Combination interventions for Hepatitis C and Cirrhosis reduction among people who inject drugs: An agent-based, networked population simulation experiment

Hepatitis C virus (HCV) infection is endemic in people who inject drugs (PWID), with prevalence estimates above 60 percent for PWID in the United States. Previous modeling studies suggest that direct acting antiviral (DAA) treatment can lower overall prevalence in this population, but treatment is often delayed until the onset of advanced liver disease (fibrosis stage 3 or later) due to cost. Lower cost interventions featuring syringe access (SA) and medically assisted treatment (MAT) for addiction are known to be less costly, but have shown mixed results in lowering HCV rates below current levels. Little is known about the potential synergistic effects of combining DAA and MAT treatment, and large-scale tests of combined interventions are rare. While simulation experiments can reveal likely long-term effects, most prior simulations have been performed on closed populations of model agents--a scenario quite different from the open, mobile populations known to most health agencies. This paper uses data from the Centers for Disease Control's National HIV Behavioral Surveillance project, IDU round 3, collected in New York City in 2012 by the New York City Department of Health and Mental Hygiene to parameterize simulations of open populations. Our results show that, in an open population, SA/MAT by itself has only small effects on HCV prevalence, while DAA treatment by itself can significantly lower both HCV and HCV-related advanced liver disease prevalence. More importantly, the simulation experiments suggest that cost effective synergistic combinations of the two strategies can dramatically reduce HCV incidence. We conclude that adopting SA/MAT implementations alongside DAA interventions can play a critical role in reducing the long-term consequences of ongoing infection

Stochastic spreading on complex networks

Complex interacting systems are ubiquitous in nature and society. Computational modeling of these systems is, therefore, of great relevance for science and engineering. Complex networks are common representations of these systems (e.g., friendship networks or road networks). Dynamical processes (e.g., virus spreading, traffic jams) that evolve on these networks are shaped and constrained by the underlying connectivity. This thesis provides numerical methods to study stochastic spreading processes on complex networks. We consider the processes as inherently probabilistic and analyze their behavior through the lens of probability theory. While powerful theoretical frameworks (like the SIS-epidemic model and continuous-time Markov chains) already exist, their analysis is computationally challenging. A key contribution of the thesis is to ease the computational burden of these methods. Particularly, we provide novel methods for the efficient stochastic simulation of these processes. Based on different simulation studies, we investigate techniques for optimal vaccine distribution and critically address the usage of mathematical models during the Covid-19 pandemic. We also provide model-reduction techniques that translate complicated models into simpler ones that can be solved without resorting to simulations. Lastly, we show how to infer the underlying contact data from node-level observations.Komplexe, interagierende Systeme sind in Natur und Gesellschaft allgegenwärtig. Die computergestützte Modellierung dieser Systeme ist daher von immenser Bedeutung für Wissenschaft und Technik. Netzwerke sind eine gängige Art, diese Systeme zu repräsentieren (z. B. Freundschaftsnetzwerke, Straßennetze). Dynamische Prozesse (z. B. Epidemien, Staus), die sich auf diesen Netzwerken ausbreiten, werden durch die spezifische Konnektivität geformt. In dieser Arbeit werden numerische Methoden zur Untersuchung stochastischer Ausbreitungsprozesse in komplexen Netzwerken entwickelt. Wir betrachten die Prozesse als inhärent probabilistisch und analysieren ihr Verhalten nach wahrscheinlichkeitstheoretischen Fragestellungen. Zwar gibt es bereits theoretische Grundlagen und Paradigmen (wie das SIS-Epidemiemodell und zeitkontinuierliche Markov-Ketten), aber ihre Analyse ist rechnerisch aufwändig. Ein wesentlicher Beitrag dieser Arbeit besteht darin, die Rechenlast dieser Methoden zu verringern. Wir erforschen Methoden zur effizienten Simulation dieser Prozesse. Anhand von Simulationsstudien untersuchen wir außerdem Techniken für optimale Impfstoffverteilung und setzen uns kritisch mit der Verwendung mathematischer Modelle bei der Covid-19-Pandemie auseinander. Des Weiteren führen wir Modellreduktionen ein, mit denen komplizierte Modelle in einfachere umgewandelt werden können. Abschließend zeigen wir, wie man von Beobachtungen einzelner Knoten auf die zugrunde liegende Netzwerkstruktur schließt

