Susceptible-infected-recovered Research Articles

Towards Inferring Network Properties from Epidemic Data

Epidemic propagation on networks represents an important departure from traditional mass-action models. However, the high-dimensionality of the exact models poses a challenge to both mathematical analysis and parameter inference. By using mean-field models, such as the pairwise model (PWM), the high-dimensionality becomes tractable. While such models have been used extensively for model analysis, there is limited work in the context of statistical inference. In this paper, we explore the extent to which the PWM with the susceptible-infected-recovered (SIR) epidemic can be used to infer disease- and network-related parameters. Data from an epidemics can be loosely categorised as being population level, e.g., daily new cases, or individual level, e.g., recovery times. To understand if and how network inference is influenced by the type of data, we employed the widely-used MLE approach for population-level data and dynamical survival analysis (DSA) for individual-level data. For scenarios in which there is no model mismatch, such as when data are generated via simulations, both methods perform well despite strong dependence between parameters. In contrast, for real-world data, such as foot-and-mouth, H1N1 and COVID19, whereas the DSA method appears fairly robust to potential model mismatch and produces parameter estimates that are epidemiologically plausible, our results with the MLE method revealed several issues pertaining to parameter unidentifiability and a lack of robustness to exact knowledge about key quantities such as population size and/or proportion of under reporting. Taken together, however, our findings suggest that network-based mean-field models can be used to formulate approximate likelihoods which, coupled with an efficient inference scheme, make it possible to not only learn about the parameters of the disease dynamics but also that of the underlying network.

Modelling and Forecasting COVID-19 Transmission Dynamics: A Susceptible-Infected-Recovered (SIR)-based Approach for Informed Decision-Making

Modelling and Forecasting COVID-19 Transmission Dynamics: A Susceptible-Infected-Recovered (SIR)-based Approach for Informed Decision-Making

Selection of models and parameter estimation for monitoring the COVID-19 epidemic in Brazil via Bayesian inference

In 2019, a new strain of coronavirus led to an outbreak of disease cases named COVID-19, evolving rapidly into a pandemic. In Brazil, delayed decision making and lack of knowledge have resulted in an alarming increase in daily transmission and deaths. In this context, researchers used mathematical models to assist in determining the parameters that act in the spread of diseases, revealing containment measures. However, numerous mathematical models exist in the literature, each with specific parameters to be specified, leading to an important question about which model best represents the pandemic behavior. In this regard, this work aims to apply the Approximate Bayesian Computation method to select the best model and simultaneously estimate the parameters to resolve the abovementioned issue. The models adopted were susceptible-infected-recovered (SIR), susceptible-exposed-infected-recovered (SEIR), susceptible-infected-recovered-susceptible (SIRS), and susceptible-exposed-infected-recovered-susceptible (SEIRS). Approximate Bayesian Computation Monte Carlo Sequencing (ABC-SMC) was used to select among four competing models to represent the number of infected individuals and to estimate the model parameters based on three periods of Brazil COVID-19 data. A forecasting test was performed to test the ABC-SMC algorithm and the selected models for two months. The result was compared with the actual number of infected that were reported. Among the teste models, it was found that the ABC-SMC algorithm had a promising performance, since the data were noisy and the models could not predict all parameters.

Multivariate Forecasting Model for COVID-19 Spread Based on Possible Scenarios in Ecuador

So far, about 770.1 million confirmed cases of COVID-19 have been counted by August 2023, and around 7 million deaths have been reported from these cases to the World Health Organization. In Ecuador, the first confirmed COVID-19 case was registered on 19 February 2020, and the country’s mortality rate reached 0.43% with 12986 deaths, suggesting the need to establish a mechanism to show the virus spread in advance. This study aims to build a dynamic model adapted to health and socio-environmental variables as a multivariate model to understand the virus expansion among the population. The model is based on Susceptible-Infected-Recovered (SIR), which is a standard model in which the population is divided into six groups with parameters such as susceptible S(t), transit stage E(t), infected I(t), recovered R(t), deceased Me(t), infected asymptomatic Ia(t), infected symptomatic Is(t) and deceased by other causes M(t) to be considered and adapted. The model was validated by using consistent data from Chile and run by inconsistent data from Ecuador. The forecast error was analyzed based on the mean absolute error between real data and model forecast, showing errors within a range from 6.33% to 8.41% for Chile, with confidence a interval of 6.17%, then 3.87% to 4.70% range for Ecuador with a confidence interval of 2.59% until 23rd December 2020 of the database. The model forecasts exponential variations in biosecurity measures, exposed population, and vaccination.

