Session B54: Focus Session: Complex and co-evolving networks - Modeling Social and Biological Networks

Human travel and time spent at destination: impact on the epidemic invasion dynamics

Human mobility has a strong impact on the spatial spread of infectious diseases. Analyses of metapopulation models, that consider the epidemic spreading on a network of populations, show that topological and traffic fluctuations favor the global epidemic invasion. These studies consider markovian mobility (i.e. the memory of the origin of traveling individuals is lost) or non-markovian mobility with homogeneous timescales (i.e. individuals travel to a destination and come back with a homogenous rate). However, the time spent at destination is found to exhibit wide fluctuations. Such varying length of stay crucially affects the mixing among individuals and hence the disease transmission dynamics. In order to explore this aspect, we present a modeling framework that, by using a time-scale separation technique, allows analyzing the behavior of spreading processes on a complex metapopulation network with non-markovian mobility characterized by heterogeneously distributed timescales. Analytical and numerical results show how the degree of heterogeneity of the length of stay is able, alone, to drive a phase transition between local outbreak and global invasion. This highlights the importance of the interplay between mobility and disease timescales in the propagation of an epidemic.   

Effect of Spatial-Dependent Utility on Social Group Domination

The mathematical modeling of social group competition has garnered much attention. We consider a model originated by Abrams and Strogatz [Nature 424, 900 (2003)] that predicts the extinction of one of two social groups. This model assigns a utility to each social group, which is constant over the entire society. We find by allowing this utility to vary over a society, through the introduction of a network or spatial dependence, this model may result in the coexistence of the two social groups.   

Evolution of opinions on social networks in the presence of competing committed groups

Using a model of pairwise social influence, the {\it binary agreement} model (Xie et. al, Phys. Rev. E 84, 011130 (2011)), we study how the presence of two groups of individuals committed to competing opinions, affect the steady-state opinion of influencable individuals on a social network. We assume that two groups committed to distinct opinions $A$ and $B$, and constituting fractions $p_A$, $p_B$ of the total population respectively, are present in the network. We show using mean-field theory that the phase diagram of this system in parameter space $(p_A,p_B)$ consists of two regions, one where two stable steady-states coexist, and the remaining where only a single stable steady-state exists. For finite networks (complete graphs, Erd\H{o}s-R\'enyi networks and Barab\'asi-Albert networks), these two regions are separated by two first order transition lines which terminate and meet tangentially at $p_A = p_B \approx 0.1623$, which constitutes a second-order transition point. Finally, we quantify how the exponentially large switching times between steady states in the co-existence region depend on the distance from the second-order transition point for equal committed fractions.   

Strategy of Competition between Two Groups based on an Inflexible Contrarian Opinion Model

We introduce an inflexible contrarian opinion (ICO) model in which a fraction p of inflexible contrarians within a group holds a strong opinion opposite to the opinion held by the rest of the group. At the initial stage, stable clusters of two opinions, A and B exist. Then we introduce inflexible contrarians which hold a strong B opinion into the opinion A group. Through their interactions, the inflexible contrarians are able to decrease the size of the largest A opinion cluster, and even destroy it. We see this kind of method in operation, when companies send free new products to potential customers in order to convince them to adopt their product and influence others to buy it. We study the ICO model, using two different strategies, on both ER and SF networks. In strategy I, the inflexible contrarians are positioned at random. In strategy II, the inflexible contrarians are chosen to be the highest degrees nodes. We find that for both strategies the size of the largest A cluster decreases to zero as $p$ increases as in a phase transition. At a critical threshold value p$_c$ the system undergoes a second-order phase transition that belongs to the same universality class of mean field percolation. We find that even for an ER type model, strategy II is significantly more effective.   

Consensus in evolving networks of mobile agents

Populations of mobile and communicating agents describe a vast array of technological and natural systems, ranging from sensor networks to animal groups. Here, we investigate how a group-level agreement may emerge in the continuously evolving networks defined by the local interactions of the moving individuals. We adopt a general scheme of motion in two dimensions and we let the individuals interact through the minimal naming game, a prototypical scheme to investigate social consensus. We distinguish different regimes of convergence determined by the emission range of the agents and by their mobility, and we identify the corresponding scaling behaviors of the consensus time. In the same way, we rationalize also the behavior of the maximum memory used during the convergence process, which determines the minimum cognitive/storage capacity needed by the individuals. Overall, we believe that the simple and general model presented in this talk can represent a helpful reference for a better understanding of the behavior of populations of mobile agents.   

Epidemic and information co-spreading in adaptive social networks

We model simultaneous evolution of an epidemic and information about the epidemic on an adaptive social network. The classical Susceptible-Infectious-Susceptible (SIS) model is extended. Susceptible and infectious nodes are each divided into informed and uninformed types. Informed nodes affect the network structure by rewiring their network connections adaptively to avoid disease exposure. The impacts of mass media information and communication on the disease spreading and network structure are explored, and stochastic simulations are compared with a moment closure approximation. When the rewiring rate is high, the infection and information levels of the population show periodic oscillations for certain ranges of contact rate, and the moment closure approximation predicts similar dynamics. The epidemic threshold in the presence of rewiring and information is considered. Our results indicate that information can play a significant role in minimizing disease spread.   

Asymptotically inspired moment-closure approximation for adaptive networks

Adaptive social networks, in which nodes and network structure co-evolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher order topological structures. We propose a moment-closure approximation based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and epidemic spread model. We show a good agreement between the improved mean-field prediction and simulations of the full network system.   

