Control of epidemic spreading on complex networks by local traffic dynamics

Optimizing protection resource allocation for traffic-driven epidemic spreading

Optimizing the allocation of protection resources to control the spreading process in networks is a central problem in public health and network security. In this paper, we propose a comprehensive adjustable resource allocation mechanism in which the over allocation of resources can be also numerically reflected and study the effects of this mechanism on traffic-driven epidemic spreading. We observe that an inappropriate resource allocation scheme can induce epidemic spreading, while an optimized heterogeneous resource allocation scheme can significantly suppress the outbreak of the epidemic. The phenomenon can be explained by the role of nodes induced by the heterogeneous network structure and traffic flow distribution. Theoretical analysis also gives an exact solution to the epidemic threshold and reveals the optimal allocation scheme. Compared to the uniform allocation scheme, the increase in traffic flow will aggravate the decline of the epidemic threshold for the heterogeneous resource allocation scheme. This indicates that the uneven resource allocation makes the network performance of suppressing epidemic degrade with the traffic load level. Finally, it is demonstrated that real-world network topology also confirms the results.

Traffic-driven epidemic spreading in multiplex networks

Recent progress on multiplex networks has provided a powerful way to abstract the diverse interaction of a network system with multiple layers. In this paper, we show that a multiplex structure can greatly affect the spread of an epidemic driven by traffic dynamics. One of the interesting findings is that the multiplex structure could suppress the outbreak of an epidemic, which is different from the typical finding of spread dynamics in multiplex networks. In particular, one layer with dense connections can attract more traffic flow and eventually suppress the epidemic outbreak in other layers. Therefore, the epidemic threshold will be larger than the minimal threshold of the layers. With a mean-field approximation, we provide explicit expressions for the epidemic threshold and for the onset of suppressing epidemic spreading in multiplex networks. We also provide the probability of obtaining a multiplex configuration that suppresses the epidemic spreading when the multiplex is composed of: (i) two Erdős-Rényi layers and (ii) two scale-free layers. Therefore, compared to the situation of an isolated network in which a disease may be able to propagate, a larger epidemic threshold can be found in multiplex structures.

Fragility and robustness of self-sustained oscillations in an epidemiological model on small-world networks

We investigate the susceptible-infected-recovered-susceptible epidemic model, typical of mathematical epidemiology, with the diversity of the durations of infection and recovery of the individuals on small-world networks. Infection spreads from infected to healthy nodes, whose infection and recovery periods denoted by τ_I and τ_R, respectively, are either fixed or uniformly distributed around a specified mean. Whenever τ_I and τ_R are narrowly distributed around their mean values, the epidemic prevalence in the stationary state is found to reach its maximal level in the typical small-world region. This non-monotonic behavior of the final epidemic prevalence is thought to be similar to the efficient navigation in small worlds with cost minimization. Besides, pronounced oscillatory behavior of the fraction of infected nodes emerges when the number of shortcuts on the underlying network become sufficiently large. Remarkably, we find that the synchronized oscillation of infection incidences is quite fragile to the variability of the two characteristic time scales τ_I and τ_R. Specifically, even in the limit of a random network (where the amplest oscillations are expected to arise for fixed τ_I and τ_R), increasing the variability of the duration of the infectious period and/or that of the refractory period will push the system to change from a self-sustained oscillation to a fixed point with negligible fluctuations in the steady state. Interestingly, negative correlation between τ_I and τ_R can give rise to the robustness of the self-sustained oscillatory phenomenon. Our findings thus highlight the pivotal role of, apart from the external seasonal driving force and demographic stochasticity, the intrinsic characteristic of the system itself in understanding the cycle of outbreaks of recurrent epidemics.

Explosive spreading on complex networks: The role of synergy

In spite of the vast literature on spreading dynamics on complex networks, the role of local synergy, i.e., the interaction of elements that when combined produce a total effect greater than the sum of the individual elements, has been studied but only for irreversible spreading dynamics. Reversible spreading dynamics are ubiquitous but their interplay with synergy has remained unknown. To fill this knowledge gap, we articulate a model to incorporate local synergistic effect into the classical susceptible-infected-susceptible process, in which the probability for a susceptible node to become infected through an infected neighbor is enhanced when the neighborhood of the latter contains a number of infected nodes. We derive master equations incorporating the synergistic effect, with predictions that agree well with the numerical results. A striking finding is that when a parameter characterizing the strength of the synergy reinforcement effect is above a critical value, the steady-state density of the infected nodes versus the basic transmission rate exhibits an explosively increasing behavior and a hysteresis loop emerges. In fact, increasing the synergy strength can promote the spreading and reduce the invasion and persistence thresholds of the hysteresis loop. A physical understanding of the synergy promoting explosive spreading and the associated hysteresis behavior can be obtained through a mean-field analysis.

