Susceptible-infected-removed Research Articles

Joint extented Kalman filter-based parameter estimation in networked SEIR models with stochastic variability: analysis using COVID-19 daily data from southern India

Graph Laplacian diffusion is utilised to augment the susceptible-infected-removed (SEIR) epidemic model by integrating a weighted network and introducing variability in the transmission rate parameter to simulate population movement across network nodes. Employing the Joint Extended Kalman filter (JEKF), our objective is to derive three critical parameters: the transmission rate (β), recovery rate (γ), and latent period rate (α). The JEKF's iterative approach continuously anticipates and updates the system state based on current parameter estimations, making it adaptable for parameter estimation in dynamic systems. Integration of model predictions with observed data further enhances accuracy. Subsequently, we offer visual insights and demonstrate our methodology through experiments conducted on a simple tree network and a small-world Watts-Strogatz graph. Our ultimate aim is to precisely determine optimal parameter values to formulate effective COVID-19 management plans tailored for South India.

Development of a multidimensional centrality metric for ranking nodes in complex networks

Ranking nodes in complex networks is a fundamental task in network science, with significant applications in fields like social networks, bioinformatics, and information dissemination. Many existing methods struggle to efficiently capture the multifaceted relationships between nodes, particularly in large-scale networks. However, they often ignore the semantic relationships between nodes when gathering information. To address these challenges, this paper introduces SAASP, a Semi-local centrality measure that combines an Augmented graph with Average Shortest Path theory to efficiently identify influential nodes in complex networks. In SAASP, the augmented graph can represent global relationships between nodes as semantic similarities, allowing distant relationships to be considered in node ranking. Additionally, it incorporates an enhanced version of average shortest path theory to handle the computational complexity associated with large networks. By extracting local subgraphs for each node and considering the extended neighborhood concept, SAASP ensures scalability while preserving key structural properties. The integration of the augmented graph and average shortest path theory enables SAASP to accurately and efficiently identify influential nodes in large-scale complex networks with lower complexity. The effectiveness of the proposed metric is demonstrated through extensive experiments using the SIR (Susceptible-Infected-Removed) model and Kendall's coefficient, where it outperforms existing centrality measures on real-world datasets.

Modelling for resource risk propagation in dynamic heterogeneous project portfolio network

Project portfolio (PP) exists resource risk that propagates because of the relationships among projects arising from resource sharing. While earlier research has highlighted the necessity to control PP resource risk (PPRR) propagation, research that can provide an in-depth analysis of PPRR propagation remains lacking. This paper proposes a PPRR propagation model to bridge this gap by applying the SIR model to PP network (PPN). In the PPRR propagation model, the dynamics and heterogeneity that PPN is characterized are analyzed, following which the dynamic heterogeneous PPN is visualized. Then, the susceptible-infected-removed (SIR) model is improved considering the dynamics and heterogeneity of PPN. Thereafter, the applicability of the PPRR propagation model is verified by a numerical example. This paper enriches theories related to PPRR management and infectious disease model. Meanwhile, utilizing the PPRR propagation model, control measures for PPRR propagation from the perspectives of infection source and immunization strategy can be obtained.

Influence of Fractional Order on the Behavior of a Normalized Time-Fractional SIR Model

In this paper, we propose a novel normalized time-fractional susceptible–infected–removed (SIR) model that incorporates memory effects into epidemiological dynamics. The proposed model is based on a newly developed normalized time-fractional derivative, which is similar to the well-known Caputo fractional derivative but is characterized by the property that the sum of its weight function equals one. This unity property is crucial because it helps with evaluating how the fractional order influences the behavior of time-fractional differential equations over time. The normalized time-fractional derivative, with its unity property, provides an intuitive understanding of how fractional orders influence the SIR model’s dynamics and enables systematic exploration of how changes in the fractional order affect the model’s behavior. We numerically investigate how these variations impact the epidemiological dynamics of our normalized time-fractional SIR model and highlight the role of fractional order in improving the accuracy of infectious disease predictions. The appendix provides the program code for the model.

Evaluating the Application of the SIR Model to a Localized Population

Objective Using data collected from the Johns Hopkins COVID-19 Repository, I investigated the reliability of the SIR (Susceptible-Infected-Removed) model. Summary of Background Data Modern pandemic responses have evolved into effective defenses when implemented correctly but present issues in epidemiological modeling efforts. Intervention strategies such as quarantining and masking limit population size (N), which affects the accuracy of modeling population-based rate systems especially in highly transmissible diseases. Methods I begin by reviewing the SIR model retroactively to the initial SARS-CoV-2 Wuhan strain. I compared the parameters available in the published literature (N = 2,717,000, β = 2, γ = 1/14) to the best-fitting SIR-yielded values by minimizing the root mean squared error function. Subsequently, I evaluated its predictive capabilities on the Delta variant using early surge data, which was later compared against a retroactive analysis. Results Using a least-squares error best-fit analysis allowed me to retroactively define remarkably accurate model parameters for the Wuhan waves. Parameters including N = 730, β = 0.46, γ = 0.043 in the first wave and N = 11,200, β = 0.198, γ = 0.07 in the second reflected effective intervention strategies. I show it is an effective predictive tool regarding the Delta variant, yielding parameters N = 50,900, β = 0.87, γ = 1/3.7 that proved accurate when compared with parameters from a full retroactive analysis (N = 60,000, β = 0.94, γ = 1/3.6). Conclusion The similarity of the yielded parameters in my results supports the SIR model’s utility in epidemiological monitoring of high-transmissibility, low-mortality outbreaks vis-à-vis various containment measures.

Cellular dynamics shape recombination frequency in coronaviruses.

