Two-stage effects of awareness cascade on epidemic spreading in multiplex networks

Effects of positive and negative social reinforcement on coupling of information and epidemic in multilayer networks

The spread of epidemics is often accompanied by the spread of epidemic-related information, and the two processes are interdependent and interactive. A social reinforcement effect frequently emerges during the transmission of both the epidemic and information. While prior studies have primarily examined the role of positive social reinforcement in this process, the influence of negative social reinforcement has largely been neglected. In this paper, we incorporate both positive and negative social reinforcement effects and establish a two-layer dynamical model to investigate the interactive coupling mechanism of information and epidemic transmission. The Heaviside step function is utilized to describe the influence mechanism of positive and negative social reinforcements in the actual transmission process. A microscopic Markov chain approach is used to describe the dynamic evolution process, and the epidemic outbreak threshold is derived. Extensive Monte Carlo numerical simulations demonstrate that while positive social reinforcement alters the outbreak threshold of both information and epidemic and promotes their spread, negative social reinforcement does not change the outbreak threshold but significantly impedes the transmission of both. In addition, publishing more accurate information through official channels, intensifying quarantine measures, promoting vaccines and treatments for outbreaks, and enhancing physical immunity can also help contain epidemics.

Epidemic dynamics with awareness cascade of positive and negative information on delayed multiplex networks

Human behavioral awareness is usually socially relevant, decisions are made based on the behavior of individuals, and this dynamic process of human awareness with herd effects is called awareness cascade. Based on the complexity of modern information dissemination, information is not monolithic. Individuals choose the type of epidemic-related information to accept, i.e., whether it is positive or negative information, according to the awareness cascade, and then take the corresponding measures to cope with the epidemic. In this paper, we use the microscopic Markov chain approach to model an information-virus dual network, where the information layer has a threshold model with awareness cascade of positive and negative information, and on the virus layer is a susceptible-infected-recovery model with epidemic infection time delay and recovery time delay. The time delay is also a non-negligible modeling factor as the complete infection of an individual and the complete recovery of an individual require sufficient time. An explicit formula for the critical threshold of epidemic spread for this model is derived. We find that positive and negative information and time delay have a significant effect on the critical threshold, and the recovery time delay is the time delay that mainly affects the epidemic size. Experiments show that the local acceptance rate of positive information has a threshold point for the spread of epidemics under awareness cascade, and that this point is significantly affected by the mass media. The local acceptance rate of negative information also divides the spread of epidemics into two stages.

Effects of behavioral observability and social proof on the coupled epidemic-awareness dynamics in multiplex networks

Despite much progress in exploring the coupled epidemic-awareness dynamics in multiplex networks, little attention has been paid to the joint impacts of behavioral observability and social proof on epidemic spreading. Since both the protective actions taken by direct neighbors and the observability of these actions have essential influence on individuals' decisions. Thus, we propose a UAPU-SIR model by integrating the effects of these two factors into the decision-making process of taking preventive measures. Specifically, a new state called taken protective actions is introduced into the original unaware-aware-unaware (UAU) model to characterize the action-taken state of individuals after getting epidemic-related information. Using the Microscopic Markov Chain Approach (MMCA), the methods and model are described, and the epidemic threshold is analytically derived. We find that both observability of protecting behaviors and social proof can reduce the epidemic prevalence and raise the epidemic threshold. Moreover, only if observability of protection actions reaches a certain threshold can accelerating information diffusion is able to inhibit disease spreading and result in higher epidemic threshold. We also discover that, reducing the forgetting rate of information is able to decrease epidemic size.

Modeling the effect of observational social learning on parental decision-making for childhood vaccination and diseases spread over household networks

In this paper, we introduce a novel model for parental decision-making about vaccinations against a childhood disease that spreads through a contact network. This model considers a bilayer network comprising two overlapping networks, which are either Erdős-Rényi (random) networks or Barabási-Albert networks. The model also employs a Bayesian aggregation rule for observational social learning on a social network. This new model encompasses other decision models, such as voting and DeGroot models, as special cases. Using our model, we demonstrate how certain levels of social learning about vaccination preferences can converge opinions, influencing vaccine uptake and ultimately disease spread. In addition, we explore how two different cultures of social learning affect the establishment of social norms of vaccination and the uptake of vaccines. In every scenario, the interplay between the dynamics of observational social learning and disease spread is influenced by the network's topology, along with vaccine safety and availability.

Epidemic spreading under game-based self-quarantine behaviors: The different effects of local and global information

During the outbreak of an epidemic, individuals may modify their behaviors in response to external (including local and global) infection-related information. However, the difference between local and global information in influencing the spread of diseases remains inadequately explored. Here, we study a simple epidemic model that incorporates the game-based self-quarantine behavior of individuals, taking into account the influence of local infection status, global disease prevalence, and node heterogeneity (non-identical degree distribution). Our findings reveal that local information can effectively contain an epidemic, even with only a small proportion of individuals opting for self-quarantine. On the other hand, global information can cause infection evolution curves shaking during the declining phase of an epidemic, owing to the synchronous release of nodes with the same degree from the quarantined state. In contrast, the releasing pattern under the local information appears to be more random. This shaking phenomenon can be observed in various types of networks associated with different characteristics. Moreover, it is found that under the proposed game-epidemic framework, a disease is more difficult to spread in heterogeneous networks than in homogeneous networks, which differs from conventional epidemic models.

