The impact of awareness on epidemic spreading in networks

Coupled infectious disease and behavior dynamics. A review of model assumptions

To comprehend the dynamics of infectious disease transmission, it is imperative to incorporate human protective behavior into models of disease spreading. While models exist for both infectious disease and behavior dynamics independently, the integration of these aspects has yet to yield a cohesive body of literature. Such an integration is crucial for gaining insights into phenomena like the rise of infodemics, the polarization of opinions regarding vaccines, and the dissemination of conspiracy theories during a pandemic. We make a threefold contribution. First, we introduce a framework todescribemodels coupling infectious disease and behavior dynamics, delineating four distinct update functions. Reviewing existing literature, we highlight a substantial diversity in the implementation of each update function. This variation, coupled with a dearth of model comparisons, renders the literature hardly informative for researchers seeking to develop models tailored to specific populations, infectious diseases, and forms of protection. Second, we advocate an approach tocomparingmodels' assumptions about human behavior, the model aspect characterized by the strongest disagreement. Rather than representing the psychological complexity of decision-making, we show that 'influence-response functions' allow one to identify which model differences generate different disease dynamics and which do not, guiding both model development and empirical research testing model assumptions. Third, we propose recommendations for future modeling endeavors and empirical research aimed atselectingmodels of coupled infectious disease and behavior dynamics. We underscore the importance of incorporating empirical approaches from the social sciences to propel the literature forward.

Effects of higher-order interactions and impulsive vaccination for rumor propagation

This paper introduces a rumor propagation model with saturation incidence, based on hypergraph theory. Hypergraphs can capture the higher-order interactions between nodes in a social network, where the node degree is substituted with hyperdegree. First, the threshold for rumor spreading model is obtained, the global asymptotically stable of the rumor-free equilibrium, and the global attractive and global asymptotically stable of the rumor-prevailing equilibrium are proved. Then, we incorporate impulsive vaccination into the model to represent the guided effect, simulating the periodic educational activities organized by official institutions to counteract rumor dissemination. By employing the comparison theorem, the paper demonstrates the global attractiveness of the rumor-free periodic solution and the persistence of the model. Finally, through numerical simulations, the paper compares the effects of higher-order and pairwise interactions on rumor spreading, validating the theoretical conclusions. The results indicate that higher-order interactions can promote rumor spreading, while impulsive vaccination can effectively decrease the scale of rumor spreading.

Paradoxes in the coevolution of contagions and institutions

Epidemic models study the spread of undesired agents through populations, be it infectious diseases through a country, misinformation in social media or pests infesting a region. In combating these epidemics, we rely neither on global top-down interventions, nor solely on individual adaptations. Instead, interventions commonly come from local institutions such as public health departments, moderation teams on social media platforms or other forms of group governance. Classic models, which are often individual or agent-based, are ill-suited to capture local adaptations. We leverage developments of institutional dynamics based on cultural group selection to study how groups attempt local control of an epidemic by taking inspiration from the successes and failures of other groups. Incorporating institutional changes into epidemic dynamics reveals paradoxes: a higher transmission rate can result in smaller outbreaks as does decreasing the speed of institutional adaptation. When groups perceive a contagion as more worrisome, they can invest in improved policies and, if they maintain these policies long enough to have impact, lead to a reduction in endemicity. By looking at the interplay between the speed of institutions and the transmission rate of the contagions, we find rich coevolutionary dynamics that reflect the complexity of known biological and social contagions.

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.

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.

Effect of Human Behavior on the Evolution of Viral Strains During an Epidemic

It is well known in the literature that human behavior can change as a reaction to disease observed in others, and that such behavioral changes can be an important factor in the spread of an epidemic. It has been noted that human behavioral traits in disease avoidance are under selection in the presence of infectious diseases. Here, we explore a complementary trend: the pathogen itself might experience a force of selection to become less “visible,” or less “symptomatic,” in the presence of such human behavioral trends. Using a stochastic SIR agent-based model, we investigated the co-evolution of two viral strains with cross-immunity, where the resident strain is symptomatic while the mutant strain is asymptomatic. We assumed that individuals exercised self-regulated social distancing (SD) behavior if one of their neighbors was infected with a symptomatic strain. We observed that the proportion of asymptomatic carriers increased over time with a stronger effect corresponding to higher levels of self-regulated SD. Adding mandated SD made the effect more significant, while the existence of a time-delay between the onset of infection and the change of behavior reduced the advantage of the asymptomatic strain. These results were consistent under random geometric networks, scale-free networks, and a synthetic network that represented the social behavior of the residents of New Orleans.

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.

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.

