Invited review: Epidemics on social networks

Since its first formulations almost a century ago, mathematical models for disease spreading contributed to understand, evaluate and control the epidemic processes.They promoted a dramatic change in how epidemiologists thought of the propagation of infectious diseases.In the last decade, when the traditional epidemiological models seemed to be exhausted, new types of models were developed.These new models incorporated concepts from graph theory to describe and model the underlying social structure.Many of these works merely produced a more detailed extension of the previous results, but some others triggered a completely new paradigm in the mathematical study of epidemic processes. In this review, we will introduce the basic concepts of epidemiology, epidemic modeling and networks, to finally provide a brief description of the most relevant results in the field.Comment: 17 pages, 13 figure

Networks and the epidemiology of infectious disease

The science of networks has revolutionised research into the dynamics of interacting elements. It could be argued that epidemiology in particular has embraced the potential of network theory more than any other discipline. Here we review the growing body of research concerning the spread of infectious diseases on networks, focusing on the interplay between network theory and epidemiology. The review is split into four main sections, which examine: the types of network relevant to epidemiology; the multitude of ways these networks can be characterised; the statistical methods that can be applied to infer the epidemiological parameters on a realised network; and finally simulation and analytical methods to determine epidemic dynamics on a given network. Given the breadth of areas covered and the ever-expanding number of publications, a comprehensive review of all work is impossible. Instead, we provide a personalised overview into the areas of network epidemiology that have seen the greatest progress in recent years or have the greatest potential to provide novel insights. As such, considerable importance is placed on analytical approaches and statistical methods which are both rapidly expanding fields. Throughout this review we restrict our attention to epidemiological issues

Dynamics of interacting diseases

Current modeling of infectious diseases allows for the study of complex and realistic scenarios that go from the population to the individual level of description. However, most epidemic models assume that the spreading process takes place on a single level (be it a single population, a meta-population system or a network of contacts). In particular, interdependent contagion phenomena can only be addressed if we go beyond the scheme one pathogen-one network. In this paper, we propose a framework that allows describing the spreading dynamics of two concurrent diseases. Specifically, we characterize analytically the epidemic thresholds of the two diseases for different scenarios and also compute the temporal evolution characterizing the unfolding dynamics. Results show that there are regions of the parameter space in which the onset of a disease's outbreak is conditioned to the prevalence levels of the other disease. Moreover, we show, for the SIS scheme, that under certain circumstances, finite and not vanishing epidemic thresholds are found even at the thermodynamic limit for scale-free networks. For the SIR scenario, the phenomenology is richer and additional interdependencies show up. We also find that the secondary thresholds for the SIS and SIR models are different, which results directly from the interaction between both diseases. Our work thus solve an important problem and pave the way towards a more comprehensive description of the dynamics of interacting diseases.Comment: 24 pages, 9 figures, 4 tables, 3 appendices. Final version accepted for publication in Physical Review

The role of caretakers in disease dynamics

One of the key challenges in modeling the dynamics of contagion phenomena is to understand how the structure of social interactions shapes the time course of a disease. Complex network theory has provided significant advances in this context. However, awareness of an epidemic in a population typically yields behavioral changes that correspond to changes in the network structure on which the disease evolves. This feedback mechanism has not been investigated in depth. For example, one would intuitively expect susceptible individuals to avoid other infecteds. However, doctors treating patients or parents tending sick children may also increase the amount of contact made with an infecteds, in an effort to speed up recovery but also exposing themselves to higher risks of infection. We study the role of these caretaker links in an adaptive network models where individuals react to a disease by increasing or decreasing the amount of contact they make with infected individuals. We find that pure avoidance, with only few caretaker links, is the best strategy for curtailing an SIS disease in networks that possess a large topological variability. In more homogeneous networks, disease prevalence is decreased for low concentrations of caretakers whereas a high prevalence emerges if caretaker concentration passes a well defined critical value.Comment: 8 pages, 9 figure

The spread of epidemic disease on networks

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are non-uniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.Comment: 12 pages, 3 figure

Data on face-to-face contacts in an office building suggests a low-cost vaccination strategy based on community linkers

Empirical data on contacts between individuals in social contexts play an important role in providing information for models describing human behavior and how epidemics spread in populations. Here, we analyze data on face-to-face contacts collected in an office building. The statistical properties of contacts are similar to other social situations, but important differences are observed in the contact network structure. In particular, the contact network is strongly shaped by the organization of the offices in departments, which has consequences in the design of accurate agent-based models of epidemic spread. We consider the contact network as a potential substrate for infectious disease spread and show that its sparsity tends to prevent outbreaks of rapidly spreading epidemics. Moreover, we define three typical behaviors according to the fraction $f$ of links each individual shares outside its own department: residents, wanderers and linkers. Linkers ($f\sim 50\%$) act as bridges in the network and have large betweenness centralities. Thus, a vaccination strategy targeting linkers efficiently prevents large outbreaks. As such a behavior may be spotted a priori in the offices' organization or from surveys, without the full knowledge of the time-resolved contact network, this result may help the design of efficient, low-cost vaccination or social-distancing strategies