Agent-based dynamic knowledge representation of Pseudomonas aeruginosa virulence activation in the stressed gut: Towards characterizing host-pathogen interactions in gut-derived sepsis

<p>Abstract</p> <p>Background</p> <p>There is a growing realization that alterations in host-pathogen interactions (HPI) can generate disease phenotypes without pathogen invasion. The gut represents a prime region where such HPI can arise and manifest. Under normal conditions intestinal microbial communities maintain a stable, mutually beneficial ecosystem. However, host stress can lead to changes in environmental conditions that shift the nature of the host-microbe dialogue, resulting in escalation of virulence expression, immune activation and ultimately systemic disease. Effective modulation of these dynamics requires the ability to characterize the complexity of the HPI, and dynamic computational modeling can aid in this task. Agent-based modeling is a computational method that is suited to representing spatially diverse, dynamical systems. We propose that dynamic knowledge representation of gut HPI with agent-based modeling will aid in the investigation of the pathogenesis of gut-derived sepsis.</p> <p>Methodology/Principal Findings</p> <p>An agent-based model (ABM) of virulence regulation in <it>Pseudomonas aeruginosa </it>was developed by translating bacterial and host cell sense-and-response mechanisms into behavioral rules for computational agents and integrated into a virtual environment representing the host-microbe interface in the gut. The resulting gut milieu ABM (GMABM) was used to: 1) investigate a potential clinically relevant laboratory experimental condition not yet developed - i.e. non-lethal transient segmental intestinal ischemia, 2) examine the sufficiency of existing hypotheses to explain experimental data - i.e. lethality in a model of major surgical insult and stress, and 3) produce behavior to potentially guide future experimental design - i.e. suggested sample points for a potential laboratory model of non-lethal transient intestinal ischemia. Furthermore, hypotheses were generated to explain certain discrepancies between the behaviors of the GMABM and biological experiments, and new investigatory avenues proposed to test those hypotheses.</p> <p>Conclusions/Significance</p> <p>Agent-based modeling can account for the spatio-temporal dynamics of an HPI, and, even when carried out with a relatively high degree of abstraction, can be useful in the investigation of system-level consequences of putative mechanisms operating at the individual agent level. We suggest that an integrated and iterative heuristic relationship between computational modeling and more traditional laboratory and clinical investigations, with a focus on identifying useful and sufficient degrees of abstraction, will enhance the efficiency and translational productivity of biomedical research.</p

Contagion dynamics in multilevel and structured populations.

