Epidemic spreading on networks with vaccination

In this paper, a new susceptible-infected-susceptible (SIS) model on complex networks with imperfect vaccination is proposed. Two types of epidemic spreading patterns (the recovered individuals have or have not immunity) on scale-free networks are discussed. Both theoretical and numerical analyses are presented. The epidemic thresholds related to the vaccination rate, the vaccination-invalid rate and the vaccination success rate on scale-free networks are demonstrated, showing different results from the reported observations. This reveals that whether or not the epidemic can spread over a network under vaccination control is determined not only by the network structure but also by the medicine's effective duration. Moreover, for a given infective rate, the proportion of individuals to vaccinate can be calculated theoretically for the case that the recovered nodes have immunity. Finally, simulated results are presented to show how to control the disease prevalence.     

Crossover from weak to strong disorder regime in the duration of epidemics

We study the susceptible–infected–recovered (SIR) model in complex networks, considering that not all individuals in the population interact in the same way. This heterogeneity between contacts is modeled by a continuous disorder. In our model, the disorder represents the contact time or the closeness between individuals. We find that the duration time of an epidemic has a crossover with the system size, from a power-law regime to a logarithmic regime depending on the transmissibility related to the strength of the disorder. Using percolation theory, we find that the duration of the epidemic scales as the average length of the branches of the infection. Our theoretical findings, supported by simulations, explains the crossover between the two regimes.     

A dynamic epidemic control model on uncorrelated complex networks

In this paper, a dynamic epidemic control model on the uncorrelated complex networks is proposed. By means of theoretical analysis, we found that the new model has a similar epidemic threshold as that of the susceptible-infectedrecovered （SIR） model on the above networks, but it can reduce the prevalence of the infected individuals remarkably. This result may help us understand epidemic spreading phenomena on real networks and design appropriate strategies to control infections.     

Rational behavior is a ‘double-edged sword’ when considering voluntary vaccination

Of particular importance for public health is how to understand strategic vaccination behavior in social networks. Social learning is a central aspect of human behavior, and it thus shapes vaccination individuals’ decision-making. Here, we study two simple models to address the impact of the more rational decision-making of individuals on voluntary vaccination. In the first model, individuals are endowed with memory capacity for their past experiences of dealing with vaccination. In addition to their current payoffs, they also take account of the historical payoffs that are discounted by a memory-decaying factor. They use such overall payoffs (weighing the current payoffs and historical payoffs) to reassess their vaccination strategies. Those who have higher overall payoffs are more likely imitated by their social neighbors. In the second model, individuals do not blindly learn the strategies of neighbors; they also combine the fraction of infection in the past epidemic season. If the fraction of infection surpasses the perceived risk threshold, individuals will increase the probability of taking vaccination. Otherwise, they will decrease the probability of taking vaccination. Then we use evolutionary game theory to study the vaccination behavior of people during an epidemiological process. To do this, we propose a two-stage model: individuals make vaccination decisions during a yearly vaccination campaign, followed by an epidemic season. This forms a feedback loop between the vaccination decisions of individuals and their health outcomes, and thus payoffs. We find that the two more rational decision-making models have nontrivial impacts on the vaccination behavior of individuals, and, as a result, on the final fraction of infection. Our results highlight that, from an individual’s viewpoint, the decisions are optimal and more rational. However, from the social viewpoint, the strategies of individuals can give rise to distinct outcomes. Namely, the rational behavior of individuals plays a ‘double-edged-sword’ role on the social effects.     

Line graphs as social networks

It was demonstrated recently that the line graphs are clustered and assortative. These topological features are known to characterize some social networks [M.E.J. Newman, Y. Park, Why social networks are different from other types of networks, Phys. Rev. E 68 (2003) 036122]; it was argued that this similarity reveals their cliquey character. In the model proposed here, a social network is the line graph of an initial network of families, communities, interest groups, school classes and small companies. These groups play the role of nodes, and individuals are represented by links between these nodes. The picture is supported by the data on the LiveJournal network of about 8×10⁶ people.     

