Extensions of mean-field approximations for environmentally-transmitted pathogen networks.

Many pathogens spread via environmental transmission, without requiring host-to-host direct contact. While models for environmental transmission exist, many are simply constructed intuitively with structures analogous to standard models for direct transmission. As model insights are generally sensitive to the underlying model assumptions, it is important that we are able understand the details and consequences of these assumptions. We construct a simple network model for an environmentally-transmitted pathogen and rigorously derive systems of ordinary differential equations (ODEs) based on different assumptions. We explore two key assumptions, namely homogeneity and independence, and demonstrate that relaxing these assumptions can lead to more accurate ODE approximations. We compare these ODE models to a stochastic implementation of the network model over a variety of parameters and network structures, demonstrating that with fewer restrictive assumptions we are able to achieve higher accuracy in our approximations and highlighting more precisely the errors produced by each assumption. We show that less restrictive assumptions lead to more complicated systems of ODEs and the potential for unstable solutions. Due to the rigour of our derivation, we are able to identify the reason behind these errors and propose potential resolutions.

Linking Immuno-Epidemiology Principles to Violence.

BACKGROUND: Societies have always struggled with violence, but recently there has been a push to understand violence as a public health issue. This idea has unified professionals in medicine, epidemiological, and psychology with a goal to end violence and heal those exposed to it. Recently, analogies have been made between community-level infectious disease epidemiology and how violence spreads within a community. Experts in public health and medicine suggest an epidemiological framework could be used to study violence. METHODS: Building upon results from community organizations which implement public health-like techniques to stop violence spread, we look to formalize the analogies between violence and infectious diseases. Then expanding on these ideas and using mathematical epidemiological principals, we formulate a susceptible-exposed-infected model to capture violence spread. Further, we ran example numerical simulations to show how a mathematical model can provide insight on prevention strategies. RESULTS: The preliminary simulations show negative effects of violence exposure have a greater impact than positive effects of preventative measures. For example, our simulation shows that when the impact of violence exposure is reduced by half, the amount of violence in a community drastically decreases in the long-term; but to reach this same outcome through an increase in the amount of after exposure support, it must be approximately fivefold. Further, we note that our simulations qualitatively agree with empirical studies. CONCLUSIONS: Having a mathematical model can give insights on the effectiveness of different strategies for violence prevention. Based on our example simulations, the most effective use of community funding is investing in protective factors, instead of support after violence exposure, but of course these results do not stand in isolation and will need to be contextualized with the rest of the research in the field.

Divergent COVID-19 Disease Trajectories Predicted by a DAMP-Centered Immune Network Model.

COVID-19 presentations range from mild to moderate through severe disease but also manifest with persistent illness or viral recrudescence. We hypothesized that the spectrum of COVID-19 disease manifestations was a consequence of SARS-CoV-2-mediated delay in the pathogen-associated molecular pattern (PAMP) response, including dampened type I interferon signaling, thereby shifting the balance of the immune response to be dominated by damage-associated molecular pattern (DAMP) signaling. To test the hypothesis, we constructed a parsimonious mechanistic mathematical model. After calibration of the model for initial viral load and then by varying a few key parameters, we show that the core model generates four distinct viral load, immune response and associated disease trajectories termed "patient archetypes", whose temporal dynamics are reflected in clinical data from hospitalized COVID-19 patients. The model also accounts for responses to corticosteroid therapy and predicts that vaccine-induced neutralizing antibodies and cellular memory will be protective, including from severe COVID-19 disease. This generalizable modeling framework could be used to analyze protective and pathogenic immune responses to diverse viral infections.

Mathematically modeling the effect of touch frequency on the environmental transmission of Clostridioides difficile in healthcare settings.