Incorporating economic constraints for optimal control of immunizing infections

It is well-known that the interruption of transmission of a disease can be achieved, provided the vaccinated population reaches a threshold depending on, among others, the efficacy of vaccines. The purpose of this paper is to address the optimal vaccination strategy by imposing the economic constraints. In particular, an S--(I,V)--S model used to describe the spreading of the disease in a well-mixed population and a cost function consisting of vaccination and infection costs are proposed. The well-definedness of the above-described modeling is provided. We were then able to provide an optimal strategy to minimize the cost for all parameters. In particular, the optimal vaccination level to minimize the cost can be completely characterized for all parameters. For instance, the optimal vaccination level can be classified by the magnitude of the failure rate of the vaccine with other parameters being given. Under these circumstances, the optimal strategy to minimize the cost is roughly to eliminate the disease locally (respectively, choose an economic optimum resulting in not to wipe out the disease completely or take no vaccination for anyone) provided the vaccine failure rate is relatively small (respectively, intermediate or large). Numerical simulations to illustrate our main results are also provided. Moreover, the data collected at the height of the Covid-19 pandemic in Taiwan are also numerically simulated to provide the corresponding optimal vaccination strategy.

Modeling the impacts of awareness and limited medical resources on the epidemic size of a multi-group SIR epidemic model

The pharmaceutical interventions of emerging infectious diseases are constrained by the available medical resources such as drugs, vaccines, hospital beds, isolation places and the efficiency of the treatment. The awareness of the population also plays an important role in reducing contacts and consequently, reducing the disease transmission rate. In this paper, we propose a multi-group Susceptible, Infected and Recovered (SIR) epidemic model incorporating the awareness of population and the saturated treatment function that describes the effects of the availability of medical resources for treatment. We assume that the treatment of the infected individuals of a group is affected by the medical resources for the treatment of each group. We calculate the basic reproduction number [Formula: see text] in the term of the awareness parameter using the next generation approach. We determine the local and global stabilities of equilibrium (disease free equilibrium and endemic equilibrium) in terms of [Formula: see text] and the availability of medical resources for treatment. We obtain that backward bifurcation occurs at [Formula: see text] along with the existence of multiple endemic equilibria when [Formula: see text] Further, we consider the special case with a single group epidemic system and ensure the existence of multiple endemic equilibria. We showed a necessary condition on the parameter related to the availability of medical resources when backward bifurcation occurs. This situation indicates that reducing the basic reproduction number below unity is not sufficient to remove the disease when the medical resources for treatment are scarce. We used numerical simulations to support and counterpart our theoretical results and discussed the impacts of the awareness of susceptible population and availability of medical resources for treatment in each group, on the epidemic size of each group. Our findings suggest that in the case of limited medical resources, the high treatment rate and awareness of the population are very helpful to control the disease (to reduce the prevalence of infection) and the eradication of disease also depends on initial population sizes. More importantly, it is also obtained that sufficient medical resources for every group are required to eradicate the disease from an entire population.

Timeliness of information disclosure during the low transmission period of COVID-19: resident-level observational study in China

BACKGROUND

Only when people feel they have received timely disclosure will they have sufficient incentive to implement community prevention and control measures. The timely and standardized information published by authorities as a response to the crisis can better inform the public and enable better preparations for the pandemic during the low transmission period of COVID-19; however, there is limited evidence of whether people consent that information is disclosed timely and influencing factors.

METHODS

A cross-sectional survey was conducted in China from 4 to 26 February 2021. Convenient sampling strategy was adopted to recruit participators. Participants were asked to filled out the questions that assessed questionnaire on the residents' attitudes to information disclosure timely. A binary logistic regression analysis was performed to identify the risk factors affecting the residents' attitudes.

RESULTS

A total of 2361 residents filled out the questionnaire. 1704 (72.17%) consented COVID-19 information has been disclosed timely. Furthermore, age (OR = 0.093, 95%CI = 0.043 ~ 0.201), gender (OR = 1.396, 95%CI = 1.085 ~ 1.797), place of residence (OR = 0.650, 95%CI = 0.525 ~ 0.804), employed status (OR = 2.757, 95%CI = 1.598 ~ 4.756), highest educational level (OR = 0.394, 95%CI = 0.176 ~ 0.880), region (OR = 0.561, 95%CI = 0.437 ~ 0.720) and impact on life by the COVID-19 (OR = 0.482, 95%CI = 0.270 ~ 0.861) were mainly factors associated with residents' attitudes.

CONCLUSIONS

The aims of this study were to evaluate the residents attitudes to information disclosure timely during the low transmission period in China and to provide a scientific basis for effective information communication in future public health crises. Timely and effective efforts to disclose information need to been made during the low transmission period. Continued improvements to local authority reporting will contribute to more effective public communication and efficient public health research responses. The development of protocols and the standardization of epidemic message templates-as well as the use of uniform operating procedures to provide regular information updates-should be prioritized to ensure a coordinated national response.

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.

