Slightly generalized Generalized Contagion: Unifying simple models of biological and social spreading

We motivate and explore the basic features of generalized contagion, a model mechanism that unifies fundamental models of biological and social contagion. Generalized contagion builds on the elementary observation that spreading and contagion of all kinds involve some form of system memory. We discuss the three main classes of systems that generalized contagion affords, resembling: simple biological contagion; critical mass contagion of social phenomena; and an intermediate, and explosive, vanishing critical mass contagion. We also present a simple explanation of the global spreading condition in the context of a small seed of infected individuals.Comment: 8 pages, 5 figures; chapter to appear in "Spreading Dynamics in Social Systems"; Eds. Sune Lehmann and Yong-Yeol Ahn, Springer Natur

Intrinsic definitions of "relative velocity" in general relativity

Given two observers, we define the "relative velocity" of one observer with respect to the other in four different ways. All four definitions are given intrinsically, i.e. independently of any coordinate system. Two of them are given in the framework of spacelike simultaneity and, analogously, the other two are given in the framework of observed (lightlike) simultaneity. Properties and physical interpretations are discussed. Finally, we study relations between them in special relativity, and we give some examples in Schwarzschild and Robertson-Walker spacetimes.Comment: 29 pages, 12 figures. New proofs in special relativity and a new open problem in general relativity (see Remark 5.2). An Appendix has been added, studying the relative velocities in Schwarzschild, with new figures. Some spelling erros fixe

Activity driven modeling of time varying networks

Network modeling plays a critical role in identifying statistical regularities and structural principles common to many systems. The large majority of recent modeling approaches are connectivity driven. The structural patterns of the network are at the basis of the mechanisms ruling the network formation. Connectivity driven models necessarily provide a time-aggregated representation that may fail to describe the instantaneous and fluctuating dynamics of many networks. We address this challenge by defining the activity potential, a time invariant function characterizing the agents' interactions and constructing an activity driven model capable of encoding the instantaneous time description of the network dynamics. The model provides an explanation of structural features such as the presence of hubs, which simply originate from the heterogeneous activity of agents. Within this framework, highly dynamical networks can be described analytically, allowing a quantitative discussion of the biases induced by the time-aggregated representations in the analysis of dynamical processes.Comment: 10 pages, 4 figure

A Pycellerator Tutorial.

We present a tutorial on using Pycellerator for biomolecular simulations. Models are described in human readable (and editable) text files (UTF8 or ASCII) containing collections of reactions, assignments, initial conditions, function definitions, and rate constants. These models are then converted into a Python program that can optionally solve the system, e.g., as a system of differential equations using ODEINT, or be run by another program. The input language implements an extended version of the Cellerator arrow notation, including mass action, Hill functions, S-Systems, MWC, and reactions with user-defined kinetic laws. Simple flux balance analysis is also implemented. We will demonstrate the implementation and analysis of progressively more complex models, starting from simple mass action through indexed cascades. Pycellerator can be used as a library that is integrated into other programs, run as a command line program, or in iPython notebooks. It is implemented in Python 2.7 and available under an open source GPL license

Coupled Contagion Dynamics of Fear and Disease: Mathematical and Computational Explorations

Background: In classical mathematical epidemiology, individuals do not adapt their contact behavior during epidemics. They do not endogenously engage, for example, in social distancing based on fear. Yet, adaptive behavior is welldocumented in true epidemics. We explore the effect of including such behavior in models of epidemic dynamics. Methodology/Principal Findings: Using both nonlinear dynamical systems and agent-based computation, we model two interacting contagion processes: one of disease and one of fear of the disease. Individuals can ‘‘contract’ ’ fear through contact with individuals who are infected with the disease (the sick), infected with fear only (the scared), and infected with both fear and disease (the sick and scared). Scared individuals–whether sick or not–may remove themselves from circulation with some probability, which affects the contact dynamic, and thus the disease epidemic proper. If we allow individuals to recover from fear and return to circulation, the coupled dynamics become quite rich, and can include multiple waves of infection. We also study flight as a behavioral response. Conclusions/Significance: In a spatially extended setting, even relatively small levels of fear-inspired flight can have a dramatic impact on spatio-temporal epidemic dynamics. Self-isolation and spatial flight are only two of many possible actions that fear-infected individuals may take. Our main point is that behavioral adaptation of some sort must b

Height and risk of death among men and women: aetiological implications of associations with cardiorespiratory disease and cancer mortality