Clostridioides difficile, formerly Clostridium difficile, is the leading cause of infectious diarrhea and one of the most common healthcare acquired infections in United States hospitals. C. difficile persists well in healthcare environments because it forms spores that can survive for long periods of time and can be transmitted to susceptible patients through contact with contaminated hands and fomites, objects or surfaces that can harbor infectious agents. Fomites can be classified as high-touch or low-touch based on the frequency they are contacted. The mathematical model in this study investigates the relative contribution of high-touch and low-touch fomites on new cases of C. difficile colonization among patients of a hospital ward. The dynamics of transmission are described by a system of ordinary differential equations representing four patient population classes and two pathogen environmental reservoirs. Parameters that have a significant effect on incidence, as determined by a global sensitivity analysis, are varied in stochastic simulations of the system to identify feasible strategies to prevent disease transmission. Results indicate that on average, under one-quarter of asymptomatically colonized patients are exposed to C. difficile via low-touch fomites. In comparison, over three-quarters of colonized patients are colonized through high-touch fomites, despite additional cleaning of high-touch fomites. Increased contacts with high-touch fomites increases the contribution of these fomites to the incidence of colonized individuals and decreasing the duration of a hospital visit reduces the amount of pathogen in the environment. Thus, enhanced efficacy of disinfection upon discharge and extra cleaning of high-touch fomites, reduced contact with high-touch fomites, and higher discharge rates, among other control measures, could lead to a decrease in the incidence of colonized individuals.

Comparing intervention strategies for reducing Clostridioides difficile transmission in acute healthcare settings: an agent-based modeling study.

BACKGROUND: Clostridioides difficile infection (CDI) is one of the most common healthcare infections. Common strategies aiming at controlling CDI include antibiotic stewardship, environmental decontamination, and improved hand hygiene and contact precautions. Mathematical models provide a framework to evaluate control strategies. Our objective is to evaluate the effectiveness of control strategies in decreasing C. difficile colonization and infection using an agent-based model in an acute healthcare setting. METHODS: We developed an agent-based model that simulates the transmission of C. difficile in medical wards. This model explicitly incorporates healthcare workers (HCWs) as vectors of transmission, tracks individual patient antibiotic histories, incorporates varying risk levels of antibiotics with respect to CDI susceptibility, and tracks contamination levels of ward rooms by C. difficile. Interventions include two forms of antimicrobial stewardship, increased environmental decontamination through room cleaning, improved HCW compliance, and a preliminary assessment of vaccination. RESULTS: Increased HCW compliance with CDI patients was ranked as the most effective intervention in decreasing colonizations, with reductions up to 56%. Antibiotic stewardship practices were highly ranked after contact precaution compliance. Vaccination and reduction of high-risk antibiotics were the most effective intervention in decreasing CDI. Vaccination reduced CDI cases to up to 90%, and the reduction of high-risk antibiotics decreased CDI cases up to 23%. CONCLUSIONS: Overall, interventions that decrease patient susceptibility to colonization by C. difficile, such as antibiotic stewardship, were the most effective interventions in reducing both colonizations and CDI cases.

Modeling the macrophage-anthrax spore interaction: Implications for early host-pathogen interactions.

Inhalational anthrax, caused by the gram positive bacteria Bacillus anthracis, is a potentially fatal form of anthrax infection. It is initiated after inhaled spores are deposited in the lung, phagocytosed by immune cells, and subsequently transported to nearby lymph nodes. Intracellular spores that successfully germinate and become vegetative bacteria can lyse their host cell and contribute to bacterial outgrowth and toxin production. To better understand the early disease dynamics of the host-pathogen interaction, we develop a mathematical model of ordinary differential Equations and estimate parameters using available data. The model which consists of two subsystems is designed in accordance with an in vitro experimental protocol in which macrophages were challenged with varying doses of spores at spore-to-macrophage ratios of 1:1, 1:2, 1:10, 1:20. Initial modeling results suggested the need to consider two distinct subpopulations of anthrax bacteria: newly germinated bacteria which cannot replicate immediately and fully vegetative bacteria that can. Additional modeling results provide insights into possible reasons why macrophage-induced killing is more effective at the 1:20 ratio.

