Interactive social contagions and co-infections on complex networks

A generalized linear threshold model for an improved description of the spreading dynamics

Many spreading processes in our real-life can be considered as a complex contagion, and the linear threshold (LT) model is often applied as a very representative model for this mechanism. Despite its intensive usage, the LT model suffers several limitations in describing the time evolution of the spreading. First, the discrete-time step that captures the speed of the spreading is vaguely defined. Second, the synchronous updating rule makes the nodes infected in batches, which cannot take individual differences into account. Finally, the LT model is incompatible with existing models for the simple contagion. Here, we consider a generalized linear threshold (GLT) model for the continuous-time stochastic complex contagion process that can be efficiently implemented by the Gillespie algorithm. The time in this model has a clear mathematical definition, and the updating order is rigidly defined. We find that the traditional LT model systematically underestimates the spreading speed and the randomness in the spreading sequence order. We also show that the GLT model works seamlessly with the susceptible-infected or susceptible-infected-recovered model. One can easily combine them to model a hybrid spreading process in which simple contagion accumulates the critical mass for the complex contagion that leads to the global cascades. Overall, the GLT model we proposed can be a useful tool to study complex contagion, especially when studying the time evolution of the spreading.

Host-parasite coevolution: Role of selection, mutation, and asexual reproduction on evolvability

The key to the survival of a species lies in understanding its evolution in an ever-changing environment. We report a theoretical model that integrates frequency-dependent selection, mutation, and asexual reproduction for understanding the biological evolution of a host species in the presence of parasites. We study the host-parasite coevolution in a one-dimensional genotypic space by considering a dynamic and heterogeneous environment modeled using a fitness landscape. It is observed that the presence of parasites facilitates a faster evolution of the host population toward its fitness maximum. We also find that the time required to reach the maximum fitness (optimization time) decreases with increased infection from the parasites. However, the overall fitness of the host population declines due to the parasitic infection. In the limit where parasites are considered to evolve much faster than the hosts, the optimization time reduces even further. Our findings indicate that parasites can play a crucial role in the survival of its host in a rapidly changing environment.

Coevolution spreading in complex networks

The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and critical phenomena of networked coevolution spreading are extremely important, which provide theoretical foundations for us to control epidemic spreading, predict collective behaviors in social systems, and so on. The coevolution spreading dynamics in complex networks has thus attracted much attention in many disciplines. In this review, we introduce recent progress in the study of coevolution spreading dynamics, emphasizing the contributions from the perspectives of statistical mechanics and network science. The theoretical methods, critical phenomena, phase transitions, interacting mechanisms, and effects of network topology for four representative types of coevolution spreading mechanisms, including the coevolution of biological contagions, social contagions, epidemic-awareness, and epidemic-resources, are presented in detail, and the challenges in this field as well as open issues for future studies are also discussed.

Critical transitions in heterogeneous networks: Loss of low-degree nodes as an early warning signal

A large number of real networks show abrupt phase transition phenomena in response to environmental changes. In this case, cascading phenomena can induce drastic and discontinuous changes in the system state and lead to collapse. Although complex network theory has been used to investigate these drastic events, we are still unable to predict them effectively. We here analyze collapse phenomena by proposing a minimal two-state dynamic on a complex network and introducing the effect of local connectivities on the evolution of network nodes. We find that a heterogeneous system of interconnected components presents a mixed response to stress and can serve as a control indicator. In particular, before the critical transition point is reached a severe loss of low-degree nodes is observed, masked by the minimal failure of higher-degree nodes. Accordingly, we suggest that a significant reduction in less connected nodes can indicate impending global failure.

Social contagions on interconnected networks of heterogeneous populations

Recently, the dynamics of social contagions ranging from the adoption of a new product to the diffusion of a rumor have attracted more and more attention from researchers. However, the combined effects of individual's heterogenous adoption behavior and the interconnected structure on the social contagions processes have yet to be understood deeply. In this paper, we study theoretically and numerically the social contagions with heterogeneous adoption threshold in interconnected networks. We first develop a generalized edge-based compartmental approach to predict the evolution of social contagion dynamics on interconnected networks. Both the theoretical predictions and numerical results show that the growth of the final recovered fraction with the intralayer propagation rate displays double transitions. When increasing the initial adopted proportion or the adopted threshold, the first transition remains continuous within different dynamic parameters, but the second transition gradually vanishes. When decreasing the interlayer propagation rate, the change in the double transitions mentioned above is also observed. The heterogeneity of degree distribution does not affect the type of first transition, but increasing the heterogeneity of degree distribution results in the type change of the second transition from discontinuous to continuous. The consistency between the theoretical predictions and numerical results confirms the validity of our proposed analytical approach.

Impacts of opinion leaders on social contagions

Opinion leaders are ubiquitous in both online and offline social networks, but the impacts of opinion leaders on social behavior contagions are still not fully understood, especially by using a mathematical model. Here, we generalize the classical Watts threshold model and address the influences of the opinion leaders, where an individual adopts a new behavior if one of his/her opinion leaders adopts the behavior. First, we choose the opinion leaders randomly from all individuals in the network and find that the impacts of opinion leaders make other individuals adopt the behavior more easily. Specifically, the existence of opinion leaders reduces the lowest mean degree of the network required for the global behavior adoption and increases the highest mean degree of the network that the global behavior adoption can occur. Besides, the introduction of opinion leaders accelerates the behavior adoption but does not change the adoption order of individuals. The developed theoretical predictions agree with the simulation results. Second, we randomly choose the opinion leaders from the top h% of the highest degree individuals and find an optimal h% for the network with the lowest mean degree that the global behavior adoption can occur. Meanwhile, the influences of opinion leaders on accelerating the adoption of behaviors become less significant and can even be ignored when reducing the value of h%.