How disease risk awareness modulates transmission: coupling infectious disease models with behavioural dynamics

Epidemiological models often assume that individuals do not change their behaviour or that those aspects are implicitly incorporated in parameters in the models. Typically, these assumptions are included in the contact rate between infectious and susceptible individuals. However, adaptive behaviours are expected to emerge and play an important role in the transmission dynamics across populations. Here, we propose a theoretical framework to couple transmission dynamics with behavioural dynamics due to infection awareness. We modelled the dynamics of social behaviour using a game theory framework, which is then coupled with an epidemiological model that captures the disease dynamics by assuming that individuals are aware of the actual epidemiological state to reduce their contacts. Results from the mechanistic model show that as individuals increase their awareness, the steady-state value of the final fraction of infected individuals in a susceptible-infected-susceptible (SIS) model decreases. We also incorporate theoretical contact networks, having the awareness parameter dependent on global or local contacts. Results show that even when individuals increase their awareness of the disease, the spatial structure itself defines the steady state.

The stochastic bifurcation analysis and stochastic delayed optimal control for epidemic model with general incidence function

In the history of the world, contagious diseases have been proved to pose serious threats to humanity that needs uttermost research in the field and its prompt implementations. With this motive, an attempt has been made to investigate the spread of such contagion by using a delayed stochastic epidemic model with general incidence rate, time-delay transmission, and the concept of cross immunity. It is proved that the system is mathematically and biologically well-posed by showing that there exist a positive and bounded global solution of the model. Necessary conditions are derived, which guarantees the permanence as well as extinction of the disease. The model is further investigated for the existence of an ergodic stationary distribution and established sufficient conditions. The non-zero periodic solution of the stochastic model is analyzed quantitatively. The analysis of optimality and time delay is used, and a proper strategy was presented for prevention of the disease. A scheme for the numerical simulations is developed and implemented in MATLAB, which reflects the long term behavior of the model. Simulation suggests that the noises play a vital role in controlling the spread of an epidemic following the proposed flow, and the case of disease extinction is directly proportional to the magnitude of the white noises. Since time delay reflects the dynamics of recurring epidemics, therefore, it is believed that this study will provide a robust basis for studying the behavior and mechanism of chronic infections.

Microscopic edge-based compartmental modeling method for analyzing the susceptible-infected-recovered epidemic spreading on networks

The edge-based compartmental modeling (EBCM) approach has been used widely to characterize the nonrecurrent epidemic spreading dynamics (e.g., the susceptible-infected-recovered model) in complex networks. By using the probability theory, we derived an individual-based formulation for this approach, which we herein refer to as the microscopic EBCM method. We found that both for small and large initial infection numbers, the epidemic evolution agreed well with the ensemble averages of our stochastic simulations on different complex networks. Moreover, we showed that the dynamical message passing model, the standard EBCM system, and the pair quenched mean-field equations can be deduced by our microscopic EBCM method. In addition, the microscopic EBCM method was used to analyze the effect of epidemic awareness on networks. Importantly, the simple EBCM model for exponential awareness was developed. Our method provides a way for handling nontrivial disease transmission processes with irreversible dynamics.

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.

Impact of information diffusion on epidemic spreading in partially mapping two-layered time-varying networks

We propose a new epidemic model considering the partial mapping relationship in a two-layered time-varying network, which aims to study the influence of information diffusion on epidemic spreading. In the model, one layer represents the epidemic-related information diffusion in the social networks, while the other layer denotes the epidemic spreading in physical networks. In addition, there just exist mapping relationships between partial pairs of nodes in the two-layered network, which characterizes the interaction between information diffusion and epidemic spreading. Meanwhile, the information and epidemics can only spread in their own layers. Afterwards, starting from the microscopic Markov chain (MMC) method, we can establish the dynamic equation of epidemic spreading and then analytically deduce its epidemic threshold, which demonstrates that the ratio of correspondence between two layers has a significant effect on the epidemic threshold of the proposed model. Finally, it is found that MMC method can well match with Monte Carlo (MC) simulations, and the relevant results can be helpful to understand the epidemic spreading properties in depth.

Optimal test-kit-based intervention strategy of epidemic spreading in heterogeneous complex networks

We propose a deterministic compartmental model of infectious disease that considers the test kits as an important ingredient for the suppression and mitigation of epidemics. A rigorous simulation (with an analytical argument) is provided to reveal the effective reduction of the final outbreak size and the peak of infection as a function of basic reproduction number in a single patch. Furthermore, to study the impact of long and short-distance human migration among the patches, we consider heterogeneous networks where the linear diffusive connectivity is determined by the network link structure. We numerically confirm that implementation of test kits in a fraction of nodes (patches) having larger degrees or betweenness centralities can reduce the peak of infection (as well as the final outbreak size) significantly. A next-generation matrix-based analytical treatment is provided to find out the critical transmission probability in the entire network for the onset of epidemics. Finally, the optimal intervention strategy is validated in two real networks: the global airport network and the transportation network of Kolkata, India.