Non-consensus Opinion Models on Complex Networks

Social dynamic opinion models have been widely studied to understand how interactions among individuals cause opinions to evolve. Most opinion models that utilize spin interaction models usually produce a consensus steady state in which only one opinion exists. Because in reality different opinions usually coexist, we focus on non-consensus opinion models in which above a certain threshold two opinions coexist in a stable relationship. We revisit and extend the non-consensus opinion (NCO) model introduced by Shao et al. (Phys. Rev. Lett. 103:01870, 2009). The NCO model in random networks displays a second order phase transition that belongs to regular mean field percolation and is characterized by the appearance (above a certain threshold) of a large spanning cluster of the minority opinion. We generalize the NCO model by adding a weight factor W to each individual’s original opinion when determining their future opinion (NCOW model). We find that as W increases the minority opinion holders tend to form stable clusters with a smaller initial minority fraction than in the NCO model. We also revisit another non-consensus opinion model based on the NCO model, the inflexible contrarian opinion (ICO) model (Li et al. in Phys. Rev. E 84:066101, 2011), which introduces inflexible contrarians to model the competition between two opinions in a steady state. Inflexible contrarians are individuals that never change their original opinion but may influence the opinions of others. To place the inflexible contrarians in the ICO model we use two different strategies, random placement and one in which high-degree nodes are targeted. The inflexible contrarians effectively decrease the size of the largest rival-opinion cluster in both strategies, but the effect is more pronounced under the targeted method. All of the above models have previously been explored in terms of a single network, but human communities are usually interconnected, not isolated. Because opinions propagate not only within single networks but also between networks, and because the rules of opinion formation within a network may differ from those between networks, we study here the opinion dynamics in coupled networks. Each network represents a social group or community and the interdependent links joining individuals from different networks may be social ties that are unusually strong, e.g., married couples. We apply the non-consensus opinion (NCO) rule on each individual network and the global majority rule on interdependent pairs such that two interdependent agents with different opinions will, due to the influence of mass media, follow the majority opinion of the entire population. The opinion interactions within each network and the interdependent links across networks interlace periodically until a steady state is reached. We find that the interdependent links effectively force the system from a second order phase transition, which is characteristic of the NCO model on a single network, to a hybrid phase transition, i.e., a mix of second-order and abrupt jump-like transitions that ultimately becomes, as we increase the percentage of interdependent agents, a pure abrupt transition. We conclude that for the NCO model on coupled networks, interactions through interdependent links could push the non-consensus opinion model to a consensus opinion model, which mimics the reality that increased mass communication causes people to hold opinions that are increasingly similar. We also find that the effect of interdependent links is more pronounced in interdependent scale free networks than in interdependent Erd?s Rényi networks.     

Emergence of communities in weighted networks

Topology and weights are closely related in weighted complex networks and this is reflected in their modular structure. We present a simple network model where the weights are generated dynamically and they shape the developing topology. By tuning a model parameter governing the importance of weights, the resulting networks undergo a gradual structural transition from a module-free topology to one with communities. The model also reproduces many features of large social networks, including the "weak links" property.     

Epidemic spreading on a scale-free network with awareness

This paper presents a modified susceptible-infected-recovered(SIR) model with the effects of awareness and vaccination to study the epidemic spreading on scale-free networks based on the mean-field theory.In this model,when susceptible individuals receive awareness from their infected neighbor nodes,they will take vaccination measures.The theoretical analysis and the numerical simulations show that the existence of awareness and vaccination can significantly improve the epidemic threshold and reduce the risk of virus outbreaks.In addition,regardless of the existence of vaccination,the awareness can increase the spreading threshold and slow the spreading speed effectively.For a given awareness and a certain spreading rate,the total number of infections reduces with the increasing vaccination rate.     

Statistical model for the effects of phase and momentum randomization on electron transport

In this paper, the study of epidemic spreading of mobile individuals on networks focuses on the system in which each node of the network may be occupied by either one individual or a void, and each individual could move to a neighbour void node. It is found that for the susceptible-infected-susceptible (SIS) model, the diffusion increases the epidemic threshold for arbitrary heterogeneous networks having the degree fluctuations, and the diffusion doesn??t affect the epidemic threshold for regular random networks. In the SI model, the diffusion suppresses the epidemic spread at the early outbreak stage, which indicates that the growth time scale of outbreaks is monotonically increasing with diffusion rate d. The heterogeneous mean-field analysis is in good agreement with the numerical simulations on annealed networks.     

