Spreading dynamics on complex dynamical networks

Abstract

With the development of network science, spreading dynamics on networks have attracted intensive research interests in a wide variety of areas, such as control theory, game theory, system science, artificial intelligence, social science, economics, biology, psychology, physics, math, and computer science. Network structure plays a key role in spreading dynamics, although spreading dynamics differ from one another. In real networked systems, the neighborhoods of individuals evolve with time. It is thus necessary to consider the coupling between spreading dynamics and network dynamics. Nowadays the research on spreading dynamics on dynamical networks usually use Monte Carlo simulation rather than theoretical methods. So, we propose a stochastic linking dynamic in this paper. It is proved to be a reversible Markov chain, which facilitates the analytical investigation of spreading dynamics on dynamical networks. With this method, we study three spreading dynamics: the evolution of cooperation, the spread of epidemics, and the evolution of vaccination behavior. Furthermore, we show the similarities and differences between evolutionary game dynamics and epidemic spreading dynamics. Our method could provide a universal framework to study spreading dynamics on complex dynamical networks.