Traffic-driven epidemic spreading in correlated networks

In spite of the extensive previous efforts on traffic dynamics and epidemic spreading in complex networks, the problem of traffic-driven epidemic spreading on correlated networks has not been addressed. Interestingly, we find that the epidemic threshold, a fundamental quantity underlying the spreading dynamics, exhibits a nonmonotonic behavior in that it can be minimized for some critical value of the assortativity coefficient, a parameter characterizing the network correlation. To understand this phenomenon, we use the degree-based mean-field theory to calculate the traffic-driven epidemic threshold for correlated networks. The theory predicts that the threshold is inversely proportional to the packet-generation rate and the largest eigenvalue of the betweenness matrix. We obtain consistency between theory and numerics. Our results may provide insights into the important problem of controlling and/or harnessing real-world epidemic spreading dynamics driven by traffic flows.

Suppression of epidemic spreading in complex networks by local information based behavioral responses

The interplay between individual behaviors and epidemic dynamics in complex networks is a topic of recent interest. In particular, individuals can obtain different types of information about the disease and respond by altering their behaviors, and this can affect the spreading dynamics, possibly in a significant way. We propose a model where individuals' behavioral response is based on a generic type of local information, i.e., the number of neighbors that has been infected with the disease. Mathematically, the response can be characterized by a reduction in the transmission rate by a factor that depends on the number of infected neighbors. Utilizing the standard susceptible-infected-susceptible and susceptible-infected-recovery dynamical models for epidemic spreading, we derive a theoretical formula for the epidemic threshold and provide numerical verification. Our analysis lays on a solid quantitative footing the intuition that individual behavioral response can in general suppress epidemic spreading. Furthermore, we find that the hub nodes play the role of "double-edged sword" in that they can either suppress or promote outbreak, depending on their responses to the epidemic, providing additional support for the idea that these nodes are key to controlling epidemic spreading in complex networks.

Identifying influential nodes in large-scale directed networks: the role of clustering

Identifying influential nodes in very large-scale directed networks is a big challenge relevant to disparate applications, such as accelerating information propagation, controlling rumors and diseases, designing search engines, and understanding hierarchical organization of social and biological networks. Known methods range from node centralities, such as degree, closeness and betweenness, to diffusion-based processes, like PageRank and LeaderRank. Some of these methods already take into account the influences of a node’s neighbors but do not directly make use of the interactions among it’s neighbors. Local clustering is known to have negative impacts on the information spreading. We further show empirically that it also plays a negative role in generating local connections. Inspired by these facts, we propose a local ranking algorithm named ClusterRank, which takes into account not only the number of neighbors and the neighbors’ influences, but also the clustering coefficient. Subject to the susceptible-infected-recovered (SIR) spreading model with constant infectivity, experimental results on two directed networks, a social network extracted from delicious.com and a large-scale short-message communication network, demonstrate that the ClusterRank outperforms some benchmark algorithms such as PageRank and LeaderRank. Furthermore, ClusterRank can also be applied to undirected networks where the superiority of ClusterRank is significant compared with degree centrality and k-core decomposition. In addition, ClusterRank, only making use of local information, is much more efficient than global methods: It takes only 191 seconds for a network with about nodes, more than 15 times faster than PageRank.

Suppressing traffic-driven epidemic spreading by edge-removal strategies

The interplay between traffic dynamics and epidemic spreading on complex networks has received increasing attention in recent years. However, the control of traffic-driven epidemic spreading remains to be a challenging problem. In this Brief Report, we propose a method to suppress traffic-driven epidemic outbreak by properly removing some edges in a network. We find that the epidemic threshold can be enhanced by the targeted cutting of links among large-degree nodes or edges with the largest algorithmic betweenness. In contrast, the epidemic threshold will be reduced by the random edge removal. These findings are robust with respect to traffic-flow conditions, network structures, and routing strategies. Moreover, we find that the shutdown of targeted edges can effectively release traffic load passing through large-degree nodes, rendering a relatively low probability of infection to these nodes.

Traffic-driven epidemic outbreak on complex networks: how long does it take?

Recent studies have suggested the necessity to incorporate traffic dynamics into the process of epidemic spreading on complex networks, as the former provides support for the latter in many real-world situations. While there are results on the asymptotic scope of the spreading dynamics, the issue of how fast an epidemic outbreak can occur remains outstanding. We observe numerically that the density of the infected nodes exhibits an exponential increase with time initially, rendering definable a characteristic time for the outbreak. We then derive a formula for scale-free networks, which relates this time to parameters characterizing the traffic dynamics and the network structure such as packet-generation rate and betweenness distribution. The validity of the formula is tested numerically. Our study indicates that increasing the average degree and/or inducing traffic congestion can slow down the spreading process significantly.

Epidemic spreading with information-driven vaccination

Epidemic spreading has been well studied in the past decade, where the main concentration is focused on the influence of network topology but little attention is paid to the individual's crisis awareness. We here study how the crisis awareness, i.e., personal self-protection, influences the epidemic spreading by presenting a susceptible-infected-recovered model with information-driven vaccination. We introduce two parameters to quantitatively characterize the crisis awareness. One is the information creation rate λ and the other is the information sensitivity η. We find that the epidemic spreading can be significantly suppressed in both the homogeneous and heterogeneous networks when both λ and η are relatively large. More interesting is that the needed vaccine will be significantly reduced when the information is well spread, which is a good news for the poor countries and regions with limited resources.