Existen numerosos procesos de contagio sobre redes, como la propagación de epidemias, los rumores, la información u otros fenómenos no lineales propios de los sistemas complejos humanos. Desde la perspectiva de la modelización matemática, los procesos de contagio en poblaciones estructuradas se están volviendo cada vez más sofisticados en lo que respecta al tipo de interacciones no triviales involucradas en ellos. Los modelos han evolucionado desde los simples métodos compartimentales a modelos estructurados en los que se tienen en cuenta las heterogeneidades de la población. Además, para visualizar estas jerarquías y heterogeneidades de los sistemas complejos humanos, también consideramos la representación multicapa de las poblaciones. En esta tesis, intentamos explorar la punta del iceberg en lo que respecta a procesos de contagio sobre poblaciones basándonos en varios modelos matemáticos. Nuestro objetivo es entender la complejidad de las dinámicas de contagio en poblaciones estructuradas y multinivel.En el primer capítulo, nos centramos en presentar el desarrollo de algunas de las teorías principales que se utilizan para estudiar los sistemas complejos. El descubrimiento de las interacciones no lineales hizo que le método del reduccionismo fuese cuestionado, dado que el comportamiento general no puede describirse como una simple superposición de pequeñas escalas. La ciencia de redes busca caracterizar los sistemas complejos de diversos campos. Al mismo tiempo, la teoría de grafos proporciona las herramientas matemáticas necesarias para describir redes realistas. Discutiremos algunas de las cantidades fundamentales y las métricas más relevantes para la caracterización de la estructura de la red, así como varios ejemplos de modelos de red. Además, repasaremos brevemente los principios básicos de las redes multicapa que rompen la limitación de un solo tipo de conexión existente en las redes monocapa, estableciendo la base para explorar y generalizar estos conceptos.A continuación, estudiaremos procesos dinámicos comenzando por una breve introducción a los modelos matemáticos que se usarán durante el resto de la tesis. En el caso de la ecuación maestra, resaltaremos el rol de los procesos de Markov así como la aproximación de campo medio, sin centrarnos en sus soluciones completas. Los métodos de modelización y las reglas de actualización que se utilizan en las simulaciones numéricas también se presentan en detalle. En esta tesis, nos centraremos en el problema de la propagación de epidemias sobre redes, un tema que despierta gran interés en el campo de los procesos de propagación y contagio. Después de revisar las propiedades y los resultados teóricos de algunos de los modelos epidemiológicos típicos, con varias simplificaciones desde el punto de vista matemático, exploraremos varias medidas importantes en el campo de la epidemiología, i.e., el número reproductivo básico y la inmunidad de grupo. Después, implementaremos un modelo clásico de epidemias sobre redes multicapa para explorar el papel que juega la direccionalidad utilizando funciones generatrices. Terminaremos el capítulo 2 modelizando un tipo especial de procesos de contagio social, en particular, utilizaremos un modelo compartimental para estudiar la propagación de la corrupción. Prestaremos atención a las condiciones críticas para que surja este tipo de comportamiento desarrollando la aproximación de campo medio y comparando sus predicciones con simulaciones. Es más, extenderemos el modelo de corrupción a un sistema de dos capas en el que los flujos de contagio pueden ser diferentes en cada capa para investigar el papel que juega el solapamiento de enlaces y las correlaciones de grado entre capas en la evolución de las actividades honestas y corruptas.Resulta evidente que la complejidad de los sistemas humanos del mundo real afecta la precisión con la que se pueden predecir las epidemias y algunas propiedades específicas de los sistemas. Sin embargo, debido al desarrollo de la ciencia de datos, fuentes de datos masivas y muy informativas pueden utilizarse para enriquecer la topología de la red de forma que se acerque a los sistemas reales. En al tercera parte de esta tesis, comenzaremos describiendo los retos y las oportunidades que han surgido durante el desarrollo de la ciencia de datos. A continuación, intentaremos conseguir una imagen más realista de la estructura interna de las redes de contacto utilizando datos reales. Además, ilustraremos la importancia de utilizar una perspectiva conducida por los datos en lo que respecta a la modelización de redes a la hora de estudiar la propagación de epidemias en redes de contacto. En este caso, la variabilidad de patrones de interacción que surge de la heterogeneidad de la población, sus comportamientos sociales, etc. puede ser capturada correctamente.Bajo este mismo desarrollo teórico, consideraremos la edad de los individuos y sus patrones de interacción social para generar redes multicapa con estructura de edad para estudiar el problema de la inmunidad de grupo del SARS-CoV-2 y evaluar el impacto que tres estrategias de vacunación pueden tener a la hora de eliminar la transmisión de la panedmia. Después, para explorar la dinámica de las enfermedades que se propagan en entornos hospitalarios (HAI, por sus siglas en inglés) cuando los pacientes están recibiendo tratamiento en ellos, utilizaremos una colección de datos espacio-temporales recogida en tres hospitales de Canadá para generar las redes de interacción entre los trabajadores hospitalarios (HCWs). Nos centraremos en determinar cuantitativemente el riesgo de que las HAIs se propaguen por las diferentes unidades de un hospital y los varios grupos de HCWs, respectivamente. Calcularemos el riesgo de las unidades espaciales usando el tiempo de llegada de la enfermedad y el número de infecciones producidas en cada unidad. En el caso de los HCWs, la probabilidad de infectarse y el número de reproducción efectivo son usados como indicador del riesgo de HCWs.Concluiremos la tesis presentando nuestras conclusiones y discutiendo algunos de los restos que quedan por explorar en el futuro.<br /

