Susceptible-infected-recovered Research Articles

SIR epidemics in interconnected networks: threshold curve and phase transition

AbstractFor simplicity of mathematical modeling of epidemic spreading, the assumption is that hosts have identical rates of disease-causing contacts. However, in the real world, the scenario is different. The network-based framework allows us to capture the complex interdependencies and structural heterogeneity present in real-world systems. We examine two distinct scenarios involving the dynamics of susceptible-infected-recovered (SIR) in interconnected networks. In the first part, we show how the epidemic threshold of a contact network changes as a result of being coupled with another network for a fixed infection strength. The model employed in this work considers both the contact networks and interconnections as generic. We have depicted the epidemic threshold curve for interconnected networks, considering the assumption that the infection could be initially present in either one or both of the networks. If the normalized infection strengths are above the threshold curve, the infection spreads, whereas if the normalized infection strengths are below the threshold curve, the disease does not spread. This is true for any level of interconnection. In the second part, we investigate the spillover phenomenon, where the disease in a novel host population network comes from a reservoir network. We have observed a clear phase transition when the number of links or the inter-network infection rate exceeds a certain threshold, keeping all other parameters constant. We observe two regimes for spillover: a major spillover region and a minor spillover region based on interpopulation links (fraction of links between two networks) and inter-network infection strength (infection rate between reservoir and host network). If the interpopulation links and inter-network infection strength are in the major spillover region, the spillover probability is high, while if the former parameters are in the minor spillover region, the spillover probability is low. When the number of infected individuals within a reservoir network is nearly equal, and the inter-network infection strength remains constant, the threshold number of links required to achieve the spillover threshold condition varies based on the network topology. Overall, this work contributes to the understanding of SIR dynamics in interconnected networks and sheds light on the behavior of epidemics in complex systems.

Effects of Intervention Timing on Health-Related Fake News: Simulation Study.

Fake health-related news has spread rapidly through the internet, causing harm to individuals and society. Despite interventions, a fenbendazole scandal recently spread among patients with lung cancer in South Korea. It is crucial to intervene appropriately to prevent the spread of fake news. This study investigated the appropriate timing of interventions to minimize the side effects of fake news. A simulation was conducted using the susceptible-infected-recovered (SIR) model, which is a representative model of the virus spread mechanism. We applied this model to the fake news spread mechanism. The parameters were set similarly to those in the digital environment, where the fenbendazole scandal occurred. NetLogo, an agent-based model, was used as the analytical tool. Fake news lasted 278 days in the absence of interventions. As a result of adjusting and analyzing the timing of the intervention in response to the fenbendazole scandal, we found that faster intervention leads to a shorter duration of fake news (intervention at 54 days = fake news that lasted for 210 days; intervention at 16 days = fake news that lasted for 187 days; and intervention at 10 days = fake news that lasted for 157 days). However, no significant differences were observed when the intervention was performed within 10 days. Interventions implemented within 10 days were effective in reducing the duration of the spread of fake news. Our findings suggest that timely intervention is critical for preventing the spread of fake news in the digital environment. Additionally, a monitoring system that can detect fake news should be developed for a rapid response.

MULTI-AGENT SIMULATION MODEL OF INFECTIOUS DISEASE SPREAD

The aim of the research is to develop a multi-agent simulation model for predicting the spread of infectious diseases, particularly COVID-19. In the context of the COVID-19 pandemic, there emerged an urgent need to create tools for forecasting and analyzing the dynamics of epidemics, as well as for evaluating the effectiveness of management decisions. The use of mathematical models in this process allows for an adequate description of the infection spread dynamics, which is essential for making informed decisions. The article discusses traditional approaches to epidemic modeling, such as the predator-prey model and the compartmental SIR (Susceptible-Infectious-Recovered) model. The predator-prey model describes the interaction between two species in an ecosystem using differential equations, which allows for modeling population dynamics. The compartmental SIR model divides the population into three groups: susceptible, infected, and recovered, which enables the analysis of the spread of infectious diseases. However, these models have limitations, particularly due to assumptions about population homogeneity and constant parameters. To more accurately model complex epidemic processes, a multi-agent simulation model was developed. In this model, agents interact within a defined area, mimicking real conditions of infection spread. Agents are divided into three classes: healthy, infected, and recovered. The movement of agents is modeled using random walk in a two-dimensional space, taking into account the possibility of contact between them, which can lead to infection. Infected agents transition to the recovered class after a certain period of illness and can no longer be infected. Modeling results showed that the multi-agent model allows for more accurate prediction of infection spread dynamics. Numerous experiments were conducted, demonstrating the model's adequacy in replicating the infection process, peak infection rates, and recovery periods. The influence of various parameters, such as the duration of illness, on the epidemic dynamics was investigated. The obtained results confirm that considering individual characteristics and behavioral traits of agents improves the accuracy of modeling. This allows the multi-agent simulation model to be used for developing effective control strategies and predicting the spread of infectious diseases, which can be useful for making management decisions in real pandemic conditions.

