Epidemic spreading on multi-layer networks with active nodes.

Investigations on spreading dynamics based on complex networks have received widespread attention these years due to the COVID-19 epidemic, which are conducive to corresponding prevention policies. As for the COVID-19 epidemic itself, the latent time and mobile crowds are two important and inescapable factors that contribute to the significant prevalence. Focusing on these two factors, this paper systematically investigates the epidemic spreading in multiple spaces with mobile crowds. Specifically, we propose a SEIS (Susceptible-Exposed-Infected-Susceptible) model that considers the latent time based on a multi-layer network with active nodes which indicate the mobile crowds. The steady-state equations and epidemic threshold of the SEIS model are deduced and discussed. And by comprehensively discussing the key model parameters, we find that (1) due to the latent time, there is a "cumulative effect" on the infected, leading to the "peaks" or "shoulders" of the curves of the infected individuals, and the system can switch among three states with the relative parameter combinations changing; (2) the minimal mobile crowds can also cause the significant prevalence of the epidemic at the steady state, which is suggested by the zero-point phase change in the proportional curves of infected individuals. These results can provide a theoretical basis for formulating epidemic prevention policies.

Suppressing epidemic spreading by optimizing the allocation of resources between prevention and treatment.

The rational allocation of resources is crucial to suppress the outbreak of epidemics. Here, we propose an epidemic spreading model in which resources are used simultaneously to prevent and treat disease. Based on the model, we study the impacts of different resource allocation strategies on epidemic spreading. First, we analytically obtain the epidemic threshold of disease using the recurrent dynamical message passing method. Then, we simulate the spreading of epidemics on the Erdos-Rényi (ER) network and the scale-free network and investigate the infection density of disease as a function of the disease infection rate. We find hysteresis loops in the phase transition of the infection density on both types of networks. Intriguingly, when different resource allocation schemes are adopted, the phase transition on the ER network is always a first-order phase transition, while the phase transition on the scale-free network transforms from a hybrid phase transition to a first-order phase transition. Particularly, through extensive numerical simulations, we find that there is an optimal resource allocation scheme, which can best suppress epidemic spreading. In addition, we find that the degree heterogeneity of the network promotes the spreading of disease. Finally, by comparing theoretical and numerical results on a real-world network, we find that our method can accurately predict the spreading of disease on the real-world network.

Repulsive synchronization in complex networks.

Synchronization in complex networks characterizes what happens when an ensemble of oscillators in a complex autonomous system become phase-locked. We study the Kuramoto model with a tunable phase-lag parameter α in the coupling term to determine how phase shifts influence the synchronization transition. The simulation results show that the phase frustration parameter leads to desynchronization. We find two global synchronization regions for α∈[0,2π) when the coupling is sufficiently large and detect a relatively rare network synchronization pattern in the frustration parameter near α=π. We call this frequency-locking configuration as "repulsive synchronization," because it is induced by repulsive coupling. Since the repulsive synchronization cannot be described by the usual order parameter r, the parameter frequency dispersion is introduced to detect synchronization.

Cooperative epidemics spreading under resource control.

The input and allocation of public resources are of crucial importance to suppressing the outbreak of infectious diseases. However, in the research on multi-disease dynamics, the impact of resources has never been taken into account. Here, we propose a two-epidemic spreading model with resource control, in which the amount of resources is introduced into the recovery rates of diseases and the allocation of resources between two diseases is regulated by a parameter. Using the dynamical message passing method, we obtain resource thresholds of the two diseases and validate them on ER networks and scale-free networks. By comparing the results on scale-free networks with different power-law exponents, we find that the heterogeneity of the network promotes the spreading of both diseases. Especially, we find optimal allocation coefficients at different resource levels. And, we get a counterintuitive conclusion that when the available resources are limited, it is a better strategy to preferentially suppress the disease with lower infection rate. In addition, we investigate the effect of interaction strength and find that great interaction strength between diseases makes two diseases with different infectivity tend to be homogeneous.

Center of mass in complex networks.

Network dynamics is always a big challenge in nonlinear dynamics. Although great advancements have been made in various types of complex systems, an universal theoretical framework is required. In this paper, we introduce the concept of center of 'mass' of complex networks, where 'mass' stands for node importance or centrality in contrast to that of particle systems, and further prove that the phase transition and evolutionary state of the system can be characterized by the activity of center of 'mass'. The steady states of several complex networks (gene regulatory networks and epidemic spreading systems) are then studied by analytically calculating the decoupled equation of the dynamic activity of center of 'mass', which is derived from the dynamic equation of the complex networks. The limitations of this method are also pointed out, such as the dynamical problems that related with the relative activities among components, and those systems that consist of oscillatory or chaotic motions.