Awareness of pandemics and the impact of COVID-19

Awareness about the occurrence of viral infectious (or other) tail risks can influence their socioeconomic inter-temporal impacts. In this regard, a branch of the literature finds that personal experiences with significant shocks can have long-lasting effects on risk-taking attitudes and the perceived probability about the occurrence of extreme, negative shocks. In this paper, we proxy the level of societal experience (awareness) in the face of the COVID-19 outbreak by past exposure of a country to epidemics, and other catastrophic events. We show that in a large cross-section of more than 150 countries, more aware societies suffered a less intense impact of the COVID-19 disease, in terms of loss of lives and, to some extent, economic damage.

Impacts of social distancing on the spread of infectious diseases with asymptomatic infection: A mathematical model

Social distancing can be divided into two categories: spontaneous social distancing adopted by the individuals themselves, and public social distancing promoted by the government. Both types of social distancing have been proved to suppress the spread of infectious disease effectively. While previous studies examined the impact of each social distancing separately, the simultaneous impacts of them are less studied. In this research, we develop a mathematical model to analyze how spontaneous social distancing and public social distancing simultaneously affect the outbreak threshold of an infectious disease with asymptomatic infection. A communication-contact two-layer network is constructed to consider the difference between spontaneous social distancing and public social distancing. Based on link overlap of the two layers, the two-layer network is divided into three subnetworks: communication-only network, contact-only network, and overlapped network. Our results show that public social distancing can significantly increase the outbreak threshold of an infectious disease. To achieve better control effect, the subnetwork of higher infection risk should be more targeted by public social distancing, but the subnetworks of lower infection risk shouldn't be overlooked. The impact of spontaneous social distancing is relatively weak. On the one hand, spontaneous social distancing in the communication-only network has no impact on the outbreak threshold of the infectious disease. On the other hand, the impact of spontaneous social distancing in the overlapped network is highly dependent on the detection of asymptomatic infection sources. Moreover, public social distancing collaborates with infection detection on controlling an infectious disease, but their impacts can't add up perfectly. Besides, public social distancing is slightly less effective than infection detection, because infection detection can also promote spontaneous social distancing.

Network models and the interpretation of prolonged infection plateaus in the COVID19 pandemic

Non-pharmaceutical intervention measures, such as social distancing, have so far been the only means to slow the spread of SARS-CoV-2. In the United States, strict social distancing during the first wave of virus spread has resulted in different types of infection dynamics. In some states, such as New York, extensive infection spread was followed by a pronounced decline of infection levels. In other states, such as California, less infection spread occurred before strict social distancing, and a different pattern was observed. Instead of a pronounced infection decline, a long-lasting plateau is evident, characterized by similar daily new infection levels. Here we show that network models, in which individuals and their social contacts are explicitly tracked, can reproduce the plateau if network connections are cut due to social distancing measures. The reason is that in networks characterized by a 2D spatial structure, infection tends to spread quadratically with time, but as edges are randomly removed, the infection spreads along nearly one-dimensional infection “corridors”, resulting in plateau dynamics. Further, we show that plateau dynamics are observed only if interventions start sufficiently early; late intervention leads to a “peak and decay” pattern. Interestingly, the plateau dynamics are predicted to eventually transition into an infection decline phase without any further increase in social distancing measures. Additionally, the models suggest that a second wave becomes significantly less pronounced if social distancing is only relaxed once the dynamics have transitioned to the decline phase. The network models analyzed here allow us to interpret and reconcile different infection dynamics during social distancing observed in various US states.

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.

Modeling the role of clusters and diffusion in the evolution of COVID-19 infections during lock-down

The dynamics of the spread of epidemics, such as the recent outbreak of the SARS-CoV-2 virus, is highly nonlinear and therefore difficult to predict. As time evolves in the present pandemic, it appears more and more clearly that a clustered dynamics is a key element of the description. This means that the disease rapidly evolves within spatially localized networks, that diffuse and eventually create new clusters. We improve upon the simplest possible compartmental model, the SIR model, by adding an additional compartment associated with the clustered individuals. This sophistication is compatible with more advanced compartmental models and allows, at the lowest level of complexity, to leverage the well-mixedness assumption. The so-obtained SBIR model takes into account the effect of inhomogeneity on epidemic spreading, and compares satisfactorily with results on the pandemic propagation in a number of European countries, during and immediately after lock-down. Especially, the decay exponent of the number of new cases after the first peak of the epidemic is captured without the need to vary the coefficients of the model with time. We show that this decay exponent is directly determined by the diffusion of the ensemble of clustered individuals and can be related to a global reproduction number, that overrides the classical, local reproduction number.