Interdisciplinary applications of finite group theory - From epidemic modeling to financial market analysis

Finite group theory has a long history. Many mathematicians have done researches on it. As time goes on, it becomes a useful tool for human as it has a lot of applications. Finite group theory becomes more than just mathematical. As a result, its applications on epidemic modeling and financial market analysis are introduced respectively. These focus on SIR (Susceptible-Infective-Recovered) model and stock markets. Whats more, there are some other applications in different areas. What we came to the conclusion is that wired groups have developed in many fields, not only in financial markets and infectious disease models, but also in many other fundamental disciplines, chemistry, physics, computer science. They are going to be showed in the following essay.

Passive and active field theories for disease spreading

The worldwide COVID-19 pandemic has led to a significant growth of interest in the development of mathematical models that allow to describe effects such as social distancing measures, the development of vaccines, and mutations. Several of these models are based on concepts from soft matter theory. Considerably less well investigated is the reverse direction, i.e. how results from epidemiological research can be of interest for the physics of colloids and polymers. In this work, we consider the susceptible-infected-recovered (SIR)-dynamical density functional theory (DDFT) model, a combination of the SIR model from epidemiology with DDFT from nonequilibrium soft matter physics, which allows for an explicit modeling of social distancing. We extend the SIR-DDFT model both from an epidemiological perspective by incorporating vaccines, asymptomaticity, reinfections, and mutations, and from a soft matter perspective by incorporating noise and self-propulsion and by deriving a phase field crystal (PFC) model that allows for a simplified description. On this basis, we investigate via computer simulations how epidemiological models are affected by the presence of non-reciprocal interactions. This is done in a numerical study of a zombie outbreak.

The futility of being selfish in vaccine distribution

We study vaccine budget-sharing strategies in the SIR (Susceptible-Infected-Recovered) model given a structured community network to investigate the benefit of sharing vaccine across communities. The network studied comprises two communities, one of which controls vaccine budget and may share it with the other. Different scenarios are considered regarding the connectivity between communities, infection rates and the unvaccinated fraction of the population. Properties of the SIR model facilitates the use of dynamic message passing (DMP) and optimal control methods to investigate preventive and reactive budget-sharing scenarios. Our results show a large set of budget-sharing strategies in which the sharing community benefits from the reduced global infection rates with no detrimental impact on its local infection rate.

Estimating Cross-Border Mobility from the Difference in Peak Timing: A Case Study of Poland–Germany Border Regions

Human mobility contributes to the fast spatiotemporal propagation of infectious diseases. During an outbreak, monitoring the infection on either side of an international border is crucial as cross-border migration increases the risk of disease importation. Due to the unavailability of cross-border mobility data, mainly during pandemics, it becomes difficult to propose reliable, model-based strategies. In this study, we propose a method for estimating commuting-type cross-border mobility flux between any pair of regions that share an international border from the observed difference in their infection peak timings. Assuming the underlying disease dynamics are governed by a Susceptible–Infected–Recovered (SIR) model, we employ stochastic simulations to obtain the maximum likelihood cross-border mobility estimate for any pair of regions. We then investigate how the estimate of cross-border mobility flux varies depending on the transmission rate. We further show that the uncertainty in the estimates decreases for higher transmission rates and larger observed differences in peak timing. Finally, as a case study, we apply the method to some selected regions along the Poland–Germany border that are directly connected through multiple modes of transportation and quantify the cross-border fluxes from the COVID-19 cases data from 20 February to 20 June 2021.

