Spreading Processes over Socio-Technical Networks with Phase-Type Transmissions

Most theoretical tools available for the analysis of spreading processes over networks assume exponentially distributed transmission and recovery times. In practice, the empirical distribution of transmission times for many real spreading processes, such as the spread of web content through the Internet, are far from exponential. To bridge this gap between theory and practice, we propose a methodology to model and analyze spreading processes with arbitrary transmission times using phase-type distributions. Phase-type distributions are a family of distributions that is dense in the set of positive-valued distributions and can be used to approximate any given distributions. To illustrate our methodology, we focus on a popular model of spreading over networks: the susceptible-infected-susceptible (SIS) networked model. In the standard version of this model, individuals informed about a piece of information transmit this piece to its neighbors at an exponential rate. In this paper, we extend this model to the case of transmission rates following a phase-type distribution. Using this extended model, we analyze the dynamics of the spread based on a vectorial representations of phase-type distributions. We illustrate our results by analyzing spreading processes over networks with transmission and recovery rates following a Weibull distribution

The Effect of Disease-induced Mortality on Structural Network Properties

As the understanding of the importance of social contact networks in the spread of infectious diseases has increased, so has the interest in understanding the feedback process of the disease altering the social network. While many studies have explored the influence of individual epidemiological parameters and/or underlying network topologies on the resulting disease dynamics, we here provide a systematic overview of the interactions between these two influences on population-level disease outcomes. We show that the sensitivity of the population-level disease outcomes to the combination of epidemiological parameters that describe the disease are critically dependent on the topological structure of the population's contact network. We introduce a new metric for assessing disease-driven structural damage to a network as a population-level outcome. Lastly, we discuss how the expected individual-level disease burden is influenced by the complete suite of epidemiological characteristics for the circulating disease and the ongoing process of network compromise. Our results have broad implications for prediction and mitigation of outbreaks in both natural and human populations.Comment: 23 pages, 6 figure

Epidemic processes in complex networks

In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world networks have a profound impact on the behavior of equilibrium and nonequilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, mathematicians, epidemiologists, computer, and social scientists share a common interest in studying epidemic spreading and rely on similar models for the description of the diffusion of pathogens, knowledge, and innovation. For this reason, while focusing on the main results and the paradigmatic models in infectious disease modeling, the major results concerning generalized social contagion processes are also presented. Finally, the research activity at the forefront in the study of epidemic spreading in coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio

Dynamical Systems on Networks: A Tutorial

We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more complicated scenarios. We briefly motivate why examining dynamical systems on networks is interesting and important, and we then give several fascinating examples and discuss some theoretical results. We also briefly discuss dynamical systems on dynamical (i.e., time-dependent) networks, overview software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than original version, some reorganization and also more pointers to interesting direction

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