Susceptible-infected-recovered Research Articles

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.

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.

Passive and active field theories for disease spreading

Abstract 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 SIR-DDFT model, a combination of the susceptible-infected-recovered (SIR) model from epidemiology with dynamical density functional theory (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.

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.

Evolutionary game dynamics and the phase portrait diversity in a pandemic scenario

Modeling the time evolution of a pandemic in distinct social and economic environments has proven to be a great challenge for scientists due to the strong coupling of infection dynamics to complex collective human behavior. In this work, we propose a relatively simple extension of the classical Susceptible-Infected-Recovered (SIR) model that encompasses evolutionary game imitation dynamics and is capable of reproducing basic features of real data such as recurrent waves with suppression and re-bounce of cases. In particular, we depict different quantitative and qualitative aspects of the infection time series by representing them as trajectories in a modified phase portrait.

Fair and effective vaccine allocation during a pandemic

This paper presents a novel model for the Vaccine Allocation Problem (VAP), which aims to allocate the available vaccines to population locations over multiple periods during a pandemic. We model the disease progression and the impact of vaccination on the spread of the disease and mortality to minimise total expected mortality and location inequity in terms of mortality ratios under total vaccine supply and hospital and vaccination centre capacity limitations at the locations. The spread of the disease is modelled through an extension of the well-established Susceptible–Infected–Recovered (SIR) epidemiological model that accounts for multiple vaccine doses. The VAP is modelled as a nonlinear mixed-integer programming model and solved to optimality using the Gurobi solver. A set of scenarios with parameters regarding the COVID-19 pandemic in the UK over 12 weeks are constructed using a hypercube experimental design on varying disease spread, vaccine availability, hospital capacity, and vaccination capacity factors. The results indicate the statistical significance of vaccine availability and the parameters regarding the spread of the disease.

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.

Impact of immune evasion, waning and boosting on dynamics of population mixing between a vaccinated majority and unvaccinated minority.

We previously demonstrated that when vaccines prevent infection, the dynamics of mixing between vaccinated and unvaccinated sub-populations is such that use of imperfect vaccines markedly decreases risk for vaccinated people, and for the population overall. Risks to vaccinated people accrue disproportionately from contact with unvaccinated people. In the context of the emergence of Omicron SARS-CoV-2 and evolving understanding of SARS-CoV-2 epidemiology, we updated our analysis to evaluate whether our earlier conclusions remained valid. We modified a previously published Susceptible-Infectious-Recovered (SIR) compartmental model of SARS-CoV-2 with two connected sub-populations: vaccinated and unvaccinated, with non-random mixing between groups. Our expanded model incorporates diminished vaccine efficacy for preventing infection with the emergence of Omicron SARS-CoV-2 variants, waning immunity, the impact of prior immune experience on infectivity, "hybrid" effects of infection in previously vaccinated individuals, and booster vaccination. We evaluated the dynamics of an epidemic within each subgroup and in the overall population over a 10-year time horizon. Even with vaccine efficacy as low as 20%, and in the presence of waning immunity, the incidence of COVID-19 in the vaccinated subpopulation was lower than that among the unvaccinated population across the full 10-year time horizon. The cumulative risk of infection was 3-4 fold higher among unvaccinated people than among vaccinated people, and unvaccinated people contributed to infection risk among vaccinated individuals at twice the rate that would have been expected based on the frequency of contacts. These findings were robust across a range of assumptions around the rate of waning immunity, the impact of "hybrid immunity", frequency of boosting, and the impact of prior infection on infectivity in unvaccinated people. Although the emergence of the Omicron variants of SARS-CoV-2 has diminished the protective effects of vaccination against infection with SARS-CoV-2, updating our earlier model to incorporate loss of immunity, diminished vaccine efficacy and a longer time horizon, does not qualitatively change our earlier conclusions. Vaccination against SARS-CoV-2 continues to diminish the risk of infection among vaccinated people and in the population as a whole. By contrast, the risk of infection among vaccinated people accrues disproportionately from contact with unvaccinated people.

MODELING AND PREDICTING THE DYNAMICS OF COVID-19 IN MALAYSIA: A STATE-SPACE APPROACH

The emergence of COVID-19 in Malaysia in January 2020 marked the beginning of a significant public health challenge. Despite the transition to the endemic phase on April 1, 2022, the global impact of the virus remains substantial. This research aims to forecast the cumulative number of detected cases and deaths by employing a state-space model derived from the Susceptible-Infectious-Recovered (SIR) model, capturing the multi-wave dynamics of COVID-19. The modeling focuses on estimating the trends within the time interval spanning from week 1 to week 12, commencing in mid-June 2022. Real-time data sourced from the Ministry of Health in Malaysia serve as the basis for model development and validation, utilizing MATLAB and Simulink for simulation purposes. The findings of the simulation reveal a direct correlation between the number of detected cases and deaths, suggesting a positive relationship with the real-life situation. This mathematical representation contributes to a deeper understanding of the ongoing dynamics of COVID-19 and provides a tool for predicting future trends, aiding in public health planning and response efforts.

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.