Coupled Information-Epidemic Spreading Dynamics with Selective Mass Media

As a pandemic emerges, information on epidemic prevention disseminates among the populace, and the propagation of that information interacts with the proliferation of the disease. Mass media serve a pivotal function in facilitating the dissemination of epidemic-related information. Investigating coupled information-epidemic dynamics, while accounting for the promotional effect of mass media in information dissemination, is of significant practical relevance. Nonetheless, in the extant research, scholars predominantly employ an assumption that mass media broadcast to all individuals equally within the network: this assumption overlooks the practical constraint imposed by the substantial social resources required to accomplish such comprehensive promotion. In response, this study introduces a coupled information-epidemic spreading model with mass media that can selectively target and disseminate information to a specific proportion of high-degree nodes. We employed a microscopic Markov chain methodology to scrutinize our model, and we examined the influence of the various model parameters on the dynamic process. The findings of this study reveal that mass media broadcasts directed towards high-degree nodes within the information spreading layer can substantially reduce the infection density of the epidemic, and raise the spreading threshold of the epidemic. Additionally, as the mass media broadcast proportion increases, the suppression effect on the disease becomes stronger. Moreover, with a constant broadcast proportion, the suppression effect of mass media promotion on epidemic spreading within the model is more pronounced in a multiplex network with a negative interlayer degree correlation, compared to scenarios with positive or absent interlayer degree correlation.

The coevolution of the spread of a disease and competing opinions in multiplex networks

The COVID-19 pandemic has resulted in a proliferation of conflicting opinions on physical distancing across various media platforms, which has had a significant impact on human behavior and the transmission dynamics of the disease. Inspired by this social phenomenon, we present a novel UAP-SIS model to study the interaction between conflicting opinions and epidemic spreading in multiplex networks, in which individual behavior is based on diverse opinions. We distinguish susceptibility and infectivity among individuals who are unaware, pro-physical distancing and anti-physical distancing, and we incorporate three kinds of mechanisms for generating individual awareness. The coupled dynamics are analyzed in terms of a microscopic Markov chain approach that encompasses the aforementioned elements. With this model, we derive the epidemic threshold which is related to the diffusion of competing opinions and their coupling configuration. Our findings demonstrate that the transmission of the disease is shaped in a significant manner by conflicting opinions, due to the complex interaction between such opinions and the disease itself. Furthermore, the implementation of awareness-generating mechanisms can help to mitigate the overall prevalence of the epidemic, and global awareness and self-awareness can be interchangeable in certain instances. To effectively curb the spread of epidemics, policymakers should take steps to regulate social media and promote physical distancing as the mainstream opinion.

The impact of disclosure of risk information on risk propagation in the industrial symbiosis network

The interdependent symbiotic relationship between enterprises may bring potential risks to the stability of the industrial symbiosis network (ISN). In order to reduce the damage caused by further risk propagation to the system, this paper establishes the multiplex network to study the impact of disclosure of risk information on risk propagation. In the multiplex network, we use a small-world network to simulate a social network and propose an evolutionary model with scale-free characteristics to simulate the symbiotic relationships between enterprises. Then we establish a risk propagation model by defining transition rules among various states. Through theoretical analysis using the Microscopic Markov Chain Approach (MMCA), we find that the proportion of disclosed enterprises, the network structure of the ISN, the recovery rate of enterprises, and the degree of symbiotic dependence affect the risk propagation threshold of the ISN. Numerical simulation results show that increasing the disclosure probability of risk information can reduce the scope of risk propagation. Moreover, once the disclosure probability of risk information reaches a certain value, the risk propagation threshold can be increased. Finally, relevant suggestions are put forward: (i) strengthening the information communication between symbiotic enterprises may reduce risks caused by information asymmetry. (ii) In addition to the authenticity and integrity of risk information, it is necessary to prevent risk information from being over-interpreted or exaggerated. (iii) Enterprises should strengthen the ability to recover from risks, appropriately reduce the degree of symbiotic dependence, and enhance risk awareness to reduce the possibility of risk occurrence.

The impact of the self-recognition ability and physical quality on coupled negative information-behavior-epidemic dynamics in multiplex networks

In recent years, as the COVID-19 global pandemic evolves, many unprecedented new patterns of epidemic transmission continue to emerge. Reducing the impact of negative information diffusion, calling for individuals to adopt immunization behaviors, and decreasing the infection risk are of great importance to maintain public health and safety. In this paper, we construct a coupled negative information-behavior-epidemic dynamics model by considering the influence of the individual's self-recognition ability and physical quality in multiplex networks. We introduce the Heaviside step function to explore the effect of decision-adoption process on the transmission for each layer, and assume the heterogeneity of the self-recognition ability and physical quality obey the Gaussian distribution. Then, we use the microscopic Markov chain approach (MMCA) to describe the dynamic process and derive the epidemic threshold. Our findings suggest that increasing the clarification strength of mass media and enhancing individuals' self-recognition ability can facilitate the control of the epidemic. And, increasing physical quality can delay the epidemic outbreak and leads to suppress the scale of epidemic transmission. Moreover, the heterogeneity of the individuals in the information diffusion layer leads to a two-stage phase transition, while it leads to a continuous phase transition in the epidemic layer. Our results can provide favorable references for managers in controlling negative information, urging immunization behaviors and suppressing epidemics.