Probabilistic Procedures for SIR and SIS Epidemic Dynamics on Erdös-Rényi Contact Networks

This paper introduces the mathematical formalization of two probabilistic procedures for susceptible-infected-recovered (SIR) and susceptible-infected-susceptible (SIS) infectious diseases epidemic models, over Erdös-Rényi contact networks. In our approach, we consider the epidemic threshold, for both models, defined by the inverse of the spectral radius of the associated adjacency matrices, which expresses the network topology. The epidemic threshold dynamics are analyzed, depending on the global dynamics of the network structure. The main contribution of this work is the relationship established between the epidemic threshold and the topological entropy of the Erdös-Rényi contact networks. In addition, a relationship between the basic reproduction number and the topological entropy is also stated. The trigger of the infectious state is studied, where the probability value of the stability of the infected state after the first instant, depending on the degree of the node in the seed set, is proven. Some numerical studies are included and illustrate the implementation of the probabilistic procedures introduced, complementing the discussion on the choice of the seed set.

Network virus propagation and security situation awareness based on Hidden Markov Model

The security situation of the network is determined by the observation state and hidden state of a complex virus system. To analyze the relationship between the two states and evaluate the trends in the security situation of the system, we construct a new model for security situation awareness based on Hidden Markov Model (HMM). Firstly, the paper examines the impact of virus propagation on network security and proposes a new SIR (Susceptible–Infected–Recovered) virus propagation model on scale-free networks. Secondly, we construct a Hidden Markov Model for network security, and this model designs and utilizes the Forward Algorithm and Viterbi Algorithm to assess the security status of epidemic networks. Finally, we ascertain the effectiveness of the model and algorithms through model examples and simulation experiments. The results show that the proposed algorithm is highly efficient in analyzing the security of virus systems and has great application value in predicting the security trends of networks.

A research of a strategy to balance the importance and dispersion of multiple critical nodes

Maximizing the range of disease or information spread is a hot research topic in complex networks. In particular, the dispersion among a group of nodes and the spreading ability of a single node are two vital factors in the propagation process. However, although some traditional algorithms have considered both factors, they have failed to address the balance between them. To solve this problem, this paper first proposes two metrics to quantify the dispersion of a group of nodes and the local spreading ability of a single node, then designs an objective function fusing these two metrics, which automatically searches for a balance between these two vital factors during the optimization process. We evaluate the proposed algorithm against seven baseline algorithms on three synthetic networks and nine real networks based on the classic susceptible-infected-recovered (SIR) model. Experimental results show that our algorithm is better than some of the centrality-based and heuristic algorithms in the final propagation scale.

Predictions from standard epidemiological models of consequences of segregating and isolating vulnerable people into care facilities.

Since the declaration of the COVID-19 pandemic, many governments have imposed policies to reduce contacts between people who are presumed to be particularly vulnerable to dying from respiratory illnesses and the rest of the population. These policies typically address vulnerable individuals concentrated in centralized care facilities and entail limiting social contacts with visitors, staff members, and other care home residents. We use a standard epidemiological model to investigate the impact of such circumstances on the predicted infectious disease attack rates, for interacting robust and vulnerable populations. We implement a general susceptible-infectious-recovered (SIR) compartmental model with two populations: robust and vulnerable. The key model parameters are the per-individual frequencies of within-group (robust-robust and vulnerable-vulnerable) and between-group (robust-vulnerable and vulnerable-robust) infectious-susceptible contacts and the recovery times of individuals in the two groups, which can be significantly longer for vulnerable people. Across a large range of possible model parameters including degrees of segregation versus intermingling of vulnerable and robust individuals, we find that concentrating the most vulnerable into centralized care facilities virtually always increases the infectious disease attack rate in the vulnerable group, without significant benefit to the robust group. Isolated care homes of vulnerable residents are predicted to be the worst possible mixing circumstances for reducing harm in epidemic or pandemic conditions.