Transmission of HIV in sexual networks in sub-Saharan Africa and Europe

We are reviewing the literature regarding sexual networks and HIV transmission in sub-Saharan Africa and Europe. On Likoma Island in Malawi, a sexual network was reconstructed using a sociometric survey in which individuals named their sexual partners. The sexual network identified one giant component including half of all sexually active individuals. More than 25% of respondents were linked through independent chains of sexual relations. HIV was more common in the sparser regions of the network due to over-representation of groups with higher HIV prevalence. A study from KwaZulu-Natal in South-Africa collected egocentric data about sexual partners and found that new infections in women in a particular area was associated with the number of life-time partners in men. Data about sexual networks and HIV transmission are not reported in Europe. It is, however, found that the annual number of sexual partners follows a scale-free network. Phylogenetic studies that determine genetic relatedness between HIV isolates obtained from infected individuals, found that patients in the early stages of infections explain a high number of new infections. In conclusion, the limited information that is available suggest that sexual networks play a role in spread of HIV. Obtaining more information about sexual networks can be of benefit for modeling studies on HIV transmission and prevention.     

Probabilistic prediction in scale-free networks: diameter changes

In complex systems, responses to small perturbations are too diverse to definitely predict how much they would be, and then such diverse responses can be predicted in a probabilistic way. Here we study such a problem in scale-free networks, for example, the diameter changes by the deletion of a single vertex for various in silico and real-world scale-free networks. We find that the diameter changes are indeed diverse and their distribution exhibits an algebraic decay with an exponent zeta asymptotically. Interestingly, the exponent zeta is robust as zeta approximately 2.2(1) for most scale-free networks and insensitive to the degree exponents gamma as long as 2相似文献   

Dynamic Analysis and Optimal Control of Rumor Spreading Model with Recurrence and Individual Behaviors in Heterogeneous Networks

This paper is devoted to investigating the impact of the recurrence of rumors and individual behaviors and control strategies related to rumor spreading in online social networks. To do this, a novel susceptible-hesitating-infected-latent-recovered (SHILR) rumor propagation model in heterogeneous networks is presented. Firstly, based on the relevant mean-field equations of the model, the threshold value is examined to demonstrate the existence and stability of rumor-free/spreading equilibrium with the help of the algebraic method. Secondly, the global stabilities of the equilibria are analyzed through applying Lyapunov stability theory and LaSalle’s invariance principle. Next, the optimal control is proposed by taking advantage of Pontryagin’s maximum principle for reducing the number of infected individuals with minimum cost. Moreover, some numerical examples are carried out to test the theoretical results. Finally, combined with practice, a model application is presented.     

Prisoner's Dilemma Game on Two Types of Positively Correlated Networks

We study the effects of degree correlations on the evolution of cooperation in the prisoner＇s dilemma game with individuals located on two types of positively correlated networks. It is shown that the positive degree correlation can either promote or inhibit the emergence of cooperation depending on network configurations. Furthermore, we investigate the probability to cooperate as a function of connectivity degree, and find that high-degree individuals generally have a higher tendency to cooperate. Finally, it is found that small-degree individuals usually change their strategy more frequently, and such change is shown to be unfavourable to cooperation for both kinds of networks.     

Cooperation and community structure in social networks

Situations of conflict giving rise to social dilemmas are widespread in society. One way of studying these important phenomena is by using simplified models of individual behavior under conflicting situations such as evolutionary game theory. Starting from the observation that individuals interact through networks of acquaintances, we study the evolution of cooperation on model and real social networks through well known paradigmatic games. Using a new payoff scheme which leaves replicator dynamics invariant, we find that cooperation is sustainable in such networks, even in the difficult case of the prisoner’s dilemma. The evolution and stability of cooperation implies the condensation of game strategies into the existing community structures of the social network in which clusters of cooperators survive thanks to their higher connectivity towards other fellow cooperators.     