Impact of random and targeted disruptions on information diffusion during outbreaks

Outbreaks are complex multi-scale processes that are impacted not only by cellular dynamics and the ability of pathogens to effectively reproduce and spread, but also by population-level dynamics and the effectiveness of mitigation measures. A timely exchange of information related to the spread of novel pathogens, stay-at-home orders, and other measures can be effective at containing an infectious disease, particularly during the early stages when testing infrastructure, vaccines, and other medical interventions may not be available at scale. Using a multiplex epidemic model that consists of an information layer (modeling information exchange between individuals) and a spatially embedded epidemic layer (representing a human contact network), we study how random and targeted disruptions in the information layer (e.g., errors and intentional attacks on communication infrastructure) impact the total proportion of infections, peak prevalence (i.e., the maximum proportion of infections), and the time to reach peak prevalence. We calibrate our model to the early outbreak stages of the SARS-CoV-2 pandemic in 2020. Mitigation campaigns can still be effective under random disruptions, such as failure of information channels between a few individuals. However, targeted disruptions or sabotage of hub nodes that exchange information with a large number of individuals can abruptly change outbreak characteristics, such as the time to reach the peak of infection. Our results emphasize the importance of the availability of a robust communication infrastructure during an outbreak that can withstand both random and targeted disruptions.

Plant Virus Adaptation to New Hosts: A Multi-scale Approach

Viruses are studied at each level of biological complexity: from within-cells to ecosystems. The same basic evolutionary forces and principles operate at each level: mutation and recombination, selection, genetic drift, migration, and adaptive trade-offs. Great efforts have been put into understanding each level in great detail, hoping to predict the dynamics of viral population, prevent virus emergence, and manage their spread and virulence. Unfortunately, we are still far from this. To achieve these ambitious goals, we advocate for an integrative perspective of virus evolution. Focusing in plant viruses, we illustrate the pervasiveness of the above-mentioned principles. Beginning at the within-cell level, we describe replication modes, infection bottlenecks, and cellular contagion rates. Next, we move up to the colonization of distal tissues, discussing the fundamental role of random events. Then, we jump beyond the individual host and discuss the link between transmission mode and virulence. Finally, at the community level, we discuss properties of virus-plant infection networks. To close this review we propose the multilayer network theory, in which elements at different layers are connected and submit to their own dynamics that feed across layers, resulting in new emerging properties, as a way to integrate information from the different levels.

Coupled spreading between information and epidemics on multiplex networks with simplicial complexes

The way of information diffusion among individuals can be quite complicated, and it is not only limited to one type of communication, but also impacted by multiple channels. Meanwhile, it is easier for an agent to accept an idea once the proportion of their friends who take it goes beyond a specific threshold. Furthermore, in social networks, some higher-order structures, such as simplicial complexes and hypergraph, can describe more abundant and realistic phenomena. Therefore, based on the classical multiplex network model coupling the infectious disease with its relevant information, we propose a novel epidemic model, in which the lower layer represents the physical contact network depicting the epidemic dissemination, while the upper layer stands for the online social network picturing the diffusion of information. In particular, the upper layer is generated by random simplicial complexes, among which the herd-like threshold model is adopted to characterize the information diffusion, and the unaware-aware-unaware model is also considered simultaneously. Using the microscopic Markov chain approach, we analyze the epidemic threshold of the proposed epidemic model and further check the results with numerous Monte Carlo simulations. It is discovered that the threshold model based on the random simplicial complexes network may still cause abrupt transitions on the epidemic threshold. It is also found that simplicial complexes may greatly influence the epidemic size at a steady state.

Transmission dynamics of disease spreading in multilayer networks with mass media

On the basis of existing disease spreading research, in this paper we propose a Hesitant-Taken-Unaware-Aware-Susceptible-Asymptomatic-Symptomatic-Recovered (HTUA-SI^{a}I^{s}R) model with mass media in a two-layer network, which consists of a virtual communication layer and a physical contact layer. Based on the UAU-SIR model, we additionally consider three practical factors, including whether individuals will disseminate information or not, the influence of unaware individuals on aware individuals, and the direct recovery of asymptomatic infected individuals. Based on the microscopic Markov chain approach (MMCA), for the proposed HTUA-SI^{a}I^{s}R model, MMCA equations are generated and the analytical expression of the epidemic threshold is obtained. Compared with Monte Carlo techniques, numerical simulations show the feasibility and effectiveness of the MMCA equations, as well as the HTUA-SI^{a}I^{s}R model theoretically. Meanwhile, extensive simulations demonstrate that the acceleration of the awareness dissemination in the virtual communication layer can effectively block the epidemic spreading and raise the epidemic threshold. However, under certain conditions, the increasing of T-state individuals will increase the U-state individuals because the T-state and U-state individuals can influence the A-state individuals losing their awareness of protection, and then promote the epidemic spreading and decrease the epidemic threshold. In addition, reducing asymptomatic infections can hinder the epidemic spreading. But, when the recovery rate of asymptomatic infections is greater than that of symptomatic infections, decreasing the tendency of individuals acquiring asymptomatic infections will lower the epidemic threshold.

Coevolving spreading dynamics of negative information and epidemic on multiplex networks

The widespread dissemination of negative information on vaccine may arise people's concern on the safety of vaccine and increase their hesitancy in vaccination, which can seriously impede the progress of epidemic control. Existing works on information-epidemic coupled dynamics focus on the suppression effects of information on epidemic. Here we propose a negative information and epidemic coupled propagation model on two-layer multiplex networks to study the effects of negative information of vaccination on epidemic spreading, where the negative information propagates on the virtual communication layer and the disease spreads on the physical contact layer. In our model, an individual getting an adverse event after vaccination will spread negative information and an individual affected by the negative information will reduce his/her willingness to get vaccinated and spread the negative information. By using the microscopic Markov chain method, we analytically predict the epidemic threshold and final infection density, which agree well with simulation results. We find that the spread of negative information leads to a lower epidemic outbreak threshold and a higher final infection density. However, the individuals' vaccination activities, but not the negative information spreading, has a leading impact on epidemic spreading. Only when the individuals obviously reduce their vaccination willingness due to negative information, the negative information can impact the epidemic spreading significantly.