Toward a model-free feedback control synthesis for treating acute inflammation.

An effective and patient-specific feedback control synthesis for inflammation resolution is still an ongoing research area. A strategy consisting of manipulating a pro and anti-inflammatory mediator is considered here as used in some promising model-based control studies. These earlier studies, unfortunately, suffer from the difficultly of calibration due to the heterogeneity of individual patient responses even under similar initial conditions. We exploit a new model-free control approach and its corresponding "intelligent" controllers for this biomedical problem. A crucial feature of the proposed control problem is as follows: the two most important outputs which must be driven to their respective desired states are sensorless. This difficulty is overcome by assigning suitable reference trajectories to the other two outputs that do have sensors. A mathematical model, via a system of ordinary differential equations, is nevertheless employed as a "virtual" patient for in silico testing. We display several simulation results with respect to the most varied situations, which highlight the effectiveness of our viewpoint.

Inflammation and Disease: Modelling and Modulation of the Inflammatory Response to Alleviate Critical Illness.

Critical illness, a constellation of interrelated inflammatory and physiological derangements occurring subsequent to severe infection or injury, affects a large number of individuals in both developed and developing countries. The prototypical complex system embodied in critical illness has largely defied therapy beyond supportive care. We have focused on the utility of data-driven and mechanistic computational modelling to help address the complexity of critical illness and provide pathways towards discovering potential therapeutic options and combinations. Herein, we review recent progress in this field, with a focus on both animal and computational models of critical illness. We suggest that therapy for critical illness can be posed as a model-based dynamic control problem, and discuss novel theoretical and experimental approaches involving biohybrid devices aimed at reprogramming inflammation dynamically. Together, these advances offer the potential for Model-based Precision Medicine for critical illness.

Pathogen transfer through environment-host contact: an agent-based queueing theoretic framework.

Queueing theory studies the properties of waiting queues and has been applied to investigate direct host-to-host transmitted disease dynamics, but its potential in modelling environmentally transmitted pathogens has not been fully explored. In this study, we provide a flexible and customizable queueing theory modelling framework with three major subroutines to study the in-hospital contact processes between environments and hosts and potential nosocomial pathogen transfer, where environments are servers and hosts are customers. Two types of servers with different parameters but the same utilization are investigated. We consider various forms of transfer functions that map contact duration to the amount of pathogen transfer based on existing literature. We propose a case study of simulated in-hospital contact processes and apply stochastic queues to analyse the amount of pathogen transfer under different transfer functions, and assume that pathogen amount decreases during the inter-arrival time. Different host behaviour (feedback and non-feedback) as well as initial pathogen distribution (whether in environment and/or in hosts) are also considered and simulated. We assess pathogen transfer and circulation under these various conditions and highlight the importance of the nonlinear interactions among contact processes, transfer functions and pathogen demography during the contact process. Our modelling framework can be readily extended to more complicated queueing networks to simulate more realistic situations by adjusting parameters such as the number and type of servers and customers, and adding extra subroutines.

Optimal control of vaccination rate in an epidemiological model of Clostridium difficile transmission.

The spore-forming, gram-negative bacteria Clostridium difficile can cause severe intestinal illness. A striking increase in the number of cases of C. difficile infection (CDI) among hospitals has highlighted the need to better understand how to prevent the spread of CDI. In our paper, we modify and update a compartmental model of nosocomial C. difficile transmission to include vaccination. We then apply optimal control theory to determine the time-varying optimal vaccination rate that minimizes a combination of disease prevalence and spread in the hospital population as well as cost, in terms of time and money, associated with vaccination. Various hospital scenarios are considered, such as times of increased antibiotic prescription rate and times of outbreak, to see how such scenarios modify the optimal vaccination rate. By comparing the values of the objective functional with constant vaccination rates to those with time-varying optimal vaccination rates, we illustrate the benefits of time-varying controls.

Solving Immunology?