Epidemics on Interacting Networks

Epidemic spreading is of great importance in public health, as well as in related fields such as infrastructure. While complex network models have been used with great success to analyze epidemic behavior on single networks, the reality is that our world is made up of a system of interacting networks that do not necessarily share common characteristics. I introduce a model for constructing interacting networks and show that the phase transtion depends on the parameters $\kappa_T, kappa_A$ and $\kappa_B$, where $\kappa_T = \langle k^2 \rangle / \langle k \rangle$ over the nodes in both networks, including internetwork links, and $\kappa_A$ and $\kappa_B$ are over the networks considered individually, with no internetwork links. For strongly interacting networks ($\kappa_T > \kappa_A and \kappa_B$), there exists only one phase transition, between a disease-free phase and an epidemic phase across both networks. For weakly interacting networks ($\kappa_T < \kappa_A$ or $\kappa_B$), a third, ``mixed,'' phase exists, where the disease enters an epidemic on one network alone. The analytic predictions are confirmed by Monte-Carlo simulations.   

Epidemic spreading on interacting networks with preferred degrees

We discuss the SIS contact process on a network of two interacting communities, each with its own preferred degree of connections. Postulating various rules for an individuals to form intra-community and inter-community links, we find novel stationary (active) states, in addition to the expected absorbing states. The dynamics of infected individuals in the two communities can be quite different. Using Monte Carlo techniques, we explore the effects on both the network structure and the contact process due to different types of interactions between the communities. We will also present a mean field analysis of contact processes on a generic $M$ interacting communities and compare these results with the simulation data.   

Scaling theory of human dynamics and network science

The increasing availability of large-scale real data has fueled simultaneous advances in network theory, aiming to characterize the scaling of complex networks, and human dynamics, capturing the temporal characteristics of human activity patterns. Yet, these two areas remain disjoint, with their separate scaling laws and modeling framework. Here we show that the exponents characterizing the degree and link weight distribution of the underlying social network can be expressed in terms of the dynamical exponents characterizing human activity patterns, establishing the first formal link between the two areas.   

Network model explains why cancer cells use inefficient pathway to produce energy

The Warburg effect---the use of the (energetically inefficient) fermentative pathway as opposed to (energetically efficient) respiration even in the presence of oxygen---is a common property of cancer metabolism. Here, we propose that the Warburg effect is in fact a consequence of a trade-off between the benefit of rapid growth and the cost for protein synthesis. Using genome-scale metabolic networks, we have modeled the cellular resources for protein synthesis as a growth defect that increases with enzyme concentration. Based on our model, we demonstrate that the cost of protein production during rapid growth drives the cell to rely on fermentation to produce ATP. We also identify an intimate link between extensive fermentation and rapid biosynthesis. Our findings emphasize the importance of protein synthesis as a limiting factor on cell proliferation and provide a novel mathematical framework to analyze cancer metabolism.   

Physiological Networks: towards systems physiology

The human organism is an integrated network where complex physiologic systems, each with its own regulatory mechanisms, continuously interact, and where failure of one system can trigger a breakdown of the entire network. Identifying and quantifying dynamical networks of diverse systems with different types of interactions is a challenge. Here, we develop a framework to probe interactions among diverse systems, and we identify a physiologic network. We find that each physiologic state is characterized by a specific network structure, demonstrating a robust interplay between network topology and function. Across physiologic states the network undergoes topological transitions associated with fast reorganization of physiologic interactions on time scales of a few minutes, indicating high network flexibility in response to perturbations. The proposed system-wide integrative approach may facilitate new dimensions to the field of systems physiology.   

Detecting and evaluating communities in complex human and biological networks

We develop a simple method for detecting the community structure in a network can by utilizing a measure of closeness between nodes. This approach readily leads to a method of coarse graining the network, which allows the detection of the natural hierarchy (or hierarchies) of community structure without appealing to an unknown resolution parameter. The closeness measure can also be used to evaluate the robustness of an individual node's assignment to its community (rather than evaluating only the quality of the global structure). Each of these methods in community detection and evaluation are illustrated using a variety of real world networks of either biological or sociological importance and illustrate the power and flexibility of the approach.   

Small-world organization of self-similar modules in functional brain networks

The modular organization of the brain implies the parallel nature of brain computations. These modules have to remain functionally independent, but at the same time they need to be sufficiently connected to guarantee the unitary nature of brain perception. Small-world architectures have been suggested as probable structures explaining this behavior. However, there is intrinsic tension between shortcuts generating small-worlds and the persistence of modularity. In this talk, we study correlations between the activity in different brain areas. We suggest that the functional brain network formed by the percolation of strong links is highly modular. Contrary to the common view, modules are self-similar and therefore are very far from being small-world. Incorporating the weak ties to the network converts it into a small-world preserving an underlying backbone of well-defined modules. Weak ties are shown to follow a pattern that maximizes information transfer with minimal wiring costs. This architecture is reminiscent of the concept of weak-ties strength in social networks and provides a natural solution to the puzzle of efficient infomration flow in the highly modular structure of the brain.   

Unraveling the rules of evolution in the yeast protein-protein interaction network

A question of fundamental importance is to understand the dynamical principles according to which biological networks have acquired their topological structures and functional modules. Here, we perform an empirical study of the yeast protein-protein interactions (PPI), combined with theoretical modeling of the genomic duplication-divergence processes. Our duplication-divergence model agrees with experimental data, and provides a novel approach to reconstruct ancestral PPI networks. Following the phylogenetic tree, our analysis unravels that the ancient networks evolve into the present day yeast network by a multiplicative growth. The rule of multiplicative growth demonstrates the relationship between the topological exponents and the evolution growth rates of interactions. An important consequence of this evolutional principle is the emergence of self-similar modular structure, which is confirmed by the analysis of functional modules of proteins.