The effect of information-driven resource allocation on the propagation of epidemic with incubation period

In the pandemic of COVID-19, there are exposed individuals who are infected but lack distinct clinical symptoms. In addition, the diffusion of related information drives aware individuals to spontaneously seek resources for protection. The special spreading characteristic and coevolution of different processes may induce unexpected spreading phenomena. Thus we construct a three-layered network framework to explore how information-driven resource allocation affects SEIS (susceptible-exposed-infected-susceptible) epidemic spreading. The analyses utilizing microscopic Markov chain approach reveal that the epidemic threshold depends on the topology structure of epidemic network and the processes of information diffusion and resource allocation. Conducting extensive Monte Carlo simulations, we find some crucial phenomena in the coevolution of information diffusion, resource allocation and epidemic spreading. Firstly, when E-state (exposed state, without symptoms) individuals are infectious, long incubation period results in more E-state individuals than I-state (infected state, with obvious symptoms) individuals. Besides, when E-state individuals have strong or weak infectious capacity, increasing incubation period has an opposite effect on epidemic propagation. Secondly, the short incubation period induces the first-order phase transition. But enhancing the efficacy of resources would convert the phase transition to a second-order type. Finally, comparing the coevolution in networks with different topologies, we find setting the epidemic layer as scale-free network can inhibit the spreading of the epidemic.

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.

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 interplay between disease spreading and awareness diffusion in multiplex networks with activity-driven structure

The interplay between disease and awareness has been extensively studied in static networks. However, most networks in reality will evolve over time. Based on this, we propose a novel epidemiological model in multiplex networks. In this model, the disease spreading layer is a time-varying network generated by the activity-driven model, while the awareness diffusion layer is a static network, and the heterogeneity of individual infection and recovery ability is considered. First, we extend the microscopic Markov chain approach to analytically obtain the epidemic threshold of the model. Then, we simulate the spread of disease and find that stronger heterogeneity in the individual activities of a physical layer can promote disease spreading, while stronger heterogeneity of the virtual layer network will hinder the spread of disease. Interestingly, we find that when the individual infection ability follows Gaussian distribution, the heterogeneity of infection ability has little effect on the spread of disease, but it will significantly affect the epidemic threshold when the individual infection ability follows power-law distribution. Finally, we find the emergence of a metacritical point where the diffusion of awareness is able to control the onset of the epidemics. Our research could cast some light on exploring the dynamics of epidemic spreading in time-varying multiplex networks.

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.

Epidemics on multilayer simplicial complexes

Simplicial complexes describe the simple fact that in social networks a link can connect more than two individuals. As we show here, this has far-reaching consequences for epidemic spreading, in particular in the context of a multilayer network model, where one layer is a virtual social network and the other one is a physical contact network. The social network layer is responsible for the transmission of information via pairwise or higher order 2-simplex interactions among individuals, while the physical layer is responsible for the epidemic spreading. We use the microscopic Markov chain approach to derive the probability transition equations and to determine epidemic outbreak thresholds. We further support these results with Monte Carlo simulations, which are in good agreement, thus confirming the analytical tractability of the proposed model. We find that information transmission rates are frequently low when actual disease transmission rates in the physical network are low or medium, and we show that this can be mitigated effectively by introducing 2-simplex interactions in the social network. The relative ease of introducing higher-order interactions in virtual social networks means that this could be exploited to inhibit epidemic outbreaks.

The impact of information dissemination on vaccination in multiplex networks

The impact of information dissemination on epidemic control is essentially subject to individual behaviors. Vaccination is one of the most effective strategies against the epidemic spread, whose correlation with the information dissemination should be better understood. To this end, we propose an evolutionary vaccination game model in multiplex networks by integrating an information-epidemic spreading process into the vaccination dynamics, and explore how information dissemination influences vaccination. The spreading process is described by a two-layer coupled susceptible-alert-infected-susceptible (SAIS) model, where the strength coefficient between two layers characterizes the tendency and intensity of information dissemination. We find that the impact of information dissemination on vaccination decision-making depends on not only the vaccination cost and network topology, but also the stage of the system evolution. For instance, in a two-layer BA scale-free network, information dissemination helps to improve vaccination density only at the early stage of the system evolution, as well as when the vaccination cost is smaller. A counter-intuitive conclusion that more information transmission cannot promote vaccination is obtained when the vaccination cost is larger. Moreover, we study the impact of the strength coefficient and individual sensitivity on the fraction of infected individuals and social cost, and unveil the role of information dissemination in controlling the epidemic.

Using awareness to Z-control a SEIR model with overexposure: Insights on Covid-19 pandemic

In this paper, we use the Z-control approach to get further insight on the role of awareness in the management of epidemics that, just like Covid-19, display a high rate of overexposure because of the large number of asymptomatic people. We focus on a SEIR model including a overexposure mechanism and consider awareness as a time-dependent variable whose dynamics is not assigned a priori. Exploiting the potential of awareness to produce social distancing and self-isolation among susceptibles, we use it as an indirect control on the class of infective individuals and apply the Z-control approach to detect what trend must awareness display over time in order to eradicate the disease. To this aim, we generalize the Z-control procedure to appropriately treat an uncontrolled model with more than two governing equations. Analytical and numerical investigations on the resulting Z-controlled system show its capability in controlling some representative dynamics within both the backward and the forward scenarios. The awareness variable is qualitatively compared to Google Trends data on Covid-19 that are discussed in the perspective of the Z-control approach, inferring qualitative indications in view of the disease control. The cases of Italy and New Zealand in the first phase of the pandemic are analyzed in detail. The theoretical framework of the Z-control approach can hence offer the chance to reflect on the use of Google Trends as a possible indicator of good management of the epidemic.