Emergent responses of the immune system result from the integration of molecular and cellular networks over time and across multiple organs. High-content and high-throughput analysis technologies, concomitantly with data-driven and mechanistic modeling, hold promise for the systematic interrogation of these complex pathways. However, connecting genetic variation and molecular mechanisms to individual phenotypes and health outcomes has proven elusive. Gaps remain in data, and disagreements persist about the value of mechanistic modeling for immunology. Here, we present the perspectives that emerged from the National Institute of Allergy and Infectious Disease (NIAID) workshop 'Complex Systems Science, Modeling and Immunity' and subsequent discussions regarding the potential synergy of high-throughput data acquisition, data-driven modeling, and mechanistic modeling to define new mechanisms of immunological disease and to accelerate the translation of these insights into therapies.

Self-harm to preferentially harm the pathogens within: non-specific stressors in innate immunity.

Therapies with increasing specificity against pathogens follow the immune system's evolutionary course in maximizing host defence while minimizing self-harm. Nevertheless, even completely non-specific stressors, such as reactive molecular species, heat, nutrient and oxygen deprivation, and acidity can be used to preferentially harm pathogens. Strategic use of non-specific stressors requires exploiting differences in stress vulnerability between pathogens and hosts. Two basic vulnerabilities of pathogens are: (i) the inherent vulnerability to stress of growth and replication (more immediately crucial for pathogens than for host cells) and (ii) the degree of pathogen localization, permitting the host's use of locally and regionally intense stress. Each of the various types of non-specific stressors is present during severe infections at all levels of localization: (i) ultra-locally within phagolysosomes, (ii) locally at the infected site, (iii) regionally around the infected site and (iv) systemically as part of the acute-phase response. We propose that hosts strategically use a coordinated system of non-specific stressors at local, regional and systemic levels to preferentially harm the pathogens within. With the rising concern over emergence of resistance to specific therapies, we suggest more scrutiny of strategies using less specific therapies in pathogen control. Hosts' active use of multiple non-specific stressors is likely an evolutionarily basic defence whose retention underlies and supplements the well-recognized immune defences that directly target pathogens.

Insights into the Role of Chemokines, Damage-Associated Molecular Patterns, and Lymphocyte-Derived Mediators from Computational Models of Trauma-Induced Inflammation.

SIGNIFICANCE: Traumatic injury elicits a complex, dynamic, multidimensional inflammatory response that is intertwined with complications such as multiple organ dysfunction and nosocomial infection. The complex interplay between inflammation and physiology in critical illness remains a challenge for translational research, including the extrapolation to human disease from animal models. RECENT ADVANCES: Over the past decade, we and others have attempted to decipher the biocomplexity of inflammation in these settings of acute illness, using computational models to improve clinical translation. In silico modeling has been suggested as a computationally based framework for integrating data derived from basic biology experiments as well as preclinical and clinical studies. CRITICAL ISSUES: Extensive studies in cells, mice, and human blunt trauma patients have led us to suggest (i) that while an adequate level of inflammation is required for healing post-trauma, inflammation can be harmful when it becomes self-sustaining via a damage-associated molecular pattern/Toll-like receptor-driven feed-forward circuit; (ii) that chemokines play a central regulatory role in driving either self-resolving or self-maintaining inflammation that drives the early activation of both classical innate and more recently recognized lymphoid pathways; and (iii) the presence of multiple thresholds and feedback loops, which could significantly affect the propagation of inflammation across multiple body compartments. FUTURE DIRECTIONS: These insights from data-driven models into the primary drivers and interconnected networks of inflammation have been used to generate mechanistic computational models. Together, these models may be used to gain basic insights as well as serving to help define novel biomarkers and therapeutic targets.

Mathematical Modeling of Early Cellular Innate and Adaptive Immune Responses to Ischemia/Reperfusion Injury and Solid Organ Allotransplantation.