Towards identifying influential nodes in complex networks using semi-local centrality metrics

The influence of the node refers to the ability of the node to disseminate information. The faster and wider the node spreads, the greater its influence. There are many classical topological metrics that can be used to evaluate the influencing ability of nodes. Degree centrality, betweenness centrality, closeness centrality and local centrality are among the most common metrics for identifying influential nodes in complex networks. Degree centrality is very simple but not very effective. Global metrics such as betweenness centrality and closeness centrality can better identify influential nodes, but they are not compatible on large-scale networks due to their high complexity. In order to design a ranking method of influential nodes, in this paper a new semi-local centrality metric is proposed based on the relative change in the average shortest path of the entire network. Meanwhile, our metric provides a quantitative global importance model to measure the overall influence of each node. To evaluate the performance of the proposed centrality metric, we use the Susceptible-Infected-Recovered (SIR) epidemic model. Experimental results on several real-world networks show that the proposed metric has competitive performance in identifying influential nodes with existing equivalent centrality metrics and has high efficiency in dealing with large-scale networks. The effectiveness of the proposed metric has been proven with numerical examples and Kendall's coefficient.

Estimating the prevalence of COVID-19 cases through the analysis of SARS-CoV-2 RNA copies derived from wastewater samples from North Dakota

The SARS-CoV-2 virus was first detected in December 2019, which prompted many researchers to investigate how the virus spreads. SARS-CoV-2 is mainly transmitted through respiratory droplets. Symptoms of the SARS-CoV-2 virus appear after an incubation period. Moreover, the asymptomatic infected individuals unknowingly spread the virus. Detecting infected people requires daily tests and contact tracing, which are expensive. The early detection of infectious diseases, including COVID-19, can be achieved with wastewater-based epidemiology, which is timely and cost-effective. In this study, we collected wastewater samples from wastewater treatment plants in several cities in North Dakota and then extracted viral RNA copies. We used log-RNA copies in the model to predict the number of infected cases using Quantile Regression (QR) and K-Nearest Neighbor (KNN) Regression. The model's performance was evaluated by comparing the Mean Absolute Percentage Error (MAPE). The QR model performs well in cities where the population is >10000. In addition, the model predictions were compared with the basic Susceptible-Infected-Recovered (SIR) model which is the golden standard model for infectious diseases.

Identifying and Ranking Influential Spreaders in Complex Networks by Localized Decreasing Gravity Model

Abstract Identifying crucial nodes in complex networks is paid more attention in recent years. Some classical methods, such as degree centrality, betweenness centrality and closeness centrality, have their advantages and disadvantages. Recently, the gravity model is applied to describe the relationship of nodes in a complex network. However, the interaction force in gravity model follows the square law of distance, which is inconsistent with the actual situation. Most people are generally affected by those who are surrounding them, which means that local influence should be emphasized. To address this issue, we propose an indexing method called localized decreasing gravity centrality by maximizing the local influence of a node. In the proposed measure, the mass and radius of gravity model are redefined, which can represent the spreading ability of the node. In addition, a decreasing weight is added to strengthen the local influence of a node. To evaluate the performance of the proposed method, we utilize four different types of networks, including interaction networks, economic networks, collaboration networks and animal social networks. Also, two different infectious disease models, susceptible-infectious-recovered (SIR) and susceptible-exposed-low risk-high risk-recovered (SELHR), are utilized to examine the spreading ability of influential nodes.

Prediction of an epidemic spread based on the adaptive genetic algorithm

In recent years, coronavirus disease 2019 (COVID-19) has plagued the world, causing huge losses to the lives and property of people worldwide. How to simulate the spread of an epidemic with a reasonable mathematical model and then use it to analyze and to predict its development trend has attracted the attention of scholars from different fields. Based on the susceptible–infected–recovered (SIR) propagation model, this work proposes the susceptible–exposed–infected–recovered–dead (SEIRD) model by introducing a specific medium having many changes such as the self-healing rate, lethality rate, and re-positive rate, considering the possibility of virus propagation through objects. Finally, this work simulates and analyzes the propagation process of nodes in different states within this model, and compares the model prediction results optimized by the adaptive genetic algorithm with the real data. The experimental results show that the susceptible–exposed–infected–recovered–dead model can effectively reflect the real epidemic spreading process and provide theoretical support for the relevant prevention and control departments.