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.

The impact of the pandemic declaration on public awareness and behavior: Focusing on COVID-19 google searches

The unprecedented outbreaks of epidemics such as the coronavirus has caused major socio-economic changes. To analyze public risk awareness and behavior in response to the outbreak of epidemic diseases, this study focuses on RSV (Relative Search Volume) provided by Google Trends. This study uses the social big data provided by Google RSV to investigate how the WHO's pandemic declaration affected public awareness and behavior. 37 OECD countries were analyzed and clustered according to the degree of reaction to the declaration, and the United States, France and Germany were selected for comparative study. The results of this study statistically confirmed that the pandemic declaration increased public awareness and had the effect of increasing searches for information on COVID-19 by more than 20%. In addition, this rapid rise in RSV also reflected interest in the COVID-19 test and had the effect of inducing individuals to be tested, which helped identify new cases. The significance of this study is that it provided the theoretical foundation for using RSV and its implications to understand and strategically utilize public awareness and behavior in situations where the WHO and governments must launch policies in response to the outbreak of new infectious diseases such as COVID-19.

Epidemic Propagation With Positive and Negative Preventive Information in Multiplex Networks

We propose a novel epidemic model based on two-layered multiplex networks to explore the influence of positive and negative preventive information on epidemic propagation. In the model, one layer represents a social network with positive and negative preventive information spreading competitively, while the other one denotes the physical contact network with epidemic propagation. The individuals who are aware of positive prevention will take more effective measures to avoid being infected than those who are aware of negative prevention. Taking the microscopic Markov chain (MMC) approach, we analytically derive the expression of the epidemic threshold for the proposed epidemic model, which indicates that the diffusion of positive and negative prevention information, as well as the topology of the physical contact network have a significant impact on the epidemic threshold. By comparing the results obtained with MMC and those with the Monte Carlo (MC) simulations, it is found that they are in good agreement, but MMC can well describe the dynamics of the proposed model. Meanwhile, through extensive simulations, we demonstrate the impact of positive and negative preventive information on the epidemic threshold, as well as the prevalence of infectious diseases. We also find that the epidemic prevalence and the epidemic outbreaks can be suppressed by the diffusion of positive preventive information and be promoted by the diffusion of negative preventive information.

Effect of heterogeneous risk perception on information diffusion, behavior change, and disease transmission

Motivated by the importance of individual differences in risk perception and behavior change in people's responses to infectious disease outbreaks (particularly the ongoing COVID-19 pandemic), we propose a heterogeneous disease-behavior-information transmission model, in which people's risk of getting infected is influenced by information diffusion, behavior change, and disease transmission. We use both a mean-field approximation and Monte Carlo simulations to analyze the dynamics of the model. Information diffusion influences behavior change by allowing people to be aware of the disease and adopt self-protection and subsequently affects disease transmission by changing the actual infection rate. Results show that (a) awareness plays a central role in epidemic prevention, (b) a reasonable fraction of overreacting nodes are needed in epidemic prevention (c) the basic reproduction number R_{0} has different effects on epidemic outbreak for cases with and without asymptomatic infection, and (d) social influence on behavior change can remarkably decrease the epidemic outbreak size. This research indicates that the media and opinion leaders should not understate the transmissibility and severity of diseases to ensure that people become aware of the disease and adopt self-protection to protect themselves and the whole population.

Disease and information spreading at different speeds in multiplex networks

Nowadays, one of the challenges we face when carrying out modeling of epidemic spreading is to develop methods to control disease transmission. In this article we study how the spreading of knowledge of a disease affects the propagation of that disease in a population of interacting individuals. For that, we analyze the interaction between two different processes on multiplex networks: the propagation of an epidemic using the susceptible-infected-susceptible dynamics and the dissemination of information about the disease-and its prevention methods-using the unaware-aware-unaware dynamics, so that informed individuals are less likely to be infected. Unlike previous related models where disease and information spread at the same time scale, we introduce here a parameter that controls the relative speed between the propagation of the two processes. We study the behavior of this model using a mean-field approach that gives results in good agreement with Monte Carlo simulations on homogeneous complex networks. We find that increasing the rate of information dissemination reduces the disease prevalence, as one may expect. However, increasing the speed of the information process as compared to that of the epidemic process has the counterintuitive effect of increasing the disease prevalence. This result opens an interesting discussion about the effects of information spreading on disease propagation.

