the pneumolysin protein controlling either the hemolytic activity or complement-activating activity, the response to D39 bacteria deficient in either neuraminidase A or B, and the differences in the response to D39 (serotype 2), 0100993 (serotype 3), and TIGR4 (serotype 4) bacteria. The model accurately reproduces infection kinetics in all cases and provides information about which mechanisms in the immune response have the greatest effect in each case. Results suggest that differences in the ability of bacteria to defeat immune response are primarily due to the ability of the bacteria to elude nonspecific clearance in the lung tissue as well as the ability to create damage to the lung epithelium.

The inverse problem in mathematical biology

Biological systems present particular challengers to model for the purposes of formulating predictions of generating biological insight. These systems are typically multi-scale, complex, and empirical observations are often sparse and subject to variability and uncertainty. This manuscript will review some of these specific challenges and introduce current methods used by modelers to construct meaningful solutions, in the context of preserving biological relevance. Opportunities to expand these methods are also discussed.