Microscopic Markov Chain Approach Research Articles

A new model of the impact of information dissemination with emotional responses on disease transmission in multilayer networks

During disease transmission, the dissemination of information about the disease prompts safety concerns among individuals. Individuals’ various emotional responses to information may affect infection prevention measures and, consequently, disease transmission. In this paper, we propose a new coupled information and disease transmission model with emotional factors in multiplex networks. Our specific focus is on the impact of diverse emotional responses on the dynamics process. We employ the Microscopic Markov Chain Approach (MMCA) to analyze the model, and obtaining state transfer equations, and deriving the disease transmission threshold. Extensive numerical simulations show that dissemination of information by relevant authorities motivates individuals to adopt scientific self-protective behaviors, thus helping to control disease transmission. Furthermore, individuals who have different emotional responses after obtaining information have varying effects on disease transmission, and reducing the anxiety response or increasing the calm response of individuals can more effectively decrease the scale of disease transmission and increase the disease transmission threshold. In summary, improving the quality of information released by the emergency management department, reducing the individual’s anxiety response, and encouraging the adoption of positive and effective protective measures are of paramount importance for epidemic prevention and control.

Probabilistic Discrete‐Time Models for Spreading Processes in Complex Networks: A Review

AbstractResearch into network dynamics of spreading processes typically employs both discrete and continuous time methodologies. Although each approach offers distinct insights, integrating them can be challenging, particularly when maintaining coherence across different time scales. This review focuses on the Microscopic Markov Chain Approach (MMCA), a probabilistic f ramework originally designed for epidemic modeling. MMCA uses discrete dynamics to compute the probabilities of individuals transitioning between epidemiological states. By treating each time step—usually a day—as a discrete event, the approach captures multiple concurrent changes within this time frame. The approach allows to estimate the likelihood of individuals or populations being in specific states, which correspond to distinct epidemiological compartments. This review synthesizes key findings from the application of this approach, providing a comprehensive overview of its utility in understanding epidemic spread.

The coupled dynamics of information-behavior-epidemic propagation considering the heterogeneity of adoption thresholds and network structures in multiplex networks

During epidemics, individual responses to prevention and control information vary significantly, affecting the execution of preventive measures. This paper introduces a novel model to analyze the co-evolution of the information-behavior-epidemic dynamic, accounting for the heterogeneity in individual behavioral adoption thresholds and network structures. The model consists of three layers: the upper layer, utilizing scale-free social networks to represent the diffusion of information; the middle and lower layers, employing community networks, to illustrate individuals’ decision-making and epidemic transmission processes, respectively. We applied the Heaviside step function to depict the effects of information and local environmental factors on individuals’ decisions. Through the microscopic Markov chain approach (MMCA), we determined the epidemic threshold. Our methodology also included extensive Monte Carlo (MC) simulations to validate our theoretical predictions. Our results reveal several key insights: (i) reducing community mobility and the threshold for adopting preventive behaviors can significantly restrain the scale of the epidemic and delay outbreaks; (ii) the level of individual activity in the physical contact network has a significant influence on epidemic transmission; (iii) integrating individuals’ behavior adoption thresholds induces a two-stage phase change, deviating from the continuous phase transition typically observed in epidemic transmission.

Coupled Simultaneous Evolution of Policy, Enterprise Innovation Awareness, and Technology Diffusion in Multiplex Networks

This study comprehensively examines the coupling effect of government policies, enterprise behavior, and existing technology on the diffusion of innovative technology. Utilizing multiplex network theory, a multiplex network model is constructed to couple policy incentives, enterprise innovation consciousness, and technology diffusion. Both global- and local-order parameters are introduced to characterize the interaction mechanisms between new and old technologies. By employing the microscopic Markov chain approach (MMCA), the threshold for technology diffusion is derived, theoretically revealing the mechanisms behind the diffusion of innovative technology. Considering the heterogeneity of enterprises, a numerical simulation is conducted on a scale-free network. The results indicate that, as the intensity of policy incentives increases, the threshold for technology diffusion decreases, promoting the spread of innovative technology. Additionally, the coupling relationship between existing technology and innovative technology influences the diffusion scale of the latter. The innovation behavior of enterprises further facilitates the adoption and dissemination of innovative technology.