Maximizing multiple influences and fair seed allocation on multilayer social networks

The dissemination of information on networks involves many important practical issues, such as the spread and containment of rumors in social networks, the spread of infectious diseases among the population, commercial propaganda and promotion, the expansion of political influence and so on. One of the most important problems is the influence-maximization problem which is to find out k most influential nodes under a certain propagate mechanism. Since the problem was proposed in 2001, many works have focused on maximizing the influence in a single network. It is a NP-hard problem and the state-of-art algorithm IMM proposed by Youze Tang et al. achieves a ratio of 63.2% of the optimum with nearly linear time complexity. In recent years, there have been some works of maximizing influence on multilayer networks, either in the situation of single or multiple influences. But most of them study seed selection strategies to maximize their own influence from the perspective of participants. In fact, the problem from the perspective of network owners is also worthy of attention. Since network participants have not had access to all information of the network for reasons such as privacy protection and corporate interests, they may have access to only part of the social network. The owners of networks can get the whole picture of the networks, and they need not only to maximize the overall influence, but also to consider allocating seeds to their customers fairly, i.e., the Fair Seed Allocation (FSA) problem. As far as we know, FSA problem has been studied on a single network, but not on multilayer networks yet. From the perspective of network owners, we propose a multiple-influence diffusion model MMIC on multilayer networks and its FSA problem. Two solutions of FSA problem are given in this paper, and we prove theoretically that our seed allocation schemes are greedy. Subsequent experiments also validate the effectiveness of our approaches.

Co-evolution spreading of multiple information and epidemics on two-layered networks under the influence of mass media

During epidemic outbreaks, there are various types of information about epidemic prevention disseminated simultaneously among the population. Meanwhile, the mass media also scrambles to report the information related to the epidemic. Inspired by these phenomena, we devise a model to discuss the dynamical characteristics of the co-evolution spreading of multiple information and epidemic under the influence of mass media. We construct the co-evolution model under the framework of two-layered networks and gain the dynamical equations and epidemic critical point with the help of the micro-Markov chain approach. The expression of epidemic critical point show that the positive and negative information have a direct impact on the epidemic critical point. Moreover, the mass media can indirectly affect the epidemic size and epidemic critical point through their interference with the dissemination of epidemic-relevant information. Though extensive numerical experiments, we examine the accuracy of the dynamical equations and expression of the epidemic critical point, showing that the dynamical characteristics of co-evolution spreading can be well described by the dynamic equations and the epidemic critical point is able to be accurately calculated by the derived expression. The experimental results demonstrate that accelerating positive information dissemination and enhancing the propaganda intensity of mass media can efficaciously restrain the epidemic spreading. Interestingly, the way to accelerate the dissemination of negative information can also alleviate the epidemic to a certain extent when the positive information hardly spreads. Current results can provide some useful clues for epidemic prevention and control on the basis of epidemic-relevant information dissemination.

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 Erdős-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.

Epidemic spreading with awareness and different timescales in multiplex networks

One of the major issues in theoretical modeling of epidemic spreading is the development of methods to control the transmission of an infectious agent. Human behavior plays a fundamental role in the spreading dynamics and can be used to stop a disease from spreading or to reduce its burden, as individuals aware of the presence of a disease can take measures to reduce their exposure to contagion. In this paper, we propose a mathematical model for the spread of diseases with awareness in complex networks. Unlike previous models, the information is propagated following a generalized Maki-Thompson rumor model. Flexibility on the timescale between information and disease spreading is also included. We verify that the velocity characterizing the diffusion of information awareness greatly influences the disease prevalence. We also show that a reduction in the fraction of unaware individuals does not always imply a decrease of the prevalence, as the relative timescale between disease and awareness spreading plays a crucial role in the systems' dynamics. This result is shown to be independent of the network topology. We finally calculate the epidemic threshold of our model, and show that it does not depend on the relative timescale. Our results provide a new view on how information influence disease spreading and can be used for the development of more efficient methods for disease control.

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.

Suppression of epidemic spreading process on multiplex networks via active immunization

Spatial epidemic spreading, a fundamental dynamical process upon complex networks, attracts huge research interest during the past few decades. To suppress the spreading of epidemic, a couple of effective methods have been proposed, including node vaccination. Under such a scenario, nodes are immunized passively and fail to reveal the mechanisms of active activity. Here, we suggest one novel model of an observer node, which can identify infection through interacting with infected neighbors and inform the other neighbors for vaccination, on multiplex networks, consisting of epidemic spreading layer and information spreading layer. In detail, the epidemic spreading layer supports susceptible-infected-recovered process, while observer nodes will be selected according to several algorithms derived from percolation theory. Numerical simulation results show that the algorithm based on large degree performs better than random placement, while the algorithm based on nodes' degree in the information spreading layer performs the best (i.e., the best suppression efficacy is guaranteed when placing observer nodes based on nodes' degree in the information spreading layer). With the help of state probability transition equation, the above phenomena can be validated accurately. Our work thus may shed new light into understanding control of empirical epidemic control.

Epidemic spreading with awareness diffusion on activity-driven networks

Acknowledging the significance of awareness diffusion and behavioral response in contagion outbreaks has been regarded as an indispensable prerequisite for a complete understanding of epidemic spreading. Recent studies from the research community have accumulated overwhelming evidence for the incessantly evolving structure of the underlying networks. Thus there is an impelling need to capture the interplay between the epidemic spreading and awareness diffusion on time-varying networks. In this paper, we consider a behavioral model in which susceptible individuals become alert and adopt a preventive behavior under the local risk perception characterized by a decision-making threshold. The impact of awareness diffusion on the epidemic threshold is investigated under the framework of activity-driven network. Results show that the local epidemic situation in risk perception and the duration of preventive effect are crucial for raising the epidemic threshold. The analytical results are corroborated by Monte Carlo simulations.

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.