GSI: An Influential Node Detection Approach in Heterogeneous Network Using Covid-19 as Use Case

The growth of COVID-19, caused by the SARS-CoV-2 virus, has turned into an unprecedented pandemic in the last century. It is crucial to identify superspreading nodes to prevent the pandemic&#x2019;s progress. Most available superspreader identification techniques consider only a single or few network metrics related to the complex network&#x2019;s topological structure. Furthermore, it is more challenging to determine influential spreaders from heterogeneous structures of networks. In a disease transmission network, the degree of heterogeneity is essential to locate the path of the infection spread. Therefore, it is required to have an extended degree of centrality to collect information from various neighborhood levels. This article presents an approach, namely, global structure influence (<inline-formula> <tex-math notation="LaTeX">${\rm GSI}$</tex-math> </inline-formula>), which considers network nodes&#x2019; local and global influence. This method can gather information from multiple levels of the neighborhood. Evaluation of our proposed method is done by considering different types of networks, i.e., social networks, highly heterogeneous human contact networks, and epidemiological networks, and also by using the benchmark susceptible-infected-recovered (SIR) epidemic model. The <inline-formula> <tex-math notation="LaTeX">${\rm GSI}$</tex-math> </inline-formula> technique provides real-spreading dynamics across various network structures and has outperformed the baseline techniques with an average Kendall&#x2019;s <inline-formula> <tex-math notation="LaTeX">$\tau$</tex-math> </inline-formula> improvement range from 0.017 to 0.278. This study will help to identify the superspeaders in real applications, where pathogens spread quickly because of close contact, such as the recently witnessed COVID-19 pandemic.

A Comparison of Monte Carlo-Based and PINN Parameter Estimation Methods for Malware Identification in IoT Networks

Malware propagation is a growing concern due to its potential impact on the security and integrity of connected devices in Internet of Things (IoT) network environments. This study investigates parameter estimation for Susceptible-Infectious-Recovered (SIR) and Susceptible–Infectious–Recovered–Susceptible (SIRS) models modeling malware propagation in an IoT network. Synthetic data of malware propagation in the IoT network is generated and a comprehensive comparison is made between two approaches: algorithms based on Monte Carlo methods and Physics-Informed Neural Networks (PINNs). The results show that, based on the infection curve measured in the IoT network, both methods are able to provide accurate estimates of the parameters of the malware propagation model. Furthermore, the results show that the choice of the appropriate method depends on the dynamics of the spreading malware and computational constraints. This work highlights the importance of considering both classical and AI-based approaches and provides a basis for future research on parameter estimation in epidemiological models applied to malware propagation in IoT networks.

A hybrid influence method based on information entropy to identify the key nodes

Identifying the key nodes in complicated networks is an essential topic. A number of methods have been developed in recent years to solve this issue more effectively. Multi-attribute ranking is a widely used and efficient method to increase the accuracy of identifying the key nodes. Using k-shell iteration information and propagation threshold differences, we thoroughly analyze the node’s position attribute and the propagation attribute to offer a hybrid influence method based on information entropy. The two attributes will be weighted using the information entropy weighting method, and then the nodes’ influence ranking will be calculated. Correlation experiments in nine different networks were carried out based on the Susceptible–Infected–Recovered (SIR) model. Among these, we use the imprecision function, Kendall’s correlation coefficient, and the complementary cumulative distribution function to validate the suggested method. The experimental results demonstrate that our suggested method outperforms previous node ranking methods in terms of monotonicity, relevance, and accuracy and performs well to achieve a more accurate ranking of nodes in the network.

The susceptible–infected–recovered model as a tool to motivate and teach differential equations: an analytic approach

Since the introduction by Kermack and McKendrick in 1927, the Susceptible–Infected–Recovered (SIR) epidemic model has been a foundational model to comprehend and predict the dynamics of infectious diseases. Almost for a century, the SIR model has been modified and extended to meet the needs of different characteristics of various infectious diseases including recent COVID-19 breakouts, which stimulates the advance in mathematical epidemiology theory significantly. Some of the mathematical ideas and techniques developed are also relevant to motivate teaching various topics in differential equations by connecting students' life experiences with current pandemics to meaningful classroom learning activities. Here, various pedagogically relevant topics from the SIR model are provided for undergraduate differential equation class, which includes (1) compartmental modelling and mass action kinetic modelling, (2) conservation rule and model reduction, (3) introduction to phase plane by removing time variable to derive trajectory equations, (4) transformation of equations to equivalent forms, (5) transformation of second-order system to second-order ODE, (6) deriving an analytic solution to the SIR equation by solving Bernoulli's equation, (7) deriving an analytic solution to the SIR equation from trajectory equations and (8) deriving an analytic solution to the SIR equation from exponential substitutions.