Impact of navigation apps on congestion and spread dynamics on a transportation network

In recent years, the widespread adoption of navigation apps by motorists has raised questions about their impact on local traffic patterns. Users increasingly rely on these apps to find better, real-time routes to minimize travel time. This study uses microscopic traffic simulations to examine the connection between navigation app use and traffic congestion. The research incorporates both static and dynamic routing to model user behavior. Dynamic routing represents motorists who actively adjust their routes based on app guidance during trips, while static routing models users who stick to known fastest paths. Key traffic metrics, including flow, density, speed, travel time, delay time, and queue lengths, are assessed to evaluate the outcomes. Additionally, we explore congestion propagation at various levels of navigation app adoption. To understand congestion dynamics, we apply a susceptible–infected–recovered (SIR) model, commonly used in disease spread studies. Our findings reveal that traffic system performance improves when 30–60% of users follow dynamic routing. The SIR model supports these findings, highlighting the most efficient congestion propagation-to-dissipation ratio when 40% of users adopt dynamic routing, as indicated by the lowest basic reproductive number. This research provides valuable insights into the intricate relationship between navigation apps and traffic congestion, with implications for transportation planning and management.

Nearly Instantaneous Time-Varying Reproduction Number for Contagious Diseases-a Direct Approach Based on Nonlinear Regression.

While the world recovers from the COVID-19 pandemic, another outbreak of contagious disease remains the most likely future risk to public safety. Now is therefore the time to equip health authorities with effective tools to ensure they are operationally prepared for future events. We propose a direct approach to obtain reliable nearly instantaneous time-varying reproduction numbers for contagious diseases, using only the number of infected individuals as input and utilisingthe dynamics of the susceptible-infected-recovered (SIR) model. Our approach is based on a multivariate nonlinear regression model simultaneously assessing parameters describing the transmission and recovery rate as a function of the SIR model. Shortly after start of a pandemic, our approach enables estimation of daily reproduction numbers. It avoids numerous sources of additional variation and provides a generic tool for monitoring the instantaneous reproduction numbers. We use Norwegian COVID-19 data as case study and demonstrate that our results are well aligned with changes in the number of infected individuals and the change points following policy interventions. Our estimated reproduction numbers are notably less volatile, provide more credible short-time predictions for the number of infected individuals, and are thus clearly favorable compared with the results obtained by two other popular approaches used for monitoring a pandemic. The proposed approach contributes to increased preparedness to future pandemics of contagious diseases, as it can be used as a simple yet powerful tool to monitor the pandemics, provide short-term predictions, and thus support decision making regarding timely and targeted control measures.

Unveiling Influence in Networks: A Novel Centrality Metric and Comparative Analysis through Graph-Based Models.

Identifying influential actors within social networks is pivotal for optimizing information flow and mitigating the spread of both rumors and viruses. Several methods have emerged to pinpoint these influential entities in networks, represented as graphs. In these graphs, nodes correspond to individuals and edges indicate their connections. This study focuses on centrality measures, prized for their straightforwardness and effectiveness. We divide structural centrality into two categories: local, considering a node's immediate vicinity, and global, accounting for overarching path structures. Some techniques blend both centralities to highlight nodes influential at both micro and macro levels. Our paper presents a novel centrality measure, accentuating node degree and incorporating the network's broader features, especially paths of different lengths. Through Spearman and Pearson correlations tested on seven standard datasets, our method proves its merit against traditional centrality measures. Additionally, we employ the susceptible-infected-recovered (SIR) model, portraying virus spread, to further validate our approach. The ultimate influential node is gauged by its capacity to infect the most nodes during the SIR model's progression. Our results indicate a notable correlative efficacy across various real-world networks relative to other centrality metrics.