Time dependent correlations between the probability of a node being infected and its centrality measures

Pandemics are a growing world-wide threat for all societies. Throughout history, various infectious diseases presented widely spread damage to human life, economic viability and general well-being. The scale of destruction of the most recent pandemic, COVID-19, has yet to be seen. This work aims to introduce intervention methodology for the prevention of global scale spread of infectious diseases. The proposed method combines time-dependent infection spreading data with the social connectivity structure of the society. SIR model simulations provided the dynamic of contamination spread in different sets of network data. Seven centrality measures parameterized the local and global importance of each node in the underlying network. At each time step the calculated values of the correlations between node infection probability and node centrality values are analyzed. Calculations show that correlations increase at the beginning of infection spread and reaches its highest value when spreading starts to become an epidemic. The peak is at the very early stages of the spreading; and with this analysis, it is possible to predict the node infection probability from time-dependent correlations data.

Modeling the competitive diffusions of rumor and knowledge and the impacts on epidemic spreading

The interaction between epidemic spreading and information diffusion is an interdisciplinary research problem. During an epidemic, people tend to take self-protective measures to reduce the infection risk. However, with the diffusion of rumor, people may be difficult to make an appropriate choice. How to reduce the negative impact of rumor and to control epidemic has become a critical issue in the social network. Elaborate mathematical model is instructive to understand such complex dynamics. In this paper, we develop a two-layer network to model the interaction between the spread of epidemic and the competitive diffusions of information. The results show that knowledge diffusion can eradicate both rumor and epidemic, where the penetration intensity of knowledge into rumor plays a vital role. Specifically, the penetration intensity of knowledge significantly increases the thresholds for rumor and epidemic to break out, even when the self-protective measure is not perfectly effective. But eradicating rumor shouldn't be equated with eradicating epidemic. The epidemic can be eradicated with rumor still diffusing, and the epidemic may keep spreading with rumor being eradicated. Moreover, the communication-layer network structure greatly affects the spread of epidemic in the contact-layer network. When people have more connections in the communication-layer network, the knowledge is more likely to diffuse widely, and the rumor and epidemic can be eradicated more efficiently. When the communication-layer network is sparse, a larger penetration intensity of knowledge into rumor is required to promote the diffusion of knowledge.

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.

The Dynamical Interplay of Collective Attention, Awareness and Epidemics Spreading in the Multiplex Social Networks During COVID-19

Leveraging social and communication technologies, we can digitally observe that the collective attention typically exhibits a heterogeneous structure. It shows that people's interests are organized in clusters around different topics, but the rising of an extraordinary emergency event, as the coronavirus disease epidemics, channels the people's attention into a more homogenized structure, shifting it as triggered by a non-random collective process. The connectedness of networked individuals, on multiple social levels, impacts on the attention, representing a tuning element of different behavioural outcomes, changing the awareness diffusion enough to produce effects on epidemics spreading. We propose a mathematical framework to model the interplay between the collective attention and the co-evolving processes of awareness diffusion, modelled as a social contagion phenomenon, and epidemic spreading on weighted multiplex networks. Our proposed modeling approach structures a systematically understanding as a social network marker of interdependent collective dynamics through the introduction of the multiplex dimension of both networked individuals and topics, quantifying the role of human-related factors, as homophily, network properties, and heterogeneity. We introduce a data-driven approach by integrating different types of data, digitally traced as user-generated data from Twitter and Google Trends, in response to an extraordinary emergency event as coronavirus disease. Our findings demonstrate how the proposed model allows us to quantify the reaction of the collective attention, proving that it can represent a social predictive marker of the awareness dynamics, unveiling the impact on epidemic spreading, for a timely crisis response planning. Simulations results shed light on the coherence between the data-driven approach and the proposed analytical model.

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.

The impact of malicious nodes on the spreading of false information

Increasing empirical evidence in recent years has shown that bots or malicious users in a social network play a critical role in the propagation of false information, while a theoretical modeling of such a problem has been largely ignored. In this paper, applying a simple contagion model, we study the effect of malicious nodes on the spreading of false information by incorporating the smart nodes who perform better than normal nodes in discerning false information. The malicious nodes, however, will always repost (or adopt) the false message as long as they receive it. We show analytically that, for a random distribution of malicious nodes, there is a critical number of malicious nodes above which the false information could outbreak in a random network. We further study three different distribution strategies of selecting malicious nodes for false information spreading. We find that malicious nodes that have large degrees, or are tightly connected, can enhance the spread. However, when they are close to the smart nodes, the spreading of false information can either be promoted or inhibited, depending on the network structure.

The effect of behavior of wearing masks on epidemic dynamics

Recently, COVID-19 has attracted a lot of attention of researchers from different fields. Wearing masks is a frequently adopted precautionary measure. In this paper, we investigate the effect of behavior of wearing masks on epidemic dynamics in the context of COVID-19. At each time, every susceptible individual chooses whether to wear a mask or not in the next time step, which depends on an evaluation of the potential costs and perceived risk of infection. When the cost of infection is high, the majority of the population choose to wear masks, where global awareness plays a significant role. However, if the mask source is limited, global awareness may give rise to a negative result. In this case, more mask source should be allocated to the individuals with high risk of infection.