Epidemic modeling using differential equations with implementation in R

The COVID-19 pandemic, like past historical events such as the Vietnam War or 9/11, will shape a generation. Mathematics educators can seize this unprecedented opportunity to teach the principles of mathematical modeling in epidemiology. Compartmental epidemiological models, such as the SIR (susceptible-infected-recovered), are widely used by researchers and educators to study and teach infectious disease dynamics, particularly for COVID-19. The SIR model is considered a fundamental mathematical model for the spread of epidemic disease and employs Ordinary Differential Equations to determine the number of individuals in each compartment of a population at a given time. In this note, we demonstrate how to build a basic SIR model. We show how to simulate, plot, and interpret the results using numerical simulation with R, a popular programming language widely used in data analysis and scientific research.

Modeling the dynamics of information propagation in the temporal and spatial environment

In this paper, we try to establish a non-smooth susceptible–infected–recovered (SIR) rumor propagation model based on time and space dimensions. First of all, we prove the existence and uniqueness of the solution. Secondly, we divide the system into two parts and discuss the existence of equilibrium points for each of them. For the left part, we define R 0 to study the relationship between R 0 and the existence of equilibrium points. For the right part, we classify many different cases by discussing the coefficients of the equilibrium point equation. Then, on this basis, we perform a bifurcation analysis of the non-spatial system and find conditions that lead to the existence of saddle-node bifurcation. Further, we consider the effect of diffusion. We specifically analyze the stability of equilibrium points. In addition, we analyze the Turing instability and Hopf bifurcation occurring at some equilibrium points. According to the Lyapunov number, we also determine the direction of the bifurcation. When I = I c , we discuss conditions for the existence of discontinuous Hopf bifurcation. Finally, through numerical simulations and combined with the practical meaning of the parameters, we prove the correctness of the previous theoretical theorem.

SLGC: Identifying influential nodes in complex networks from the perspectives of self-centrality, local centrality, and global centrality

Identifying influential nodes in complex networks and ranking their importance plays an important role in many fields such as public opinion analysis, marketing, epidemic prevention and control. To solve the issue of the existing node centrality measure only considering the specific statistical feature of a single dimension, a SLGC model is proposed that combines a node’s self-influence, its local neighborhood influence, and global influence to identify influential nodes in the network. The exponential function of e is introduced to measure the node’s self-influence; in the local neighborhood, the node’s one-hop neighboring nodes and two-hop neighboring nodes are considered, while the information entropy is introduced to measure the node’s local influence; the topological position of the node in the network and the shortest path between nodes are considered to measure the node’s global influence. To demonstrate the effectiveness of the proposed model, extensive comparison experiments are conducted with eight existing node centrality measures on six real network data sets using node differentiation ability experiments, susceptible–infected–recovered (SIR) model and network efficiency as evaluation criteria. The experimental results show that the method can identify influential nodes in complex networks more accurately.

Identifying key nodes in complex networks based on an improved gravity model

The identification of key nodes in complex networks is a hot topic. Therefore, it attracts increasing attention from different fields, like airline networks and social networks. To identify the key nodes in complex network, we suggest an improved gravity model method that takes propagation features into account. Relevant experiments were carried out in four actual airline networks based on the Susceptible Infected Recovered (SIR) model. First, we analyze the correlation between the proposed method and other benchmark methods.Then, Kendall’s correlation coefficient and the imprecision function were used as evaluation metrics to analyze and validate the proposed method. Empirical results reveal that the suggested method outperforms previous benchmark methods in terms of precision and effectiveness for identifying key nodes, especially in the US air network, where Kendall’s tau achieves a 107% improvement compared to the gravity centrality method.