Detecting community structure from coherent oscillation of excitable systems

Many networks are proved to have community structures. On the basis of the fact that the dynamics on networks are intensively affected by the related topology, in this paper the dynamics of excitable systems on networks and a corresponding approach for detecting communities are discussed. Dynamical networks are formed by interacting neurons; each neuron is described using the FHN model. For noisy disturbance and appropriate coupling strength, neurons may oscillate coherently and their behavior is tightly related to the community structure. Synchronization between nodes is measured in terms of a correlation coefficient based on long time series. The correlation coefficient matrix can be used to project network topology onto a vector space. Then by the K-means cluster method, the communities can be detected. Experiments demonstrate that our algorithm is effective at discovering community structure in artificial networks and real networks, especially for directed networks. The results also provide us with a deep understanding of the relationship of function and structure for dynamical networks.     

The value of less connected agents in Boolean networks

In multiagent systems, agents often face binary decisions where one seeks to take either the minority or the majority side. Examples are minority and congestion games in general, i.e., situations that require coordination among the agents in order to depict efficient decisions. In minority games such as the El Farol Bar Problem, previous works have shown that agents may reach appropriate levels of coordination, mostly by looking at the history of past decisions. Not many works consider any kind of structure of the social network, i.e., how agents are connected. Moreover, when structure is indeed considered, it assumes some kind of random network with a given, fixed connectivity degree. The present paper departs from the conventional approach in some ways. First, it considers more realistic network topologies, based on preferential attachments. This is especially useful in social networks. Second, the formalism of random Boolean networks is used to help agents to make decisions given their attachments (for example acquaintances). This is coupled with a reinforcement learning mechanism that allows agents to select strategies that are locally and globally efficient. Third, we use agent-based modeling and simulation, a microscopic approach, which allows us to draw conclusions about individuals and/or classes of individuals. Finally, for the sake of illustration we use two different scenarios, namely the El Farol Bar Problem and a binary route choice scenario. With this approach we target systems that adapt dynamically to changes in the environment, including other adaptive decision-makers. Our results using preferential attachments and random Boolean networks are threefold. First we show that an efficient equilibrium can be achieved, provided agents do experimentation. Second, microscopic analysis show that influential agents tend to consider few inputs in their Boolean functions. Third, we have also conducted measurements related to network clustering and centrality that help to see how agents are organized.     

System of mobile agents to model social networks

We propose a model of mobile agents to construct social networks, based on a system of moving particles by keeping track of the collisions during their permanence in the system. We reproduce not only the degree distribution, clustering coefficient, and shortest path length of a large database of empirical friendship networks recently collected, but also some features related with their community structure. The model is completely characterized by the collision rate, and above a critical collision rate we find the emergence of a giant cluster in the universality class of two-dimensional percolation. Moreover, we propose possible schemes to reproduce other networks of particular social contacts, namely, sexual contacts.     

Selective investment promotes cooperation in public goods game

Most previous investigations on spatial Public Goods Game assume that individuals treat neighbors equivalently, which is in sharp contrast with realistic situations, where bias is ubiquitous. We construct a model to study how a selective investment mechanism affects the evolution of cooperation. Cooperators selectively contribute to just a fraction among their neighbors. According to the interaction result, the investment network can be adapted. On selecting investees, three patterns are considered. In the random pattern, cooperators choose their investees among the neighbors equiprobably. In the social-preference pattern, cooperators tend to invest to individuals possessing large social ties. In the wealth-preference pattern, cooperators are more likely to invest to neighbors with higher payoffs. Our result shows robustness of selective investment mechanism that boosts emergence and maintenance of cooperation. Cooperation is more or less hampered under the latter two patterns, and we prove the anti-social-preference or anti-wealth-preference pattern of selecting investees can accelerate cooperation to some extent. Furthermore, the theoretical analysis of our mechanism on double-star networks coincides with simulation results. We hope our finding could shed light on better understanding of the emergence of cooperation among adaptive populations.