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.

Multilayer modeling of adoption dynamics in energy demand management

Due to the emergence of new technologies, the whole electricity system is undergoing transformations on a scale and pace never observed before. The decentralization of energy resources and the smart grid have forced utility services to rethink their relationships with customers. Demand response (DR) seeks to adjust the demand for power instead of adjusting the supply. However, DR business models rely on customer participation and can only be effective when large numbers of customers in close geographic vicinity, e.g., connected to the same transformer, opt in. Here, we introduce a model for the dynamics of service adoption on a two-layer multiplex network: the layer of social interactions among customers and the power-grid layer connecting the households. While the adoption process-based on peer-to-peer communication-runs on the social layer, the time-dependent recovery rate of the nodes depends on the states of their neighbors on the power-grid layer, making an infected node surrounded by infectious ones less keen to recover. Numerical simulations of the model on synthetic and real-world networks show that a strong local influence of the customers' actions leads to a discontinuous transition where either none or all the nodes in the network are infected, depending on the infection rate and social pressure to adopt. We find that clusters of early adopters act as points of high local pressure, helping maintaining adopters, and facilitating the eventual adoption of all nodes. This suggests direct marketing strategies on how to efficiently establish and maintain new technologies such as DR schemes.

Effects of asymptomatic infection on the dynamical interplay between behavior and disease transmission in multiplex networks

Multiplex network theory is widely introduced to deepen the understanding of the dynamical interplay between self-protective behavior and epidemic spreading. Most of the existing studies assumed that all infected individuals can transmit disease- related information or can be perceived by their neighbors. However, owing to lack of distinct symptoms for patients in the initial stage of infection, the disease information cannot be transmitted in the population, which may lead to the wrong perception of infection risk and inappropriate behavior response. In this work, we divide infected individuals into Exposed-state (without obvious clinical symptoms) individuals and Infected-state (with evident clinical symptoms) individuals, both of whom can spread disease, but only Infected-state individuals can diffuse disease information. Then, in this work we establish UAU-SEIS (Unaware–Aware–Unaware–Susceptible–Exposed–Infected–Susceptible) model in multiplex networks and analyze the effect of asymptomatic infection and the isolation of Infected-state individuals on the density of infection and the epidemic threshold. Furthermore, we extend the UAU-SEIS model by taking the individual heterogeneity into consideration. Combined Markov chain approach and Monte-Carlo Simulations, we find that asymptomatic infection has an effect on the density of infected individuals and the epidemic threshold, and the extent of the effect is influenced by whether Infected-state individuals are isolated or treated. In addition, results show that the individual heterogeneity can lower the density of infected individuals, but cannot enhance the epidemic threshold.

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We study the impact of asymptomatic infection on the epidemic spread dynamics in multiplex networks.

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We assume infected can be isolation and non isolation, then compare the research results of these two cases.

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We take the individual heterogeneity into consideration and study whether it affect research results.

Epidemics on networks: Reducing disease transmission using health emergency declarations and peer communication

Understanding individual decisions in a world where communications and information move instantly via cell phones and the internet, contributes to the development and implementation of policies aimed at stopping or ameliorating the spread of diseases. In this manuscript, the role of official social network perturbations generated by public health officials to slow down or stop a disease outbreak are studied over distinct classes of static social networks. The dynamics are stochastic in nature with individuals (nodes) being assigned fixed levels of education or wealth. Nodes may change their epidemiological status from susceptible, to infected and to recovered. Most importantly, it is assumed that when the prevalence reaches a pre-determined threshold level,P * , information, called awareness in our framework, starts to spread, a process triggered by public health authorities. Information is assumed to spread over the same static network and whether or not one becomes a temporary informer, is a function of his/her level of education or wealth and epidemiological status. Stochastic simulations show that threshold selectionP * and the value of the average basic reproduction number impact the final epidemic size differentially. For the Erdős-Rényi and Small-world networks, an optimal choice forP * that minimize the final epidemic size can be identified under some conditions while for Scale-free networks this is not case.