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

Awareness of disease outbreaks can trigger changes in human behavior and has a significant impact on the spread of epidemics. Previous studies usually considered the coupled awareness-epidemic dynamics to be two competing processes that interact in the information and epidemic layers. However, these studies mostly assumed that all aware individuals have the same reduced infectivity and that different neighbors have the same influence on one's perception, ignoring the heterogeneity of individuals. In this paper, we propose a coupled awareness-epidemic spreading model in multiplex networks incorporating three types of heterogeneity: (1) the heterogeneity of individual responses to disease outbreaks, (2) the influence heterogeneity in the epidemic layer, and (3) the influence heterogeneity in the information layer. The theoretical analysis shows that the influence heterogeneity in the information layer has two-stage effects on the epidemic threshold. Moreover, we find that the epidemic threshold in the higher stage depends on the heterogeneity of individual responses and the influence heterogeneity in the epidemic layer, while the epidemic threshold in the lower stage is independent of awareness spreading and individual behaviors. The results give us a better understanding of how individual heterogeneity affects epidemic spreading and provide some practical implications for the control of epidemics.

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

Awareness of disease outbreaks can trigger changes in human behavior and has a significant impact on the spread of epidemics. Previous studies usually considered the coupled awareness-epidemic dynamics to be two competing processes that interact in the information and epidemic layers. However, these studies mostly assumed that all aware individuals have the same reduced infectivity and that different neighbors have the same influence on one's perception, ignoring the heterogeneity of individuals. In this paper, we propose a coupled awareness-epidemic spreading model in multiplex networks incorporating three types of heterogeneity: (1) the heterogeneity of individual responses to disease outbreaks, (2) the influence heterogeneity in the epidemic layer, and (3) the influence heterogeneity in the information layer. The theoretical analysis shows that the influence heterogeneity in the information layer has two-stage effects on the epidemic threshold. Moreover, we find that the epidemic threshold in the higher stage depends on the heterogeneity of individual responses and the influence heterogeneity in the epidemic layer, while the epidemic threshold in the lower stage is independent of awareness spreading and individual behaviors. The results give us a better understanding of how individual heterogeneity affects epidemic spreading and provide some practical implications for the control of epidemics.

Impact of directionality and correlation on contagion

The threshold model has been widely adopted for modelling contagion processes on social networks, where individuals are assumed to be in one of two states: inactive or active. This paper studies the model on directed networks where nodal inand out-degrees may be correlated. To understand how directionality and correlation affect the breakdown of the system, a theoretical framework based on generating function technology is developed. First, the effects of degree and threshold heterogeneities are identified. It is found that both heterogeneities always decrease systematic robustness. Then, the impact of the correlation between nodal in- and out-degrees is investigated. It turns out that the positive correlation increases the systematic robustness in a wide range of the average in-degree, while the negative correlation has an opposite effect. Finally, a comparison between undirected and directed networks shows that the presence of directionality and correlation always make the system more vulnerable.

Infection prevention behaviour and infectious disease modelling: a review of the literature and recommendations for the future

Background

Given the importance of person to person transmission in the spread of infectious diseases, it is critically important to ensure that human behaviour with respect to infection prevention is appropriately represented within infectious disease models. This paper presents a large scale scoping review regarding the incorporation of infection prevention behaviour in infectious disease models. The outcomes of this review are contextualised within the psychological literature concerning health behaviour and behaviour change, resulting in a series of key recommendations for the incorporation of human behaviour in future infectious disease models.

Methods

The search strategy focused on terms relating to behaviour, infectious disease and mathematical modelling. The selection criteria were developed iteratively to focus on original research articles that present an infectious disease model with human-human spread, in which individuals’ self-protective health behaviour varied endogenously within the model. Data extracted included: the behaviour that is modelled; how this behaviour is modelled; any theoretical background for the modelling of behaviour, and; any behavioural data used to parameterise the models.

Results

Forty-two papers from an initial total of 2987 were retained for inclusion in the final review. All of these papers were published between 2002 and 2015. Many of the included papers employed a multiple, linked models to incorporate infection prevention behaviour. Both cognitive constructs (e.g., perceived risk) and, to a lesser extent, social constructs (e.g., social norms) were identified in the included papers. However, only five papers made explicit reference to psychological health behaviour change theories. Finally, just under half of the included papers incorporated behavioural data in their modelling.

Conclusions

By contextualising the review outcomes within the psychological literature on health behaviour and behaviour change, three key recommendations for future behavioural modelling are made. First, modellers should consult with the psychological literature on health behaviour/ behaviour change when developing new models. Second, modellers interested in exploring the relationship between behaviour and disease spread should draw on social psychological literature to increase the complexity of the social world represented within infectious disease models. Finally, greater use of context-specific behavioural data (e.g., survey data, observational data) is recommended to parameterise models.

Electronic supplementary material

The online version of this article (10.1186/s12889-018-5223-1) contains supplementary material, which is available to authorized users.

Resource control of epidemic spreading through a multilayer network

While the amount of resource is an important factor in control of contagions, outbreaks may occur when they reach a finite fraction of the population. An unexplored issue is how much the resource amount is invested to control this outbreak. Here we analyze a mechanic model of epidemic spreading, which considers both resource factor and network layer. We find that there is a resource threshold, such that a significant fraction of the total population may be infected (i.e., an outbreak will occur) if the amount of resource is below this threshold, but the outbreak may be effectively eradicated if it is beyond the threshold. The threshold is dependent upon both the connection strength between the layers and their internal structure. We also find that the layer-layer connection strength can lead to the phase transition from the first-order phase to the continuous one or vice versa, whereas the internal connection can result in a different kind of phase transition (i.e., the so-called hybrid phase transition) apart from first-order and continuous one. Our results could have important implications for government decisions on public health resources devoted to epidemic disease control.

