Epidemic Diffusion on Complex Networks

Both diffusion and epidemic are well studied in the stochastic systems and complex networks, respectively. Here we combine these two fields and study epidemic diffusion in complex networks. Instead of studying the threshold of infection, which was focused on in previous works, we focus on the diffusion behayiour. We find that the epidemic diffusion in a complex network is an anomalous superdiffusion with varying diffusion exponent and that γ is influenced seriously by the network structure, such as the clustering coefficient and the degree distribution. Numerical simulations have confirmed the theoretical predictions.     

Epidemic Spread in Weighted Scale-Free Networks

We investigate the detailed epidemic spreading process in scale-free networks with link weights that denote familiarity between two individuals. It is found that the spreading velocity reaches a peak quickly then decays in a power-law form. Numerical study exhibits that the nodes with larger strength is preferential to be infected, but the hierarchical dynamics are not dearly found, which is different from the well-known result in the unweighed network case. In addition, also by numerical study, we demonstrate that larger dispersion of weight of networks results in slower spreading, which indicates that epidemic spreads more quickly on unweighted scale-free networks than on weighted scale-free networks with the same condition.     

Modular Epidemic Spreading in Small-World Networks

We study the epidemic spreading of the susceptible-infected-susceptible model on small-world networks with modular structure. It is found that the epidemic threshold increases linearly with the modular strength. Furthermore, the modular structure may influence the infected density in the steady state and the spreading velocity at the beginning of propagation. Practically, the propagation can be hindered by strengthening the modular structure in the view of network topology. In addition, to reduce the probability of reconnection between modules may also help to control the propagation.     

Epidemic Propagation and Microscopic Structure of Complex Networks

How the microscopic structure of complex network takes influence on the epidemic propagation is investigated. Special attention is paid to the growing network where its average degree changes with time. A formula for the final density of infected individuals is given and is confirmed by numerical simulations. Our results show that the final density of refractory increases nonlinearly with both the average degree of nodes and the adjustable random parameter of network structure.     

Periodic Wave of Epidemic Spreading in Community Networks

It was reported by Cummings ef al. [Nature 427 （2004） 344] that there are periodic waves in the spatiotemporal data of epidemics. For understanding the mechanism, we study the epidemic spreading on community networks by both the SIS model and the SIRS model. We find that with the increase of infection rate, the number of total infected nodes may be stabilized at a fixed point, oscillatory waves, and periodic cycles. Moreover, the epidemic spreading in the SIS model can be explained by an analytic map.     

Epidemic Dynamics with Feedback Mechanism in Exponential Networks

We introduce a feedback mechanism to study the spreading of an epidemic by analytical methods and large scale simulations in exponential networks. It is found that introducing the feedback mechanism can reduce the density of infected individuals, Furthermore, it does not change the epidemic threshold （critical point） λc. These results can help us to understand epidemic spreading phenomena on social networks more practically and design appropriate strategies to control social infections.     

Epidemic Spreading in Contact Networks Based on Exposure Level

Most epidemic models for the spread of diseases in contact networks take the assumption of the infected probability of a susceptible agent dependent on its absolute number of infectious neighbours. We introduce a new epidemic model in which the infected probability of a susceptible agent in contact networks depends not on its degree but on its exposure level. We find that effective average infection rate ^-λ （i.e., the average number of infections produced by a single contact between infected individuals and susceptible individuals） has an epidemic threshold ^λc = 1, which is related to recovery rate, epidemic mechanisms and topology of contact network. Furthermore, we show the dominating importance of epidemic mechanisms in determining epidemic patterns and discussed the implications of our model for infection control policy.     

Epidemic centrality — is there an underestimated epidemic impact of network peripheral nodes?

In the study of disease spreading on empirical complex networks in SIR model, initially infected nodes can be ranked according to some measure of their epidemic impact. The highest ranked nodes, also referred to as “superspreaders”, are associated to dominant epidemic risks and therefore deserve special attention. In simulations on studied empirical complex networks, it is shown that the ranking depends on the dynamical regime of the disease spreading. A possible mechanism leading to this dependence is illustrated in an analytically tractable example. In systems where the allocation of resources to counter disease spreading to individual nodes is based on their ranking, the dynamical regime of disease spreading is frequently not known before the outbreak of the disease. Therefore, we introduce a quantity called epidemic centrality as an average over all relevant regimes of disease spreading as a basis of the ranking. A recently introduced concept of phase diagram of epidemic spreading is used as a framework in which several types of averaging are studied. The epidemic centrality is compared to structural properties of nodes such as node degree, k-cores and betweenness. There is a growing trend of epidemic centrality with degree and k-cores values, but the variation of epidemic centrality is much smaller than the variation of degree or k-cores value. It is found that the epidemic centrality of the structurally peripheral nodes is of the same order of magnitude as the epidemic centrality of the structurally central nodes. The implications of these findings for the distributions of resources to counter disease spreading are discussed.