The coevolution of contagion and behavior with increasing and decreasing awareness

Understanding the effects of individual awareness on epidemic phenomena is important to comprehend the coevolving system dynamic, to improve forecasting, and to better evaluate the outcome of possible interventions. In previous models of epidemics on social networks, individual awareness has often been approximated as a generic personal trait that depends on social reinforcement, and used to introduce variability in state transition probabilities. A novelty of this work is to assume that individual awareness is a function of several contributing factors pooled together, different by nature and dynamics, and to study it for different epidemic categories. This way, our model still has awareness as the core attribute that may change state transition probabilities. Another contribution is to study positive and negative variations of awareness, in a contagion-behavior model. Imitation is the key mechanism that we model for manipulating awareness, under different network settings and assumptions, in particular regarding the degree of intentionality that individuals may exhibit in spreading an epidemic. Three epidemic categories are considered-disease, addiction, and rumor-to discuss different imitation mechanisms and degree of intentionality. We assume a population with a heterogeneous distribution of awareness and different response mechanisms to information gathered from the network. With simulations, we show the interplay between population and awareness factors producing a distribution of state transition probabilities and analyze how different network and epidemic configurations modify transmission patterns.

The influence of awareness on epidemic spreading on random networks

During an outbreak, the perceived infection risk of an individual affects his/her behavior during an epidemic to lower the risk. We incorporate the awareness of infection risk into the Volz-Miller SIR epidemic model, to study the effect of awareness on disease dynamics. We consider two levels of awareness, the local one represented by the prevalence among the contacts of an individual, and the global one represented by the prevalence in the population. We also consider two possible effects of awareness: reducing infection rate or breaking infectious edges. We use the next generation matrix method to obtain the basic reproduction number of our models, and show that awareness acquired during an epidemic does not affect the basic reproduction number. However, awareness acquired from outbreaks in other regions before the start of the local epidemic reduces the basic reproduction number. Awareness always reduces the final size of an epidemic. Breaking infectious edges causes a larger reduction than reducing the infection rate. If awareness reduces the infection rate, the reduction increases with both local and global awareness. However, if it breaks infectious edges, the reduction may not be monotonic. For the same awareness, the reduction may reach a maximum on some intermediate infection rates. Whether local or global awareness has a larger effect on reducing the final size depends on the network degree distribution and the infection rate.

Epidemic Spread on One-Way Circular-Coupled Networks

Real epidemic spreading networks are often composed of several kinds of complex networks interconnected with each other, such as Lyme disease, and the interrelated networks may have different topologies and epidemic dynamics. Moreover, most human infectious diseases are derived from animals, and zoonotic infections always spread on directed interconnected networks. So, in this article, we consider the epidemic dynamics of zoonotic infections on a unidirectional circular-coupled network. Here, we construct two unidirectional three-layer circular interactive networks, one model has direct contact between interactive networks, the other model describes diseases transmitted through vectors between interactive networks, which are established by introducing the heterogeneous mean-field approach method. Then we obtain the basic reproduction numbers and stability of equilibria of the two models. Through mathematical analysis and numerical simulations, it is found that basic reproduction numbers of the models depend on the infection rates, infection periods, average degrees, and degree ratios. Numerical simulations illustrate and expand these theoretical results very well.

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.

Bifurcation analysis of a network-based SIR epidemic model with saturated treatment function

In this paper, we present a study on a network-based susceptible-infected-recovered (SIR) epidemic model with a saturated treatment function. It is well known that treatment can have a specific effect on the spread of epidemics, and due to the limited resources of treatment, the number of patients during severe disease outbreaks who need to be treated may exceed the treatment capacity. Consequently, the number of patients who receive treatment will reach a saturation level. Thus, we incorporated a saturated treatment function into the model to characterize such a phenomenon. The dynamics of the present model is discussed in this paper. We first obtained a threshold value R₀, which determines the stability of a disease-free equilibrium. Furthermore, we investigated the bifurcation behavior at R₀=1. More specifically, we derived a condition that determines the direction of bifurcation at R₀=1. If the direction is backward, then a stable disease-free equilibrium concurrently exists with a stable endemic equilibrium even though R₀<1. Therefore, in this case, R₀<1 is not sufficient to eradicate the disease from the population. However, if the direction is forward, we find that for a range of parameters, multiple equilibria could exist to the left and right of R₀=1. In this case, the initial infectious invasion must be controlled to a lower level so that the disease dies out or approaches a lower endemic steady state.

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.

Complex contagion leads to complex dynamics in models coupling behaviour and disease

Models coupling behaviour and disease as two unique but interacting contagions have existed since the mid 2000s. In these coupled contagion models, behaviour is typically treated as a 'simple contagion'. However, the means of behaviour spread may in fact be more complex. We develop a family of disease-behaviour coupled contagion compartmental models in order to examine the effect of behavioural contagion type on disease-behaviour dynamics. Coupled contagion models treating behaviour as a simple contagion and a complex contagion are investigated, showing that behavioural contagion type can have a significant impact on dynamics. We find that a simple contagion behaviour leads to simple dynamics, while a complex contagion behaviour supports complex dynamics with the possibility of bistability and periodic orbits.