Report on DIMACS Working Group Meeting: Mathematical Sciences Methods for the Study of Deliberate Releases of Biological Agents and their Consequences

55 pages, 1 article*Report on DIMACS Working Group Meeting: Mathematical Sciences Methods for the Study of Deliberate Releases of Biological Agents and their Consequences* (Castillo-Chavez, Carlos; Roberts, Fred S.) 55 page

Multilayer Networks

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure

Toward Digital Twin Oriented Modeling of Complex Networked Systems and Their Dynamics: A Comprehensive Survey

This paper aims to provide a comprehensive critical overview on how entities and their interactions in Complex Networked Systems (CNS) are modelled across disciplines as they approach their ultimate goal of creating a Digital Twin (DT) that perfectly matches the reality. We propose four complexity dimensions for the network representation and five generations of models for the dynamics modelling to describe the increasing complexity level of the CNS that will be developed towards achieving DT (e.g. CNS dynamics modelled offline in the 1st generation v.s. CNS dynamics modelled simultaneously with a two-way real time feedback between reality and the CNS in the 5th generation). Based on that, we propose a new framework to conceptually compare diverse existing modelling paradigms from different perspectives and create unified assessment criteria to evaluate their respective capabilities of reaching such an ultimate goal. Using the proposed criteria, we also appraise how far the reviewed current state-of-the-art approaches are from the idealised DTs. Finally, we identify and propose potential directions and ways of building a DT-orientated CNS based on the convergence and integration of CNS and DT utilising a variety of cross-disciplinary techniques

EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks

Package EpiModel provides tools for building, simulating, and analyzing mathematical models for the population dynamics of infectious disease transmission in R. Several classes of models are included, but the unique contribution of this software package is a general stochastic framework for modeling the spread of epidemics on networks. EpiModel integrates recent advances in statistical methods for network analysis (temporal exponential random graph models) that allow the epidemic modeling to be grounded in empirical data on contacts that can spread infection. This article provides an overview of both the modeling tools built into EpiModel, designed to facilitate learning for students new to modeling, and the application programming interface for extending package EpiModel, designed to facilitate the exploration of novel research questions for advanced modelers

Statistical Techniques Complement UML When Developing Domain Models of Complex Dynamical Biosystems

Computational modelling and simulation is increasingly being used to complement traditional wet-lab techniques when investigating the mechanistic behaviours of complex biological systems. In order to ensure computational models are fit for purpose, it is essential that the abstracted view of biology captured in the computational model, is clearly and unambiguously defined within a conceptual model of the biological domain (a domain model), that acts to accurately represent the biological system and to document the functional requirements for the resultant computational model. We present a domain model of the IL-1 stimulated NF-κB signalling pathway, which unambiguously defines the spatial, temporal and stochastic requirements for our future computational model. Through the development of this model, we observe that, in isolation, UML is not sufficient for the purpose of creating a domain model, and that a number of descriptive and multivariate statistical techniques provide complementary perspectives, in particular when modelling the heterogeneity of dynamics at the single-cell level. We believe this approach of using UML to define the structure and interactions within a complex system, along with statistics to define the stochastic and dynamic nature of complex systems, is crucial for ensuring that conceptual models of complex dynamical biosystems, which are developed using UML, are fit for purpose, and unambiguously define the functional requirements for the resultant computational model