Impact of message fatigue in information-disease coupled dynamics on temporal simplicial networks

During information diffusion, individuals typically experience fatigue and mental exhaustion due to repeated exposure to similar information, which is a state called message fatigue. To address message fatigue in information diffusion and group interactions, we developed a novel coupled information-disease spreading model within the framework of multiplex temporal networks. Here, the information network simulates the process of disease-related information diffusion using a temporal simplicial network. Furthermore, we utilize a threshold model to characterize the effects of message fatigue. We describe the dynamic evolutionary equations of the model by the microscopic Markov chain (MMC) approach to determine the epidemic threshold. We also validated the proposed model using a number of Monte Carlo (MC) simulations. The experimental results of the MC simulations and MMC theoretical results are in good agreement. Our research has shown that message fatigue can lead to a two-stage change in the information-disease coupled spreading. Raising the threshold for message fatigue and preventing a large number of individuals from experiencing it can help inhibit the disease spreading. In short, excessive publicizing of related-disease information can backfire. The results can facilitate us to accurately capture the spreading characteristics of real-world diseases.

Research on the Propagation Model of Unsafe Behaviors among Construction Workers Based on a Two-Layer NAN-SIRS Network

Unsafe behaviors among construction workers are a leading cause of safety accidents in the construction industry, and studying the mechanism of unsafe behavior propagation among construction workers is essential for reducing the occurrence of safety accidents. Safety attitude plays a pivotal role in predicting workers’ behavioral intentions. We propose a propagation model of unsafe behaviors based on a two-layer complex network, in which the upper layer depicts the change in construction workers’ safety attitudes, and the lower layer represents the propagation of unsafe behaviors. In this model, we consider the impact of individual heterogeneity and herd mentality on the transmission rate, establishing a partial mapping relationship based on behavioral feedback. After that, by building a probability transition tree, we establish the risk state transition equation in detail using the microscopic Markov chain approach (MMCA) and analyze the established equations to deduce the propagation threshold of unsafe behaviors analytically. The results show that enhancing the influence of individual heterogeneity and behavioral feedback increases the threshold for the spread of unsafe behaviors, thereby reducing its scale, while herd mentality amplifies the spread. Furthermore, the coexistence of safety education and behavioral feedback may lead to one of the mechanisms fails. This research enhances understanding of the propagation mechanism of unsafe behaviors and provides a foundation for managers to implement effective measures to suppress the propagation of unsafe behaviors among construction workers.

Personnel staffing and scheduling during disease outbreaks: A contact network-based analysis

Personnel scheduling in organizations can be disrupted by unforeseen events that require efficient planning. A recent example is the COVID-19 pandemic that disrupted global operations, compromising people’s health and safety. Many organizations were forced to transition to full remote work to prevent the spread of the virus and ensure employee safety. Although working entirely remotely is effective for some organizations, others must balance workplace occupancy and infection risk to keep their operations functioning efficiently despite a global health crisis. We address this issue by developing a days-off scheduling model that captures employees’ interactions through the underlying contact network. To solve the problem, we propose a Mixed Integer Linear Programming model considering a Microscopic Markov Chain Approach to determine the probability of infection in a contact network that mimics the employees’ interactions. The model determines, during a given planning period, the optimal staffing mix to maximize occupancy while minimizing the risk of infection in the presence of testing protocols. We conduct sensitivity analysis to assess the approach’s robustness while considering different contact networks and testing strategies. Through extensive computational analysis, we show that the degree of contact among employees is not the sole factor to consider when defining personnel scheduling policies during disease outbreaks. The decision-maker must balance the employee allocation with tailored testing interventions based on management’s priorities to mitigate the effects while ensuring the desired occupancy at a lower risk.

Multi-information and epidemic coupling propagation considering indirect contact on two-layer networks

This research provides an in-depth examination of the interplay between diverse information propagation and epidemic spread within a two-layer network, placing particular emphasis on the implications of both direct and indirect modes of disease transmission. Individuals are categorized based on their susceptibility to and their capacity for disease propagation, while the influence of varying infection rates on epidemic expansion is investigated. Information is bifurcated into constructive narratives with beneficial outcomes, and detrimental narratives originating from rumors. The method of information dispersion incorporates considerations such as herd behavior, preventative costs, and individual risk perception. Utilizing the Microscopic Markov Chain Approach (MMCA), a dynamic equation is formulated to delineate epidemic propagation and the epidemic threshold for the proposed model is calculated. Results demonstrate that promoting swift dissemination of positive information, concurrently with curbing the spread of negative narratives, can appreciably mitigate epidemic proliferation. The findings also imply that facilitating access to beneficial information, minimizing the consequences of harmful narratives, decreasing prevention-related expenses, and enhancing personal risk perception can significantly reduce the ultimate magnitude of the epidemic. Notably, the study reveals that indirect contact can considerably augment epidemic spread. As the infection rate via indirect contact escalities, the extent of epidemic transmission broadens and the threshold for epidemic transmission diminishes.

