The impact of individual heterogeneity on the coupled awareness-epidemic dynamics in multiplex networks

Impact of simplicial complexes on epidemic spreading in partially mapping activity-driven multiplex networks

Over the past decade, the coupled spread of information and epidemic on multiplex networks has become an active and interesting topic. Recently, it has been shown that stationary and pairwise interactions have limitations in describing inter-individual interactions , and thus, the introduction of higher-order representation is significant. To this end, we present a new two-layer activity-driven network epidemic model, which considers the partial mapping relationship among nodes across two layers and simultaneously introduces simplicial complexes into one layer, to investigate the effect of 2-simplex and inter-layer mapping rate on epidemic transmission. In this model, the top network, called the virtual information layer, characterizes information dissemination in online social networks, where information can be diffused through simplicial complexes and/or pairwise interactions. The bottom network, named as the physical contact layer, denotes the spread of infectious diseases in real-world social networks. It is noteworthy that the correspondence among nodes between two networks is not one-to-one but partial mapping. Then, a theoretical analysis using the microscopic Markov chain (MMC) method is performed to obtain the outbreak threshold of epidemics, and extensive Monte Carlo (MC) simulations are also carried out to validate the theoretical predictions. It is obviously shown that MMC method can be used to estimate the epidemic threshold; meanwhile, the inclusion of simplicial complexes in the virtual layer or introductory partial mapping relationship between layers can inhibit the spread of epidemics. Current results are conducive to understanding the coupling behaviors between epidemics and disease-related information.

The SAITS epidemic spreading model and its combinational optimal suppression control

In this paper, an SAITS epidemic model based on a single layer static network is proposed and investigated. This model considers a combinational suppression control strategy to suppress the spread of epidemics, which includes transferring more individuals to compartments with low infection rate and with high recovery rate. The basic reproduction number of this model is calculated and the disease-free and endemic equilibrium points are discussed. An optimal control problem is formulated to minimize the number of infections with limited resources. The suppression control strategy is investigated and a general expression for the optimal solution is given based on the Pontryagin's principle of extreme value. The validity of the theoretical results is verified by numerical simulations and Monte Carlo simulations.

Effect of local and global information on the dynamical interplay between awareness and epidemic transmission in multiplex networks

Recent few years have witnessed a growing interest in exploring the dynamical interplay between awareness and epidemic transmission within the framework of multiplex networks. However, both local and global information have significant impacts on individual awareness and behavior, which have not been adequately characterized in the existing works. To this end, we propose a local and global information controlled spreading model to explore the dynamics of two spreading processes. In the upper layer, we construct a threshold model to describe the awareness diffusion process and introduce local and global awareness information as variables into an individual awareness ratio. In the lower layer, we adopt the classical susceptible-infected-susceptible model to represent the epidemic propagation process and introduce local and global epidemic information into individual precaution degree to reflect individual heterogeneity. Using the microscopic Markov chain approach, we theoretically derive the threshold for epidemic outbreaks. Our findings suggest that the local and global information can motivate individuals to increase self-protection awareness and take more precaution measures, thereby reducing disease infection probability and suppressing the spread of epidemics.

Interplay of simplicial awareness contagion and epidemic spreading on time-varying multiplex networks

There has been growing interest in exploring the dynamical interplay of epidemic spreading and awareness diffusion within the multiplex network framework. Recent studies have demonstrated that pairwise interactions are not enough to characterize social contagion processes, but the complex mechanisms of influence and reinforcement should be considered. Meanwhile, the physical social interaction of individuals is not static but time-varying. Therefore, we propose a novel sUAU-tSIS model to characterize the interplay of simplicial awareness contagion and epidemic spreading on time-varying multiplex networks, in which one layer with 2-simplicial complexes is considered the virtual information layer to address the complex contagion mechanisms in awareness diffusion and the other layer with time-varying and memory effects is treated as the physical contact layer to mimic the temporal interaction pattern among population. The microscopic Markov chain approach based theoretical analysis is developed, and the epidemic threshold is also derived. The experimental results show that our theoretical method is in good agreement with the Monte Carlo simulations. Specifically, we find that the synergistic reinforcement mechanism coming from the group interactions promotes the diffusion of awareness, leading to the suppression of the spreading of epidemics. Furthermore, our results illustrate that the contact capacity of individuals, activity heterogeneity, and memory strength also play important roles in the two dynamics; interestingly, a crossover phenomenon can be observed when investigating the effects of activity heterogeneity and memory strength.