Influence maximization based on simplicial contagion models

In recent years, the exploration of node centrality has received significant attention and extensive investigation, primarily fuelled by its applications in diverse domains such as product recommendations, opinion propagation, disease spread, and other scenarios requiring the maximization of node influence. Despite various perspectives emphasizing the indispensability of higher-order networks, research specifically delving into node centrality within the realm of hypergraphs has been relatively constrained. This study delves into the Simplicial Contagion Model (SCM) within the context of influence maximization (IM), specifically utilizing the susceptible-infected-recovered (SIR) model for illustration. To address the optimization challenge associated with IM on SCM, we present a comprehensive theoretical framework grounded in the message passing process. Additionally, we conduct a thorough stability analysis of equilibrium solutions within the self-consistent equations. Furthermore, we introduce a metric called collective influence and propose an adaptive algorithm, known as the Collective Influence Adaptive (CIA), to identify influential propagators in the spreading process. Notably, our algorithm distinguishes itself by prioritizing collective influence over individual influence, resulting in demonstrably superior performance, a characteristic substantiated by a comprehensive array of experiments.

Analytical Properties and Numerical Preservation of an Age-Group Susceptible-Infected-Recovered Model: Application to the Diffusion of Information

Abstract This paper analyzes an age-group susceptible-infected-recovered (SIR) model. Theoretical results concerning the conservation of the total population, the positivity of the analytical solution, and the final size of the epidemic are derived. Since the model is a nonlinear system of ordinary differential equations (ODEs), a numerical approximation is considered, based on Standard and non-Standard Finite Difference methods, and on a Modified Patankar-Runge–Kutta (MPRK) method. The numerical preservation of the qualitative properties of the analytical solution is studied. The obtained results are applied to the diffusion of information in social networks, and the effectiveness of the different numerical approaches is shown through several numerical tests on real data.

Using an epidemiological model to explore the interplay between sharing and advertising in viral videos

How to exploit social networks to make internet content spread rapidly and consistently is an interesting question in marketing management. Although epidemic models have been employed to comprehend the spread dynamics of internet content, such as viral videos, the effects of advertising and individual sharing on information dissemination are difficult to distinguish. This gap forbids us to evaluate the efficiency of marketing strategies. In this paper, we modify a classic mean-field SIR (susceptible–infected–recovered) model, incorporating the influences of sharing and advertising in viral videos. We mathematically analyze the global stability of the system and propose an agent-based modeling approach to evaluate the efficiency of sharing and advertising. We further provide a case study of music videos on YouTube to show the validity of our model.

Identifying influential spreaders in complex network based on the node’s weight and spreading probability

Identifying influential spreaders is a crucial aspect of network science with various applications, including rumor control, viral marketing and epidemic spread limitation. Despite the availability of various methods for identifying these spreaders in complex networks, there remains a fundamental question regarding their accurate and discriminative identification. To address the issues and account for each node’s propagation ability, we propose an algorithm to identify influential spreaders based on the node’s weight and spreading probability (NWSP) for identifying influential spreaders. The effectiveness of the proposed method is evaluated using the Susceptible–Infected–Recovered (SIR) model, Kendall’s Tau ([Formula: see text]) and monotonicity. The proposed method is compared with several well-known metrics, including degree centrality, K-shell decomposition, betweenness centrality, closeness centrality, eigenvector centrality and the centrality method based on node spreading probability (SPC), in ten real networks. Experimental results demonstrate the superiority ability of the proposed algorithm to accurately and discriminatively identify influential spreaders.

Temporal logics for compartmental models

Abstract This paper introduces two logic frameworks for the study of SIR (Susceptible-Infected-Recovered) and SIRS compartmental epidemic models, one based on Linear Temporal Logic and the other on Computation Tree Logic. We provide a short literature overview on compartmental models and other related works using logics, and then define our logics with their respective axiomatizations, and demonstrate their soundness and completeness proofs.

GDLC: A new Graph Deep Learning framework based on centrality measures for intrusion detection in IoT networks

The increasing growth of the Internet of Things (IoT) with the diverse and dynamic nature of devices made detecting and preventing network intrusions more important and challenging. As new and sophisticated cyber-attacks are being used, there is an increasing need for advanced intrusion detection systems that can adapt to emerging threats. The majority of existing methods in the literature lack a comprehensive consideration of complex network features namely the centrality measures. Previous works overlooked the potential insights that can be obtained from the structured relationships within network traffic data. In this study, we propose an approach called Graph Deep Learning framework based on Centrality measures (GDLC). Our approach includes an algorithm to dynamically select the most appropriate centrality measures according to the network’s topological properties created from traffic data. After that, they are integrated with Artificial Intelligence (AI) techniques, specifically the deep learning models: CNN, LSTM, and GRU. We tested our methodology on multiple publicly available cybersecurity datasets, having different network structures and sizes. First, we employ the Susceptible Infectious Recovered (SIR) model to validate the importance of the added centrality measures in identifying the most influential nodes that can be the subject of intrusion attacks. Then, through extensive experimentation and evaluation, we test the effectiveness of our approach in improving the accuracy of the Network Intrusion Detection System (NIDS). The obtained results indicate a significant enhancement in detection rates, that can reach up to 7.7%. This improvement demonstrates the practical value of our proposed methodology and highlights its high capacity to adapt to varying network structures. Integrating AI and complex network features is a promising approach for enhancing the capabilities of the Network Intrusion Detection System, contributing to a more resilient cybersecurity framework.