Promoting information diffusion through interlayer recovery processes in multiplex networks

For information diffusion in multiplex networks, the effect of interlayer contagion on spreading dynamics has been explored in different settings. Nevertheless, the impact of interlayer recovery processes, i.e., the transition of nodes to stiflers in all layers after they become stiflers in any layer, still remains unclear. In this paper, we propose a modified ignorant-spreader-stifler model of rumor spreading equipped with an interlayer recovery mechanism. We find that the information diffusion can be effectively promoted for a range of interlayer recovery rates. By combining the mean-field approximation and the Markov chain approach, we derive the evolution equations of the diffusion process in two-layer homogeneous multiplex networks. The optimal interlayer recovery rate that achieves the maximal enhancement can be calculated by solving the equations numerically. In addition, we find that the promoting effect on a certain layer can be strengthened if information spreads more extensively within the counterpart layer. When applying the model to two-layer scale-free multiplex networks, with or without degree correlation, similar promoting effect is also observed in simulations. Our work indicates that the interlayer recovery process is beneficial to information diffusion in multiplex networks, which may have implications for designing efficient spreading strategies.

Global stability for epidemic models on multiplex networks

In this work, we consider an epidemic model in a two-layer network in which the dynamics of susceptible-infected-susceptible process in the physical layer coexists with that of a cyclic process of unaware-aware-unaware in the virtual layer. For such multiplex network, we shall define the basic reproduction number [Formula: see text] in the virtual layer, which is similar to the basic reproduction number [Formula: see text] defined in the physical layer. We show analytically that if [Formula: see text] and [Formula: see text], then the disease and information free equilibrium is globally stable and if [Formula: see text] and [Formula: see text], then the disease free and information saturated equilibrium is globally stable for all initial conditions except at the origin. In the case of [Formula: see text], whether the disease dies out or not depends on the competition between how well the information is transmitted in the virtual layer and how contagious the disease is in the physical layer. In particular, it is numerically demonstrated that if the difference in [Formula: see text] and [Formula: see text] is greater than the product of [Formula: see text], the deviation of [Formula: see text] from 1 and the relative infection rate for an aware susceptible individual, then the disease dies out. Otherwise, the disease breaks out.

Competition of simple and complex adoption on interdependent networks

We consider the competition of two mechanisms for adoption processes: a so-called complex threshold dynamics and a simple susceptible-infected-susceptible (SIS) model. Separately, these mechanisms lead, respectively, to first-order and continuous transitions between nonadoption and adoption phases. We consider two interconnected layers. While all nodes on the first layer follow the complex adoption process, all nodes on the second layer follow the simple adoption process. Coupling between the two adoption processes occurs as a result of the inclusion of some additional interconnections between layers. We find that the transition points and also the nature of the transitions are modified in the coupled dynamics. In the complex adoption layer, the critical threshold required for extension of adoption increases with interlayer connectivity whereas in the case of an isolated single network it would decrease with average connectivity. In addition, the transition can become continuous depending on the detailed interlayer and intralayer connectivities. In the SIS layer, any interlayer connectivity leads to the extension of the adopter phase. Besides, a new transition appears as a sudden drop of the fraction of adopters in the SIS layer. The main numerical findings are described by a mean-field type analytical approach appropriately developed for the threshold-SIS coupled system.

Behavioural change models for infectious disease transmission: a systematic review (2010-2015)

We review behavioural change models (BCMs) for infectious disease transmission in humans. Following the Cochrane collaboration guidelines and the PRISMA statement, our systematic search and selection yielded 178 papers covering the period 2010-2015. We observe an increasing trend in published BCMs, frequently coupled to (re)emergence events, and propose a categorization by distinguishing how information translates into preventive actions. Behaviour is usually captured by introducing information as a dynamic parameter (76/178) or by introducing an economic objective function, either with (26/178) or without (37/178) imitation. Approaches using information thresholds (29/178) and exogenous behaviour formation (16/178) are also popular. We further classify according to disease, prevention measure, transmission model (with 81/178 population, 6/178 metapopulation and 91/178 individual-level models) and the way prevention impacts transmission. We highlight the minority (15%) of studies that use any real-life data for parametrization or validation and note that BCMs increasingly use social media data and generally incorporate multiple sources of information (16/178), multiple types of information (17/178) or both (9/178). We conclude that individual-level models are increasingly used and useful to model behaviour changes. Despite recent advancements, we remain concerned that most models are purely theoretical and lack representative data and a validation process.

Lévy random walks on multiplex networks

Random walks constitute a fundamental mechanism for many dynamics taking place on complex networks. Besides, as a more realistic description of our society, multiplex networks have been receiving a growing interest, as well as the dynamical processes that occur on top of them. Here, inspired by one specific model of random walks that seems to be ubiquitous across many scientific fields, the Lévy flight, we study a new navigation strategy on top of multiplex networks. Capitalizing on spectral graph and stochastic matrix theories, we derive analytical expressions for the mean first passage time and the average time to reach a node on these networks. Moreover, we also explore the efficiency of Lévy random walks, which we found to be very different as compared to the single layer scenario, accounting for the structure and dynamics inherent to the multiplex network. Finally, by comparing with some other important random walk processes defined on multiplex networks, we find that in some region of the parameters, a Lévy random walk is the most efficient strategy. Our results give us a deeper understanding of Lévy random walks and show the importance of considering the topological structure of multiplex networks when trying to find efficient navigation strategies.