Abstract. In this paper, we develop a rigorous, unified framework based on Ordinary Differential Equations (ODEs) to study epidemic routing and its variations. These ODEs can be derived as limits of Markovian models under a natural scaling as the number of nodes increases. While an analytical study of Markovian models is quite complex and numerical solution impractical for large networks, the corresponding ODE models yield closed-form expressions for several performance metrics of interest, and a numerical solution complexity that does not increase with the number of nodes. Using this ODE approach, we investigate how resources such as buffer space and power can be traded for faster delivery, illustrating the differences among the various epidemic schemes considered. Finally we consider the effect of buffer management by complementing the forwarding models with Markovian and fluid buffer models.

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by non-mean-field-type social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner’s Dilemma, the Rock–Scissors–Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.

We present a model of contagion that unifies and generalizes existing models of the spread of social influences and microorganismal infections. Our model incorporates individual memory of exposure to a contagious entity (e.g. a rumor or disease), variable magnitudes of exposure (dose sizes), and heterogeneity in the susceptibility of individuals. Through analysis and simulation, we examine in detail the case where individuals may recover from an infection and then immediately become susceptible again (analogous to the so-called SIS model). We identify three basic classes of contagion models which we call epidemic threshold, vanishing critical mass, and critical mass classes, where each class of models corresponds to different strategies for prevention or facilitation. We find that the conditions for a particular contagion model to belong to one of the these three classes depend only on memory length and the probabilities of being infected by one and two exposures, respectively. These parameters are in principle measurable for real contagious influences or entities, thus yielding empirical implications for our model. We also study the case where individuals attain permanent immunity once recovered, finding that epidemics inevitably die out but may be surprisingly persistent when individuals possess memory.

The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consideration of implicit dynamic models, meaning statistical models for stochastic dynamical systems which are specified by a simulation algorithm to generate sample paths. Inference procedures that operate on implicit models are said to have the plug-and-play property. Our work builds on recently developed plug-and-play inference methodology for partially observed Markov models. We introduce a class of implicitly specified Markov chains with stochastic transition rates, and we demonstrate its applicability to open problems in statistical inference for biological systems. As one example, these models are shown to give a fresh perspective on measles transmission dynamics. As a second example, we present a mechanistic analysis of cholera incidence data, involving interaction between two competing strains of the pathogen Vibrio cholerae. 1. Introduction. A

We investigate the collective behavior of processes in terms of differential equations, using chemistry as a stepping stone. Chemical reactions can be converted to ordinary differential equations, and also to processes in a stochastic process algebra. Conversely, certain stochastic processes (in Chemical Parametric Form, or CPF) can be converted to chemical reactions. CPF is a subset of π-calculus, but is already more powerful that what is strictly needed to represent chemistry: it supports also parameterization and compositional reuse of models. The mapping of CPF to chemistry thus induces a parametric and compositional mapping of CPF to differential equations; the indirect mapping through chemistry is easier to define and understand than a direct mapping. As an example, we derive a quantitative interleaving law from the differential equations. 1

Abstract. We present a new bio-inspired approach applied to a problem of stereo images matching. This approach is based on an artifical epidemic process, that we call “the infection algorithm. ” The problem at hand is a basic one in computer vision for 3D scene reconstruction. It has many complex aspects and is known as an extremely difficult one. The aim is to match the contents of two images in order to obtain 3D informations which allow the generation of simulated projections from a viewpoint that is different from the ones of the initial photographs. This process is known as view synthesis. The algorithm we propose exploits the image contents in order to only produce the necessary 3D depth information, while saving computational time. It is based on a set of distributed rules, that propagate like an artificial epidemy over the images. Experiments on a pair of real images are presented, and realistic reprojected images have been generated. 1

An encounter-based network is a frequently-disconnected wireless ad-hoc network requiring nearby neighbors to store and forward data utilizing mobility and encounters over time. Using traditional approaches such as gateways or firewalls for deterring worm propagation in encounter-based networks is inappropriate. We propose models for the worm interaction approach that relies upon automated beneficial worm generation to alleviate problems of worm propagation in such networks. We study and analyze the impact of key mobile node characteristics including node cooperation, immunization, on-off behavior on the worm propagations and interactions. We validate our proposed model using extensive simulations. We also find that, in addition to immunization, cooperation can reduce the level of worm infection. Furthermore, on-off behavior linearly impacts only timing aspect but not the overall infection. Using realistic mobile network measurements, we find that encounters are non-uniform, the trends are consistent with the model but the magnitudes are drastically different. Immunization seems to be the most effective in such scenarios. These findings provide insight that we hope would aid to develop counter-worm protocols in future encounterbased networks.

In social systems, meaning can be communicated in addition to underlying processes of the information exchange. Meaning processing incurs on information processing with hindsight, while information processing recursively follows the time axis. The sole assumption of social relatedness as a variable among groups of agents provides sufficient basis for deriving the logistic map as a first-order approximation of the social system. The anticipatory formulation of this equation can be derived for both anticipation in the interaction term and in the aggregation among subgroups. Using this formula in a cellular automaton, an observer is generated as a reflection of the system under observation. The social system of interactions among observations can improve on the representations entertained by each of the observing systems.

Previously we have formulated transmission models of untreated tuberculosis epidemics (Blower et al., Nature, Medicine 1 (1995), 815 821); in this paper, we present time-dependent uncertainty and sensitivity analyses in order to quantitatively understand the transmission dynamics of tuberculosis epidemics in the absence of treatment. The time-dependent uncertainty analysis enabled us to evaluate the variability in the epidemiological outcome variables of the model during the progression of a tuberculosis epidemic. Calculated values (from the uncertainty analysis) for the disease incidence, disease prevalence, and mortality rates were approximately consistent with historical data. The time-dependent sensitivity analysis revealed that only a few of the model's input parameters significantly affected the severity of a tuberculosis epidemic; these parameters were the disease reactivation rate, the fraction of infected individuals who develop tuberculosis soon after infection, the number of individuals that an infectious individual infects per year, the disease death rate, and the population recruitment rate. Our analysis demonstrates that it is possible to improve our understanding of the behavior of tuberculosis epidemics by applying time-dependent uncertainty and sensitivity analysis to a transmission model.]

Abstract — An encounter-based network is a frequently-disconnected wireless ad-hoc network requiring immediate neighbors to store and forward aggregated data for information disseminations. Using traditional approaches such as gateways or firewalls to deter worm propagation in encounter-based networks is inappropriate. We propose a worm interaction approach that relies upon automated beneficial worm generation to alleviate problems of worm propagations in such networks. To understand the dynamics of worm interactions and their performance, we mathematically model worm interactions based on major worm interaction factors, including worm interaction types, network characteristics, and node characteristics using ordinary differential equations and analyze their effects on our proposed metrics. We validate our proposed model using extensive synthetic and trace-driven simulations. We find that all worm interaction factors significantly affect the pattern of worm propagations. For example, immunization linearly decreases the infection of susceptible nodes, while on-off behavior only impacts the duration of infection. Using realistic mobile network measurements, we find that encounters are “bursty”, multi-group, and non-uniform. The trends from the trace-driven simulations are consistent with the model, in general. Immunization and timely deployment seem to be most effective in countering worm attacks in such scenarios, while cooperation may help in a specific case. These findings provide insight that we hope would aid in the development of counter-worm protocols in future encounter-based networks. I.