Susceptible-infected-recovered Model Research Articles

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.

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.

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.

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.

Rural community response to accidental toxic gas release: An individual emergency response model during self-organized evacuations

The emergency response ability in rural areas is weaker than in urban areas. Once a major accident occurs in a rural area, it is more likely to cause serious consequences. Thus, we propose a individual emergency response model during self-organized evacuations after accidental toxic gas releases in rural areas. The proposed model can reproduce emergency information dissemination and individual emergency decision-making in self-organized evacuations. We propose an improved susceptible infected recovered model for emergency information dissemination process. At the same time, we propose a emergency decision-making mechanism to simulate individual emergency actions. In this model, individual personality characteristics will affect the accessing and disseminating individual emergency information. Then, we conduct a simulation experiment based on methanol leakage in a rural community. Through comparative experiments, we found that the traditional model may be too pessimistic in estimating emergency information dissemination results, underestimating shadow evacuation. In noncompliance evacuation areas, loudspeakers can inhibit individuals from unnecessarily evacuating who are close to it, and may cause individuals far away from it to evacuate unnecessarily. When formulating emergency response strategies, managers should focus on groups with weak access to information and consider the impact of loudspeaker locations on individual emergency response actions.

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.

Towards investigating influencers in complex social networks using electric potential concept from a centrality perspective

Influencers in complex social networks are crucial for shaping the dynamics of information dissemination, viral marketing strategies, and controlling public opinion. This raises an important question: which influencers wield the most power within these networks, and how can we effectively identify and strategically utilize a key group of disseminators to maximize their influence across various domains? To address this, various heuristic strategies have been developed, targeting specific scenarios. However, these strategies often fall short by focusing solely on nodal topology and ignoring the intricate interconnections among nodes. This oversight can lead to imprecise evaluations and reduce the effectiveness of information spread. To overcome these limitations, a comprehensive approach that considers both the local and global topological dynamics of networks is essential. This paper introduces a novel centrality measure, electric potential centrality (EPC), which incorporates both the degree of nodes and the distances between them. Inspired by the concept of electric potential, EPC is designed to identify key influencers by extensively analyzing topological features, including local connections and the overall network structure. The effectiveness of EPC is rigorously evaluated through experiments on both synthesized and real-world networks, which are undirected and unweighted. Our findings reveal that EPC significantly surpasses existing methodologies, exhibiting the strongest correlation with baseline metrics within the susceptible–infected–recovered model.

Susceptible-Infected-Recovered Model of Mathematics Anxiety Behavior on Students' Mathematics Study Results at Aquino Catholic High School Amurang

This study aims to see the spread of mathematics anxiety behavior on the results of students' mathematics studies at Aquino Catholic High School Amurang by using the SIR (Susceptible-Infected-Recovered) mathematical model. A total of 88 samples were collected and categorized into three groups based on predetermined criteria. These groups consisted of 47 students categorized as susceptible, 27 as infected, and 14 as recovered. The parameters in this study measure the rate of change within these three groups over a 365-day period, equivalent to one year. Two equilibrium points are obtained that can interpret populations free from math anxiety behavior or endemic math anxiety behavior. The stability analysis of the two equilibrium points shows that the equilibrium point free from math anxiety behavior is locally asymptotically stable. Additionally, this study also reveals that math anxiety behavior will disappear in less than 40 days through the basic reproduction number (Ro) obtained, which is 0.99 or less than 1. Keywords: Amurang; mathematics anxiety; SIR model

Implementation of mathematics model in public health: Albanian case study

This article presents a detailed examination of the application of the Susceptible-Infected-Recovered (SIR) mathematical model in analyzing the COVID-19 pandemic in Albania. The study integrates the SIR model with real-world data, including vaccination rates and population statistics, to simulate the dynamics of the pandemic over a specified period. Our focus is on the comparison between the model's predictions and the actual epidemiological data from Albania, considering reported cases, recoveries, and fatalities. The simulation results are visualized through graphical representations, offering insights into the epidemic's progression and the effectiveness of public health interventions. This study also provides a projection for the year 2024, emphasizing the evolving nature of the pandemic and the role of mathematical modeling in public health decision-making. The comparison highlights the strengths and limitations of using the SIR model in real-world scenarios and underscores the importance of adaptive strategies in public health planning. This case study serves as an example of the critical role of mathematical models in understanding and managing public health crises.