Analyzing epidemics and designing policies with a modified SIR model

This research paper aims to study the impact of COVID-19 on the economy, where we have extended the standard epidemiological model, the Susceptible–Infected–Recovered (SIR) model. In the economy’s dynamics, we have incorporated aggregate demand and aggregate supply and further set up a system of three-dimensional nonlinear differential equations, which is more likely the Labor–Infected–Quarantine (LIQ) model, an extension of the SIR model. Here, we have derived the steady-state condition and analyzed the model’s stability. In addition, we have done a comparative static analysis of parameters with some policy implications. We aim to achieve the twin objective, i.e., controlling the pandemic and reviving the economy under the set of the policy mix.

Development and Impact Analysis of a Multi-Pandemic Real-Time Data Dashboard: A Comparative Analytical Approach

This research presents the development and implementation of a Multi Pandemic Real-Time Data Dashboard, designed to facilitate enhanced comparative analysis across various global pandemics. Utilizing a combination of real-time data acquisition, statistical modeling, and predictive analytics, the dashboard provides a dynamic platform for analyzing pandemic trends and outcomes. Our methodology involved integrating diverse data sources, employing mathematical models such as the SIR (Susceptible, Infected, Recovered) model and machine learning algorithms for data processing and trend prediction. Key findings indicate that the dashboard effectively identifies patterns in pandemic spread and impact, offering valuable insights for public health decision-making. The research underscores the significance of advanced data analytics in managing public health crises, highlighting the dashboard’s potential in aiding proactive pandemic response and policy formulation.

Contagion dynamics in time-varying metapopulation networks with node's activity and attractiveness.

The metapopulation network model is a mathematical framework used to study the spatial spread of epidemics with individuals' mobility. In this paper, we develop a time-varying network model in which the activity of a population is correlated with its attractiveness in mobility. By studying the spreading dynamics of the SIR (susceptible-infectious-recovered)-type disease in different correlated networks based on the proposed model, we theoretically derive the mobility threshold and numerically observe that increasing the correction between activity and attractiveness results in a reduced mobility threshold but suppresses the fraction of infected subpopulations. It also introduces greater heterogeneity in the spatial distribution of infected individuals. Additionally, we investigate the impact of nonpharmaceutical interventions on the spread of epidemics in different correlation networks. Our results show that the simultaneous implementation of self-isolation and self-protection is more effective in negatively correlated networks than that in positively correlated or non-correlated networks. Both self-isolation and self-protection strategies enhance the mobility threshold and, thus, slow down the spread of the epidemic. However, the effectiveness of each strategy in reducing the fraction of infected subpopulations varies in different correlated networks. Self-protection is more effective in positively correlated networks, whereas self-isolation is more effective in negatively correlated networks. Our study will provide insights into epidemic prevention and control in large-scale time-varying metapopulation networks.

Study of fractional order SIR model with M-H type treatment rate and its stability analysis

In this manuscript, we analyze a fractional-order susceptible-infected-recovered (SIR) mathematical model with a nonlinear incidence rate and nonlinear treatment rate for the control of infectious illness. The incidence rate of infection is considered as Holling type II and the treatment rate is considered as Monod-Haldane (MH) type. The existence and uniqueness criteria for the new model, as well as the non-negativity and boundedness, have been established. We also provide an ideal control strategy for the SIR model using the treatment rate as a control parameter. The solution of the suggested model is approximated using the fractional-order Taylor's method. With the help of MATLAB (2018a), we perform numerical simulations and illustrate the results through graphical representations.