The impact of the global and local awareness diffusion on epidemic transmission considering the heterogeneity of individual influences

In this paper, we propose a coupled awareness-epidemic spreading model considering the heterogeneity of individual influences, which aims to explore the interaction between awareness diffusion and epidemic transmission. The considered heterogeneities of individual influences are threefold: the heterogeneity of individual influences in the information layer, the heterogeneity of individual influences in the epidemic layer and the heterogeneity of individual behavioral responses to epidemics. In addition, the individuals' receptive preference for information and the impacts of individuals' perceived local awareness ratio and individuals' perceived epidemic severity on self-protective behavior are included. The epidemic threshold is theoretically established by the microscopic Markov chain approach and the mean-field approach. Results indicate that the critical local and global awareness ratios have two-stage effects on the epidemic threshold. Besides, either the heterogeneity of individual influences in the information layer or the strength of individuals' responses to epidemics can influence the epidemic threshold with a nonlinear way. However, the heterogeneity of individual influences in the epidemic layer has few effect on the epidemic threshold, but can affects the magnitude of the final infected density.

The effect of information literacy heterogeneity on epidemic spreading in information and epidemic coupled multiplex networks

With the COVID-19 pandemic, better understanding of the co-evolution of information and epidemic diffusion networks is important for pandemic-related policies. Using the microscopic Markov chain method, this study proposed an aware-susceptible-infected model (ASI) to explore the effect of information literacy on the spreading process in such multiplex networks. We first introduced a parameter that adjusts the self-protection related execution ability of aware individuals in order to emphasis the importance of protective behaviors compared to awareness in decreasing the infection probability. The model also captures individuals' heterogeneity in their information literacy. Simulation experiments found that the high information-literate individuals are more sensitive to information adoption. In addition, epidemic information can help to suppress the epidemic diffusion only when individuals' abilities of transforming awareness into actual protective behaviors attain a threshold. In communities dominated by highly literate individuals, a larger information literacy gap can improve awareness acquisition and thus help to suppress the epidemic among the whole group. By contrast, in communities dominated by low information-literate individuals, a smaller information literacy gap can better prevent the epidemic diffusion. This study contributes to the literature by revealing the importance of individuals' heterogeneity of information literacy on epidemic spreading in different communities and has implications for how to inform people when a new epidemic disease emerges.

Effect of load-capacity heterogeneity on cascading overloads in networks

Heterogeneity in the load capacity of nodes is a common characteristic of many real-world networks that can dramatically affect their robustness to cascading overloads. However, most studies seeking to model cascading failures have ignored variations in nodal load capacity and functionality. The present study addresses this issue by extending the local load redistribution model to include heterogeneity in nodal load capacity and heterogeneity in the types of nodes employed in the network configuration and exploring how these variations affect network robustness. Theoretical and numerical analyses demonstrate that the extent of cascading failure is influenced by heterogeneity in nodal load capacity, while it is relatively insensitive to heterogeneity in nodal configuration. Moreover, the probability of cascading failure initiation at the critical state increases as the range of nodal load capacities increases. However, for large-scale networks with degree heterogeneity, a wide range of nodal load capacities can also suppress the spread of failure after its initiation. In addition, the analysis demonstrates that heterogeneity in nodal load capacity increases and decreases the extent of cascading failures in networks with sublinear and superlinear load distributions, respectively. These findings may provide some practical implications for controlling the spread of cascading failure.