A mathematical model of the early inflammatory response in transplantation is formulated with ordinary differential equations. We first consider the inflammatory events associated only with the initial surgical procedure and the subsequent ischemia/reperfusion (I/R) events that cause tissue damage to the host as well as the donor graft. These events release damage-associated molecular pattern molecules (DAMPs), thereby initiating an acute inflammatory response. In simulations of this model, resolution of inflammation depends on the severity of the tissue damage caused by these events and the patient's (co)-morbidities. We augment a portion of a previously published mathematical model of acute inflammation with the inflammatory effects of T cells in the absence of antigenic allograft mismatch (but with DAMP release proportional to the degree of graft damage prior to transplant). Finally, we include the antigenic mismatch of the graft, which leads to the stimulation of potent memory T cell responses, leading to further DAMP release from the graft and concomitant increase in allograft damage. Regulatory mechanisms are also included at the final stage. Our simulations suggest that surgical injury and I/R-induced graft damage can be well-tolerated by the recipient when each is present alone, but that their combination (along with antigenic mismatch) may lead to acute rejection, as seen clinically in a subset of patients. An emergent phenomenon from our simulations is that low-level DAMP release can tolerize the recipient to a mismatched allograft, whereas different restimulation regimens resulted in an exaggerated rejection response, in agreement with published studies. We suggest that mechanistic mathematical models might serve as an adjunct for patient- or sub-group-specific predictions, simulated clinical studies, and rational design of immunosuppression.

Combining robust state estimation with nonlinear model predictive control to regulate the acute inflammatory response to pathogen.

The inflammatory response aims to restore homeostasis by means of removing a biological stress, such as an invading bacterial pathogen. In cases of acute systemic inflammation, the possibility of collateral tissue damage arises, which leads to a necessary down-regulation of the response. A reduced ordinary differential equations (ODE) model of acute inflammation was presented and investigated in [10]. That system contains multiple positive and negative feedback loops and is a highly coupled and nonlinear ODE. The implementation of nonlinear model predictive control (NMPC) as a methodology for determining proper therapeutic intervention for in silico patients displaying complex inflammatory states was initially explored in [5]. Since direct measurements of the bacterial population and the magnitude of tissue damage/dysfunction are not readily available or biologically feasible, the need for robust state estimation was evident. In this present work, we present results on the nonlinear reachability of the underlying model, and then focus our attention on improving the predictability of the underlying model by coupling the NMPC with a particle filter. The results, though comparable to the initial exploratory study, show that robust state estimation of this highly nonlinear model can provide an alternative to prior updating strategies used when only partial access to the unmeasurable states of the system are available.

Simple mathematical models do not accurately predict early SIV dynamics.

Upon infection of a new host, human immunodeficiency virus (HIV) replicates in the mucosal tissues and is generally undetectable in circulation for 1-2 weeks post-infection. Several interventions against HIV including vaccines and antiretroviral prophylaxis target virus replication at this earliest stage of infection. Mathematical models have been used to understand how HIV spreads from mucosal tissues systemically and what impact vaccination and/or antiretroviral prophylaxis has on viral eradication. Because predictions of such models have been rarely compared to experimental data, it remains unclear which processes included in these models are critical for predicting early HIV dynamics. Here we modified the "standard" mathematical model of HIV infection to include two populations of infected cells: cells that are actively producing the virus and cells that are transitioning into virus production mode. We evaluated the effects of several poorly known parameters on infection outcomes in this model and compared model predictions to experimental data on infection of non-human primates with variable doses of simian immunodifficiency virus (SIV). First, we found that the mode of virus production by infected cells (budding vs. bursting) has a minimal impact on the early virus dynamics for a wide range of model parameters, as long as the parameters are constrained to provide the observed rate of SIV load increase in the blood of infected animals. Interestingly and in contrast with previous results, we found that the bursting mode of virus production generally results in a higher probability of viral extinction than the budding mode of virus production. Second, this mathematical model was not able to accurately describe the change in experimentally determined probability of host infection with increasing viral doses. Third and finally, the model was also unable to accurately explain the decline in the time to virus detection with increasing viral dose. These results suggest that, in order to appropriately model early HIV/SIV dynamics, additional factors must be considered in the model development. These may include variability in monkey susceptibility to infection, within-host competition between different viruses for target cells at the initial site of virus replication in the mucosa, innate immune response, and possibly the inclusion of several different tissue compartments. The sobering news is that while an increase in model complexity is needed to explain the available experimental data, testing and rejection of more complex models may require more quantitative data than is currently available.