Study of lump and periodic waves along with rogue waves and breathers for mathematical modeling of biological dynamical system

Globally, infectious diseases pose a significant threat. Notable cases include influenza, Hepatitis B and HIV. COVID-19, caused by the coronavirus, has been the subject of recent discussion due to its great transmissibility. This study explores the Susceptible–Infectious–Recovered (SIR) epidemic model, explaining several analytical approaches to comprehend the nonlinear incident rates and geographic dispersion. The model investigates phenomena such as M-shaped solitons, homoclinic breather-like solitons, lump waves (LWs), lump solution (LS) with one or two kinks, rogue waves (RWs), periodic waves (PWs) and periodic cross-kink waves. These solutions aid in understanding the disease spread and informing containment strategies by identifying optimal outbreak control methods. This work studies localized wave solutions in nonlinear wave equations, known as soliton solutions including the LS. RWs are characterized by unexpectedly large amplitude and rapid profile changes, drawing attention for their erratic features. PWs exhibit periodic repetitions over time and space. Besides, some type of solitons with special waveforms are the periodic cross-kink, M-shaped and homoclinic breather-like solitons. Graphical representation visualizes the behavior of these effective waves, providing insights into virus spread in specific regions over time. SIR models help identify optimal strategies for controlling outbreaks. The work adds to our understanding of epidemic dynamics by illuminating how the movement of susceptible and infected individuals affects the spread of disease.

SIR Fractional Order of Simulated Covid-19 Cases using Adams Bashforth-Moulton Method

Fractional order derivative has been widely used in many different areas such as bioengineering, fluid mechanics, circuits systems, biomathematics, and biomedicine. This study introduces the system of the fractional differential equation on SIR (Susceptible-Infected-Recovered) model to simulate the COVID-19 in Malaysia. The fractional derivative is described in Caputo sense and solved by the Adams Bashforth Moulton method. The Runge-Kutta method is used to prove and validate the numerical results obtained. The graphical representations of the simulation with difference fractional order have been presented. The derivative order, with values more than 0.5 are acceptable and reliable.

A novel higher-order Deffuant–Weisbuch networks model incorporating the Susceptible Infected Recovered framework

The literature on opinion dynamics lacks consideration of the changing states of nodes during the process of opinion interaction, as observed in the literature on social networks. To address this gap, this paper proposes an adapted three-dimensional Deffuant–Weisbuch model based on the Susceptible Infected Recovered (SIR) model, which explores the impact of node state changes on opinion interaction. We incorporate the SIR model to describe changes in node state and improve the trust threshold by taking into account nodes’ emotional factor, cognitive ability, and state of the arts. The model is also modified using the opinion natural evolution coefficient and accounts for dynamic changes in social network structure. We validate our model with different network types and structures, and verify our results using the Louvain algorithm and index of centrality. Our model reveals that under different network types and structures, multiple opinion cliques are formed, and the opinions of ordinary nodes tend to converge around those of opinion leaders, indicating the guiding role of opinion leaders in shaping public opinion.

Investigating disaster response for resilient communities through social media data and the Susceptible-Infected-Recovered (SIR) model: A case study of 2020 Western U.S. wildfire season

Effective disaster response is critical for communities to remain resilient and advance the development of smart cities. Responders and decision-makers would benefit from reliable, timely measures of the issues impacting their communities during a disaster, and social media offers a potentially rich data source. Social media can reflect public concerns and behaviors during a disaster, offering valuable insights for decision-makers to understand evolving situations and optimize resource allocation. We used Bidirectional Encoder Representations from Transformers (BERT) topic modeling to cluster topics from Twitter data. Then, we conducted a temporal-spatial analysis to examine the distribution of these topics across different regions during the 2020 western U.S. wildfire season. Our results show that Twitter users mainly focused on three topics: “health impact,” “damage,” and “evacuation.” We used the Susceptible-Infected-Recovered (SIR) theory to explore the magnitude and velocity of topic diffusion on Twitter. The results displayed a clear relationship between topic trends and wildfire propagation patterns. The estimated parameters obtained from the SIR model in selected cities revealed that residents exhibited a high level of several concerns during the wildfire. Our study offers a quantitative approach to measure disaster response and support community resilience enhancement.

A temporal approach to online discussion during disasters: Applying SIR infectious disease model to predict topic growth and examining effects of temporal distance

Discussions on social media during major disasters are robust and often have multiple frames of reference. Temporal perspectives, however, are still lacking in current understandings of social-mediated discussions during disasters and crises, but incorporating temporal perspectives can significantly enhance environmental scanning efforts as prescribed in the issues management framework. The purpose of the current research is twofold: to apply and validate the SIR (Susceptible-Infectious-Recovered) model to examine topics’ growth over time on social media and to understand how future orientation of social media users (an indicator of temporal distance) affects their construal of a disaster through supervised machine learning. We based our analysis on Twitter discussions during the Texas winter storm in 2021. Results of the study show great fit of the SIR model for topic growth, and that temporal distance affects users’ construal of the event in line with core predictions of construal level theory. Theoretical, methodological, and practical implications on social-mediated discussions related to climate change-induced and -intensified disasters and issues management are discussed.