Unification of theoretical approaches for epidemic spreading on complex networks

Abstract

Models of epidemic spreading on complex networks have attracted great attention among researchers in physics, mathematics, and epidemiology due to their success in predicting and controlling scenarios of epidemic spreading in real-world scenarios. To understand the interplay between epidemic spreading and the topology of a contact network, several outstanding theoretical approaches have been developed. An accurate theoretical approach describing the spreading dynamics must take both the network topology and dynamical correlations into consideration at the expense of increasing the complexity of the equations. In this short survey we unify the most widely used theoretical approaches for epidemic spreading on complex networks in terms of increasing complexity, including the mean-field, the heterogeneous mean-field, the quench mean-field, dynamical messagepassing, link percolation, and pairwise approximation. We build connections among these approaches to provide new insights into developing an accurate theoretical approach to spreading dynamics on complex networks.

Emergence of hysteresis loop in social contagions on complex networks

“…1(b,d)]. Our theory agrees well with the simulation results in most cases, and differences between theory and simulation are induced by the strong dynamical correlations among the states of neighbors and finite-size network 5 .…”

“…Social contagion processes are everywhere range from the spread of health behavior to the diffusion of new products and the spread of innovation 1–5 . Uncovering the spreading mechanisms of different social contagions could help us predict and control contagion dynamics 6–8 .…”

Output-Feedback Control for Discrete-Time Spreading Models in Complex Networks

“…Given that the system presents a high non-linear behavior, our analytical approach is based on determining a bilinear dynamics (15) and (20) that upper bounds the non-linear system. Following this approach, it is possible to determine two sufficient conditions (17) and (18) that ensure that the extinction state will be asymptotically stable.…”

“…Thus, in this case, it seems appropriate considering that V m = V c . Finally, the dynamics (20) establishes an alternative upper bound for (5).…”

“…Unfortunately, this model fails to capture real-world complexity. Data available show that real-world computer networks are not homogeneous and, instead, follow a power law structure in the number of connections of the nodes [20][21][22].…”