Interaction between epidemic spread and collective behavior in scale-free networks with community structure

Many real-world networks exhibit community structure: the connections within each community are dense, while connections between communities are sparser. Moreover, there is a common but non-negligible phenomenon, collective behaviors, during the outbreak of epidemics, are induced by the emergence of epidemics and in turn influence the process of epidemic spread. In this paper, we explore the interaction between epidemic spread and collective behavior in scale-free networks with community structure, by constructing a mathematical model that embeds community structure, behavioral evolution and epidemic transmission. In view of the differences among individuals' responses in different communities to epidemics, we use nonidentical functions to describe the inherent dynamics of individuals. In practice, with the progress of epidemics, individual behaviors in different communities may tend to cluster synchronization, which is indicated by the analysis of our model. By using comparison principle and Gers˘gorin theorem, we investigate the epidemic threshold of the model. By constructing an appropriate Lyapunov function, we present the stability analysis of behavioral evolution and epidemic dynamics. Some numerical simulations are performed to illustrate and complement our theoretical results. It is expected that our work can deepen the understanding of interaction between cluster synchronization and epidemic dynamics in scale-free community networks.

Effect of time varying transmission rates on the coupled dynamics of epidemic and awareness over a multiplex network

A non-linear stochastic model is presented to study the effect of time variation of transmission rates on the co-evolution of epidemics and its corresponding awareness over a two layered multiplex network. In the model, the infection transmission rate of a given node in the epidemic layer depends upon its awareness probability in the awareness layer. Similarly, the infection information transmission rate of a node in the awareness layer depends upon its infection probability in the epidemic layer. The spread of disease resulting from physical contacts is described in terms of a Susceptible Infected Susceptible process over the epidemic layer and the spread of information about the disease outbreak is described in terms of an Unaware Aware Unaware process over the virtual interaction mediated awareness layer. The time variation of the transmission rates and the resulting co-evolution of these mutually competing processes are studied in terms of a network topology dependent parameter ( α ). Using a second order linear theory, it is shown that in the continuous time limit, the co-evolution of these processes can be described in terms of damped and driven harmonic oscillator equations. From the results of a Monte-Carlo simulation, it is shown that for a suitable choice of the parameter ( α ) , the two processes can either exhibit sustained oscillatory or damped dynamics. The damped dynamics corresponds to the endemic state. Furthermore, for the case of an endemic state, it is shown that the inclusion of the awareness layer significantly lowers the disease transmission rate and reduces the size of the epidemic. The infection probability of the nodes in the endemic state is found to have a dependence on both the transmission rates and on their absolute degrees in each of the network layers and on the relative differences between their degrees in the respective layers.

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.

Coupling dynamics of epidemic spreading and information diffusion on complex networks

The interaction between disease and disease information on complex networks has facilitated an interdisciplinary research area. When a disease begins to spread in the population, the corresponding information would also be transmitted among individuals, which in turn influence the spreading pattern of the disease. In this paper, firstly, we analyze the propagation of two representative diseases (H7N9 and Dengue fever) in the real-world population and their corresponding information on Internet, suggesting the high correlation of the two-type dynamical processes. Secondly, inspired by empirical analyses, we propose a nonlinear model to further interpret the coupling effect based on the SIS (Susceptible-Infected-Susceptible) model. Both simulation results and theoretical analysis show that a high prevalence of epidemic will lead to a slow information decay, consequently resulting in a high infected level, which shall in turn prevent the epidemic spreading. Finally, further theoretical analysis demonstrates that a multi-outbreak phenomenon emerges via the effect of coupling dynamics, which finds good agreement with empirical results. This work may shed light on the in-depth understanding of the interplay between the dynamics of epidemic spreading and information diffusion.

Lumping of degree-based mean-field and pair-approximation equations for multistate contact processes

Contact processes form a large and highly interesting class of dynamic processes on networks, including epidemic and information-spreading networks. While devising stochastic models of such processes is relatively easy, analyzing them is very challenging from a computational point of view, particularly for large networks appearing in real applications. One strategy to reduce the complexity of their analysis is to rely on approximations, often in terms of a set of differential equations capturing the evolution of a random node, distinguishing nodes with different topological contexts (i.e., different degrees of different neighborhoods), such as degree-based mean-field (DBMF), approximate-master-equation (AME), or pair-approximation (PA) approaches. The number of differential equations so obtained is typically proportional to the maximum degree k_{max} of the network, which is much smaller than the size of the master equation of the underlying stochastic model, yet numerically solving these equations can still be problematic for large k_{max}. In this paper, we consider AME and PA, extended to cope with multiple local states, and we provide an aggregation procedure that clusters together nodes having similar degrees, treating those in the same cluster as indistinguishable, thus reducing the number of equations while preserving an accurate description of global observables of interest. We also provide an automatic way to build such equations and to identify a small number of degree clusters that give accurate results. The method is tested on several case studies, where it shows a high level of compression and a reduction of computational time of several orders of magnitude for large networks, with minimal loss in accuracy.