OBJECTIVES: Height is inversely associated with cardiovascular disease mortality risk and has shown variable associations with cancer incidence and mortality. The interpretation of findings from previous studies has been constrained by data limitations. Associations between height and specific causes of death were investigated in a large general population cohort of men and women from the West of Scotland. DESIGN: Prospective observational study. SETTING: Renfrew and Paisley, in the West of Scotland. SUBJECTS: 7052 men and 8354 women aged 45-64 were recruited into a study in Renfrew and Paisley, in the West of Scotland, between 1972 and 1976. Detailed assessments of cardiovascular disease risk factors, morbidity and socioeconomic circumstances were made at baseline. MAIN OUTCOME MEASURES: Deaths during 20 years of follow up classified into specific causes. RESULTS: Over the follow up period 3347 men and 2638 women died. Height is inversely associated with all cause, coronary heart disease, stroke, and respiratory disease mortality among men and women. Adjustment for socioeconomic position and cardiovascular risk factors had little influence on these associations. Height is strongly associated with forced expiratory volume in one second (FEV1) and adjustment for FEV1 considerably attenuated the association between height and cardiorespiratory mortality. Smoking related cancer mortality is not associated with height. The risk of deaths from cancer unrelated to smoking tended to increase with height, particularly for haematopoietic, colorectal and prostate cancers. Stomach cancer mortality was inversely associated with height. Adjustment for socioeconomic position had little influence on these associations. CONCLUSION: Height serves partly as an indicator of socioeconomic circumstances and nutritional status in childhood and this may underlie the inverse associations between height and adulthood cardiorespiratory mortality. Much of the association between height and cardiorespiratory mortality was accounted for by lung function, which is also partly determined by exposures acting in childhood. The inverse association between height and stomach cancer mortality probably reflects Helicobacter pylori infection in childhood resulting inor being associated withshorter height. The positive associations between height and several cancers unrelated to smoking could reflect the influence of calorie intake during childhood on the risk of these cancers

Dynamics of multi-stage infections on networks

This paper investigates the dynamics of infectious diseases with a nonexponentially distributed infectious period. This is achieved by considering a multistage infection model on networks. Using pairwise approximation with a standard closure, a number of important characteristics of disease dynamics are derived analytically, including the final size of an epidemic and a threshold for epidemic outbreaks, and it is shown how these quantities depend on disease characteristics, as well as the number of disease stages. Stochastic simulations of dynamics on networks are performed and compared to output of pairwise models for several realistic examples of infectious diseases to illustrate the role played by the number of stages in the disease dynamics. These results show that a higher number of disease stages results in faster epidemic outbreaks with a higher peak prevalence and a larger final size of the epidemic. The agreement between the pairwise and simulation models is excellent in the cases we consider

Evaluating the Combined Effectiveness of Influenza Control Strategies and Human Preventive Behavior

Control strategies enforced by health agencies are a major type of practice to contain influenza outbreaks. Another type of practice is the voluntary preventive behavior of individuals, such as receiving vaccination, taking antiviral drugs, and wearing face masks. These two types of practices take effects concurrently in influenza containment, but little attention has been paid to their combined effectiveness. This article estimates this combined effectiveness using established simulation models in the urbanized area of Buffalo, NY, USA. Three control strategies are investigated, including: Targeted Antiviral Prophylaxis (TAP), workplace/school closure, community travel restriction, as well as the combination of the three. All control strategies are simulated with and without regard to individual preventive behavior, and the resulting effectiveness are compared. The simulation outcomes suggest that weaker control strategies could suffice to contain influenza epidemics, because individuals voluntarily adopt preventive behavior, rendering these weaker strategies more effective than would otherwise have been expected. The preventive behavior of individuals could save medical resources for control strategies and avoid unnecessary socio-economic interruptions. This research adds a human behavioral dimension into the simulation of control strategies and offers new insights into disease containment. Health policy makers are recommended to review current control strategies and comprehend preventive behavior patterns of local populations before making decisions on influenza containment

Exact equations for SIR epidemics on tree graphs

We consider Markovian susceptible-infectious-removed (SIR) dynamics on time-invariant weighted contact networks where the infection and removal processes are Poisson and where network links may be directed or undirected. We prove that a particular pair-based moment closure representation generates the expected infectious time series for networks with no cycles in the underlying graph. Moreover, this “deterministic” representation of the expected behaviour of a complex heterogeneous and finite Markovian system is straightforward to evaluate numerically

Ross, Macdonald, and a Theory for the Dynamics and Control of Mosquito-Transmitted Pathogens

Ronald Ross and George Macdonald are credited with developing a mathematical model of mosquito-borne pathogen transmission. A systematic historical review suggests that several mathematicians and scientists contributed to development of the Ross-Macdonald model over a period of 70 years. Ross developed two different mathematical models, Macdonald a third, and various “Ross-Macdonald” mathematical models exist. Ross-Macdonald models are best defined by a consensus set of assumptions. The mathematical model is just one part of a theory for the dynamics and control of mosquito-transmitted pathogens that also includes epidemiological and entomological concepts and metrics for measuring transmission. All the basic elements of the theory had fallen into place by the end of the Global Malaria Eradication Programme (GMEP, 1955–1969) with the concept of vectorial capacity, methods for measuring key components of transmission by mosquitoes, and a quantitative theory of vector control. The Ross-Macdonald theory has since played a central role in development of research on mosquito-borne pathogen transmission and the development of strategies for mosquito-borne disease prevention