Modeling the host response to inhalation anthrax.

Inhalation anthrax, an often fatal infection, is initiated by endospores of the bacterium Bacillus anthracis, which are introduced into the lung. To better understand the pathogenesis of an inhalation anthrax infection, we propose a two-compartment mathematical model that takes into account the documented early events of such an infection. Anthrax spores, once inhaled, are readily taken up by alveolar phagocytes, which then migrate rather quickly out of the lung and into the thoracic/mediastinal lymph nodes. En route, these spores germinate to become vegetative bacteria. In the lymph nodes, the bacteria kill the host cells and are released into the extracellular environment where they can be disseminated into the blood stream and grow to a very high level, often resulting in the death of the infected person. Using this framework as the basis of our model, we explore the probability of survival of an infected individual. This is dependent on several factors, such as the rate of migration and germination events and treatment with antibiotics.

Using nonlinear model predictive control to find optimal therapeutic strategies to modulate inflammation.

Modulation of the inflammatory response has become a key focal point in the treatment of critically ill patients. Much of the computational work in this emerging field has been carried out with the goal of unraveling the primary drivers, interconnections, and dynamics of systemic inflammation. To translate these theoretical efforts into clinical approaches, the proper biological targets and specific manipulations must be identified. In this work, we pursue this goal by implementing a nonlinear model predictive control (NMPC) algorithm in the context of a reduced computational model of the acute inflammatory response to severe infection. In our simulations, NMPC successfully identifies patient-specific therapeutic strategies, based on simulated observations of clinically accessible inflammatory mediators, which outperform standardized therapies, even when the latter are derived using a general optimization routine. These results imply that a combination of computational modeling and NMPC may be of practical use in suggesting novel immuno-modulatory strategies for the treatment of intensive care patients.

Tuberculosis research: going forward with a powerful "translational systems biology" approach.

Due to the complexity of the immune response to a Mycobacterium tuberculosis infection, identifying new, effective therapies and vaccines to combat it has been a problematic issue. Although many advances have been made in understanding particular mechanisms involved, they have, to date, proved insufficient to provide real breakthroughs in this area of tuberculosis research. The term "Translational Systems Biology" has been formally proposed to describe the use of experimental findings combined with mathematical modeling and/or engineering principles to understand complex biological processes in an integrative fashion for the purpose of enhancing clinical practice. This opinion piece discusses the importance of using a Translational Systems Biology approach for tuberculosis research as a means by which to go forward with the potential for significant breakthroughs to occur.

Competition Between Transients in the Rate of Approach to a Fixed Point.

The goal of this paper is to provide and apply tools for analyzing a specific aspect of transient dynamics not covered by previous theory. The question we address is whether one component of a perturbed solution to a system of differential equations can overtake the corresponding component of a reference solution as both converge to a stable node at the origin, given that the perturbed solution was initially farther away and that both solutions are nonnegative for all time. We call this phenomenon tolerance, for its relation to a biological effect. We show using geometric arguments that tolerance will exist in generic linear systems with a complete set of eigenvectors and in excitable nonlinear systems. We also define a notion of inhibition that may constrain the regions in phase space where the possibility of tolerance arises in general systems. However, these general existence theorems do not not yield an assessment of tolerance for specific initial conditions. To address that issue, we develop some analytical tools for determining if particular perturbed and reference solution initial conditions will exhibit tolerance.