The correlation between independent edge and triangle degrees promote the explosive information spreading

In recent years, a novel phenomenon of explosive information spreading has been observed in the simplicial configuration model under the higher-order interactions, where a discontinuous transition exists. The model usually considers that the independent edge degree (i.e., the number of single edges attached to a node excluding those belonging to the triangles) and triangle degree (i.e., the number of triangles connected to a node) are uncorrelated. However, whether these degrees correlation exist in real networks and induce the explosive transition of information spreading at higher-order interactions is not very clear. Based on the real social networks data analysis, we find that the triangle degree increases with the independent edge degree approximatively as a power law, indicating a positive correlation between them. To understand how these correlations affect the spreading dynamics, we use an information-spreading model with higher-order interactions on synthetic networks and control the correlated strength of these degrees. Interestingly, our results reveal that the correlated structure would accelerate the information spreading with a fast-spreading speed. In addition, we uncover that the higher-order interactions will induce a discontinuous transition and that there is a bistable region with healthy and endemic states co-existing. Further, we discover that a highly correlated independent edge and triangle degrees will reduce the spreading threshold, which means the correlated structure promotes explosive information spreading. Finally, we utilize the microscopic Markov chain approach(MMCA) to explain the simulations. Our findings may shed some light on understanding the fast-spreading phenomenon of information in real life.

Impact of multiple doses of vaccination on epidemiological spread in multiple networks

Epidemic spread is frequently accompanied by the diffusion of information, prompting individuals to adopt preventive measures, including home quarantine, vaccination, and wearing masks. The interplay spreading processes present significant challenges in studying the mechanisms of epidemic infectious diseases and the prevention and control of public health emergencies. Therefore, this paper incorporates the impact of government encouragement of multiple doses of vaccination on the evolutionary process of epidemic propagation, and investigates the interplay between the epidemic spreading and the diffusion of awareness in multiplex networks. The microscopic Markov chain approach is utilized to derive evolutionary equations for various states and capture an epidemic spread threshold, they are consistent with simulation results. Numerical results indicate that intensifying vaccination efforts and enhancing vaccine efficacy can effectively mitigate the magnitude of epidemic spreading and delay the disease outbreak threshold. It is worth noting that receiving multiple vaccine doses significantly reduces the magnitude of epidemic spreading compared to receiving a single dose. Therefore, increasing vaccine coverage, enhancing vaccine efficacy, and administering multiple vaccine doses can effectively mitigate the spread of epidemics in real-world scenarios.

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.

Epidemic spreading with an awareness-based adaptive mechanism in temporal multiplex networks

Social interaction, which is intricate and time-varying, has emerged as a pivotal consideration in epidemic spreading. In this paper, we devise a UAU–SIS model for simulating awareness diffusion and epidemic spreading on temporal multiplex networks. Drawing inspiration from individuals’ self-protection behaviors, a novel adaptive update mechanism is developed. To provide a more precise representation of the collective social interactions encompassing individuals, we introduce the higher-order network structure encompassing temporal variability. Building upon the established framework of the microscopic Markov chain approach (MMCA) for static networks, we extend its applicability to the condition of temporal networks and derive the threshold within the coupled dynamics. Our extensive simulations illuminate the dual role of awareness in epidemic mitigation. Beyond solely diminishing infection probabilities through self-protective measures, individual awareness additionally facilitates to change the network structure to separate them from the infected. By elucidating these fundamental characteristics, our research contributes to advancing more effective strategies for epidemic mitigation and containment.

Coupled Propagation Dynamics of Information and Infectious Disease on Two-Layer Complex Networks with Simplices

The mutual influence between information and infectious diseases during the spreading process is becoming increasingly prominent. To elucidate the impact of factors such as higher-order interactions, interpersonal distances, and asymptomatic carriers on the coupled propagation of information and infectious diseases, a novel coupled spreading model is constructed based on a two-layer complex network, where one layer is a higher-order network and another layer is a weighted network. The higher-order interactions in information propagation are characterized using a 2-simplex, and a sUARU (simplicial unaware-aware-removed-unaware) model is employed to articulate information propagation. The inter-individual social distances in disease propagation are represented by the weights of a weighted network, and an SEIS (susceptible-exposed-infected-susceptible) model is utilized to describe disease propagation. The dynamic equations of coupled spreading are formulated utilizing the microscopic Markov chain approach. An analytical expression for the epidemic threshold is obtained by deriving it from the steady-state form of the dynamic equations. Comprehensive simulations are conducted to scrutinize the dynamic characteristics of the coupled spreading model. The findings indicate that enhancing the effects of higher-order interactions in information propagation and increasing inter-individual social distances both lead to higher outbreak thresholds and greater spreading of diseases. Additionally, a stronger infectivity among asymptomatic carriers and an extended incubation period are favorable for the outbreak and spread of an epidemic. These findings can provide meaningful guidance for the prevention and control of real-world epidemics.