Analytical solution of epidemic threshold for coupled information-epidemic dynamics on multiplex networks with alterable heterogeneity

The phase transition of epidemic spreading model on networks is one of the most important concerns of physicists to theoretical epidemiology. In this paper, we present an analytical expression of epidemic threshold for interplay between epidemic spreading and human behavior on multiplex networks. The threshold formula proposed in this paper reveals the relation between the threshold on single-layer networks and that on multiplex networks, which means that the theoretical conclusions of single-layer networks can be used to improve the threshold accuracy of multiplex networks. To verify how well our formula works in different networks, we build a network model with constant total number of edges but gradually changing the heterogeneity of the network, from scale-free network to Erdős-Rényi random network. By use of theoretical analysis and computer simulations, we find that the heterogeneity of information layer behaves as a "double-edged sword" on the epidemic threshold: The strong heterogeneity can effectively improve the epidemic threshold (which means the disease outbreak requires a higher infection probability) when the awareness probability α is low, while the opposite effect takes place for high α. Meanwhile, the weak heterogeneity of the information layer is effective in suppressing the epidemic prevalence when the awareness probability is neither too high nor too low.

Asymmetrical dynamics of epidemic propagation and awareness diffusion in multiplex networks

To better explore asymmetrical interaction between epidemic spreading and awareness diffusion in multiplex networks, we distinguish susceptibility and infectivity between aware and unaware individuals, relax the degree of immunization, and take into account three types of generation mechanisms of individual awareness. We use the probability trees to depict the transitions between distinct states for nodes and then write the evolution equation of each state by means of the microscopic Markovian chain approach (MMCA). Based on the MMCA, we theoretically analyze the possible steady states and calculate the critical threshold of epidemics, related to the structure of epidemic networks, the awareness diffusion, and their coupling configuration. The achieved analytical results of the mean-field approach are consistent with those of the numerical Monte Carlo simulations. Through the theoretical analysis and numerical simulations, we find that global awareness can reduce the final scale of infection when the regulatory factor of the global awareness ratio is less than the average degree of the epidemic network but it cannot alter the onset of epidemics. Furthermore, the introduction of self-awareness originating from infected individuals not only reduces the epidemic prevalence but also raises the epidemic threshold, which tells us that it is crucial to enhance the early warning of symptomatic individuals during pandemic outbreaks. These results give us a more comprehensive and deep understanding of the complicated interaction between epidemic transmission and awareness diffusion and also provide some practical and effective recommendations for the prevention and control of epidemics.

Coevolution spreading in complex networks

The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and critical phenomena of networked coevolution spreading are extremely important, which provide theoretical foundations for us to control epidemic spreading, predict collective behaviors in social systems, and so on. The coevolution spreading dynamics in complex networks has thus attracted much attention in many disciplines. In this review, we introduce recent progress in the study of coevolution spreading dynamics, emphasizing the contributions from the perspectives of statistical mechanics and network science. The theoretical methods, critical phenomena, phase transitions, interacting mechanisms, and effects of network topology for four representative types of coevolution spreading mechanisms, including the coevolution of biological contagions, social contagions, epidemic-awareness, and epidemic-resources, are presented in detail, and the challenges in this field as well as open issues for future studies are also discussed.

A colored mean-field model for analyzing the effects of awareness on epidemic spreading in multiplex networks

We study the impact of susceptible nodes' awareness on epidemic spreading in social systems, where the systems are modeled as multiplex networks coupled with an information layer and a contact layer. We develop a colored heterogeneous mean-field model taking into account the portion of the overlapping neighbors in the two layers. With theoretical analysis and numerical simulations, we derive the epidemic threshold which determines whether the epidemic can prevail in the population and find that the impacts of awareness on threshold value only depend on epidemic information being available in network nodes' overlapping neighborhood. When there is no link overlap between the two network layers, the awareness cannot help one to raise the epidemic threshold. Such an observation is different from that in a single-layer network, where the existence of awareness almost always helps.