Dynamics of information diffusion and disease transmission in time-varying multiplex networks with asymmetric activity levels

While the interaction between information and disease in static networks has been extensively investigated, many studies have ignored the characteristics of network evolution. In this study, we construct a new two-layer coupling model to explore the interactions between information and disease. The upper layer describes the diffusion of disease-related information, and the lower layer represents the disease transmission. We then use power-law distributions to examine the influence of asymmetric activity levels on dynamic propagation, revealing a mapping relationship characterizing the interconnected propagation of information and diseases among partial nodes within the network. Subsequently, we derive the disease outbreak threshold by using the microscopic Markov-chain approach (MMCA). Finally, we perform extensive Monte Carlo (MC) numerical simulations to verify the accuracy of our theoretical results. Our findings indicate that the activity levels of individuals in the disease transmission layer have a more significant influence on disease transmission compared with the individual activity levels in the information diffusion layer. Moreover, reducing the damping factor can delay disease outbreaks and suppress disease transmission, while improving individual quarantine measures can contribute positively to disease control. This study provides valuable insights into policymakers for developing outbreak prevention and control strategies.

Coupled dynamics of endemic disease transmission and gradual awareness diffusion in multiplex networks

Understanding the interplay between human behavioral phenomena and infectious disease dynamics has been one of the central challenges of mathematical epidemiology. However, socio-cognitive processes critical for the initiation of desired behavioral responses during an outbreak have often been neglected or oversimplified in earlier models. Combining the microscopic Markov chain approach with the law of total probability, we herein institute a mathematical model describing the dynamic interplay between stage-based progression of awareness diffusion and endemic disease transmission in multiplex networks. We analytically derived the epidemic thresholds for both discrete-time and continuous-time versions of our model, and we numerically demonstrated the accuracy of our analytic arguments in capturing the time course and the steady state of the coupled disease-awareness dynamics. We found that our model is exact for arbitrary unclustered multiplex networks, outperforming a widely adopted probability-tree-based method, both in the prediction of the time-evolution of a contagion and in the final epidemic size. Our findings show that informing the unaware individuals about the circulating disease will not be sufficient for the prevention of an outbreak unless the distributed information triggers strong awareness of infection risks with adequate protective measures, and that the immunity of highly-aware individuals can elevate the epidemic threshold, but only if the rate of transition from weak to strong awareness is sufficiently high. Our study thus reveals that awareness diffusion and other behavioral parameters can nontrivially interact when producing their effects on epidemiological dynamics of an infectious disease, suggesting that future public health measures should not ignore this complex behavioral interplay and its influence on contagion transmission in multilayered networked systems.

Nonlinear effect of sentiments and opinion sharing on vaccination decision in face of an outbreak: A multiplex network approach

The formation and sharing of opinions greatly influenced recent COVID vaccinations. There were many vaccine-related discussions on various social media platforms, including Twitter, Facebook, and Instagram, which affected immunization uptake. Individuals’ attitudes towards vaccinations influenced how disease spread and epidemics evolved, as communities may hold different views on the risks and benefits of vaccines. We explore this complex interaction and feedback between opinions and vaccination by constructing a vaccination behavior model on a two-layer multiplex network, where the upper layer describes sharing opinions about vaccines and the other layer follows a SIR framework to track disease spread and its dynamics. Coupled opinion sharing of vaccine and disease transmission yields synergistic interactions with each other. We deployed a Microscopic Markov Chain approach to compute the epidemic threshold and showed that it is much higher compared to a case when there is no opinion sharing or formation. We show that opinion sharing has a significant impact on vaccine coverage and disease prevalence, but that depends on the efficacy of vaccination. Furthermore, negative and positive opinions about vaccination differ in weight, which affects their spread. Network topology also plays a significant role in escalating infections in the network population. Our model demonstrates that heterogeneity in population awareness plays a critical role in vaccine uptake and disease propagation. This multiplex disease-opinion model also exhibits a similar qualitative description of the data as the empirical vaccine uptake and tweet dynamics under specific parameter regimes and settings. Our investigation is helpful for public health policymakers in designing vaccination strategies in a heterogeneous population, as opinion sharing is a very common feature in the current era of technological evolution.

SHI1I2R competitive information spreading model in online and offline two-layer networks in emergencies

Previous research on information propagation has primarily focused on either online social networks or offline social networks. Additionally, there remains a gap in understanding the propagation of competitive information in emergency scenarios. This paper introduces an SHI1I2R information spreading model to investigate the dynamics of competitive information dissemination and interactions in online and offline two-layer networks during emergencies. To enhance the accuracy of information propagation modeling, we depart from the conventional assumption of constant spreading and decay rates and instead propose nonlinear spreading and interest decay rates within the SHI1I2R model. Employing a microscopic Markov chain approach, we conduct theoretical analysis and derive the spreading threshold of information in two-layer networks. Subsequently, we perform numerical simulations to validate the effectiveness of the SHI1I2R model and explore the factors influencing information propagation. Our findings indicate that information spreads more rapidly and extensively in two-layer networks compared to one-layer networks. Furthermore, the final scale of information dissemination and the speed of propagation follow the order: random network > small-world network > scale-free network > regular network.

The impact of individual behavioral adoption heterogeneity on epidemic transmission in multiplex networks

Abstract In recent years, the impact of information diffusion and individual behavior adoption patterns on epidemic transmission in complex networks has received significant attention. In the immunization behavior adoption process, different individuals often make behavioral decisions in different ways, and it is of good practical importance to study the influence of individual heterogeneity on the behavior adoption process. In this paper, we propose a three-layer coupled model to analyze the co-evolution process of official information diffusion, immunization behavior adoption and epidemic transmission in multiplex networks, which focuses on the individual heterogeneity on adoption behavior patterns. Specifically, we investigate the impact of the credibility of social media and the risk sensitivity of the population on behavioral adoption, in further study of the effect of behavioral adoption heterogeneity on epidemic transmission. Then we use the microscopic Markov chain approach (MMCA) to describe the dynamics process and capture the evolution of the epidemic threshold. Finally, we conduct extensive simulations to prove our findings. Our results suggest that enhancing the credibility of social media can raise the epidemic transmission threshold, it is effective to control the epidemic transmission during the dynamic process. In addition, improving an individual's risk sensitivity and thus taking effective protective measures can also reduce the size of the infected individuals and delay the epidemic outbreak. Our study explores the role of individual heterogeneity in behavioral adoption in real networks, more clearly models the credibility of social media and risk sensitivity of the population on the epidemic transmission dynamic, and provides a useful reference for managers to formulate epidemic control and prevention policies.

Capturing COVID-19 spread and interplay with multi-hop contact tracing intervention.

A preemptive multi-hop contact tracing scheme that tracks not only the direct contacts of those who tested positive for COVID-19, but also secondary or tertiary contacts has been proposed and deployed in practice with some success. We propose a mathematical methodology for evaluating this preemptive contact tracing strategy that combines the contact tracing dynamics and the virus transmission mechanism in a single framework using microscopic Markov Chain approach (MMCA). We perform Monte Carlo (MC) simulations to validate our model and show that the output of our model provides a reasonable match with the result of MC simulations. Utilizing the formulation under a human contact network generated from real-world data, we show that the cost-benefit tradeoff can be significantly enhanced through an implementation of the multi-hop contact tracing as compared to traditional contact tracing. We further shed light on the mechanisms behind the effectiveness of the multi-hop testing strategy using the framework. We show that our mathematical framework allows significantly faster computation of key attributes for multi-hop contact tracing as compared to MC simulations. This in turn enables the investigation of these attributes for large contact networks, and constitutes a significant strength of our approach as the contact networks that arise in practice are typically large.

Study on the interaction between information dissemination and infectious disease dissemination under government prevention and management

In recent years, public health emergencies have occurred frequently around the world, and infectious diseases are one of the most destructive and influential events. The coupling effect between infectious disease transmission and information dissemination has been a research hotspot that scholars have focused on in recent years. Analyzing how to effectively prevent the impact of information dissemination on the process of infectious disease transmission from the perspective of government prevention and control has important theoretical significance. Firstly, this paper investigates the COVID-19 epidemic and establishes a coupled multi-channel network UFAT-SEIR transmission model under government prevention and management based on the characteristics of infectious disease transmission and information transmission. Considering the individual's ability to recognize information, the interaction between false information and real information, and the impact of group polarization, the step function is used to explore the results of the user's information decision-making process. Secondly, the microscopic Markov chain approach (MMCA) is constructed to derive the transmission threshold of infectious diseases related to the information transmission layer. Finally, simulation is performed based on the impact of government prevention and management actions on parameters. The research findings can provide relevant strategies and suggestions for the government to prevent and control the spread of infectious diseases.