Coronavirus genomes have evolutionary histories shaped extensively by recombination. Yet, how often recombination occurs at a cellular level, or the factors that regulate recombination rates, are poorly understood. Utilizing experimental co-infections with pairs of genetically distinct coronaviruses, we found that recombination is both frequent and rare during coinfection. Recombination occurred in every instance of co-infection yet resulted in relatively few recombinant RNAs. By integrating a discrete-time Susceptible-Infected-Removed (SIR) model, we found that rates of recombination are determined primarily by rates of cellular co-infection, rather than other possible barriers such as RNA compartmentalization. By staggering the order and timing of infection with each virus we also found that rates of co-infection are themselves heavily influenced by genetic and ecological mechanisms, including superinfection exclusion and the relative fitness of competing viruses. Our study highlights recombination as a potent yet regulated force: frequent enough to ensure a steady influx of genetic variation but also infrequent enough to maintain genomic integrity. As recombination is thought to be an important driver of host-switching and disease emergence, our study provides new insights into the factors that regulate coronavirus recombination and evolution more broadly.

A combined neural ODE-Bayesian optimization approach to resolve dynamics and estimate parameters for a modified SIR model with immune memory

We propose a novel hybrid approach that integrates Neural Ordinary Differential Equations (NODEs) with Bayesian optimization to address the dynamics and parameter estimation of a modified time-delay-type Susceptible-Infected-Removed (SIR) model incorporating immune memory. This approach leverages a neural network to produce continuous multi-wave infection profiles by learning from both data and the model. The time-delay component of the SIR model, expressed through a convolutional integral, results in an integro-differential equation. To resolve these dynamics, we extend the NODE framework, employing a Runge-Kutta solver, to handle the challenging convolution integral, enabling us to fit the data and learn the parameters and dynamics of the model. Additionally, through Bayesian optimization, we enhance prediction accuracy while focusing on long-term dynamics. Our model, applied to COVID-19 data from Mexico, South Africa, and South Korea, effectively learns critical time-dependent parameters and provides accurate short- and long-term predictions. This combined methodology allows for early prediction of infection peaks, offering significant lead time for public health responses.

Exact solution for a discrete-time SIR model

We propose a nonstandard finite difference scheme for the Susceptible–Infected–Removed (SIR) continuous model. We prove that our discretized system is dynamically consistent with its continuous counterpart and we derive its exact solution. We end with the analysis of the long-term behavior of susceptible, infected and removed individuals, illustrating our results with examples. In contrast with the SIR discrete-time model available in the literature, our new model is simultaneously mathematically and biologically sound.

Inference of human contact networks based on epidemic data

A key challenge in epidemic modeling is the lack of adequate data on population interactions (such as traffic flow or mobility patterns) which result in the spread of infectious diseases. Knowledge of social contact patterns is crucial for public health professionals to devise effective non-pharmaceutical interventions to control epidemics. This paper focuses on inferring social contact rates from reported infection counts during the spread of an infectious disease, addressing the increased difficulty that arises when dealing with “sparse” contact networks where only a small subset of the edges have non-zero weights. Specifically, a new geographically constrained lasso approach for network reconstruction for non-homogeneous mixing Susceptible-Infected-Removed (SIR) disease spread models is presented. The new network reconstruction method can explicitly account for the spatial proximity of network nodes in estimating the disease transmission rates and predicting the future evolution of the epidemic dynamics. Extensive numerical experiments are presented to show the proposed method outperforms existing approaches in terms of accuracy of contact identification under various graph topologies. A case study based on real data from the COVID-19 pandemic is presented to demonstrate the application of the approach for inferring contact structures and a counterfactual scenario analysis to assess effectiveness of containment strategies.

Numerical solutions and simulations of the fractional COVID‐19 model via Pell–Lucas collocation algorithm

The aim of this study is to present the evolution of COVID‐19 pandemic in Turkey. For this, the SIR (Susceptible, Infected, Removed) model with the fractional order derivative is employed. By applying the collocation method via the Pell–Lucas polynomials (PLPs) to this model, the approximate solutions of model with fractional order derivative are obtained. Hence, the comments are made about the susceptible population, the infected population, and the recovered population. For the method, firstly, PLPs are expressed in matrix form for a selected number of . With the help of this matrix relationship, the matrix forms of each term in the SIR model with the fractional order derivative are constituted. For implementation and visualization, we utilize MATLAB. Moreover, the outcomes for the Runge–Kutta method (RKM) are obtained using MATLAB, and these results are compared with the results obtained with the Pell–Lucas collocation method (PLCM). From all simulations, it is concluded that the presented method is effective and reliable.

Dynamic properties of rumor propagation model induced by Lévy noise on social networks

Abstract Social networks are inevitably subject to disruptions from the physical world, such as sudden internet outages that sever local connections and impede information flow. While Gaussian white noise, commonly used to simulate stochastic disruptions, only fluctuates within a narrow range around its mean and fails to capture large-scale variations, Lévy noise can effectively compensate for this limitation. Therefore, a susceptible–infected–removed rumor propagation model with Lévy noise is constructed on homogeneous and heterogeneous networks, respectively. Then, the existence of a global positive solution and the asymptotic path-wise of the solution are derived on heterogeneous networks, and the sufficient conditions of rumor extinction and persistence are investigated. Subsequently, theoretical results are verified through numerical calculations and the sensitivity analysis related to the threshold is conducted on the model parameters. Through simulation experiments on Watts–Strogatz (WS) and Barabási–Albert networks, it is found that the addition of noise can inhibit the spread of rumors, resulting in a stochastic resonance phenomenon, and the optimal noise intensity is obtained on the WS network. The validity of the model is verified on three real datasets by particle swarm optimization algorithm.

A simple modification to the classical SIR model to estimate the proportion of under-reported infections using case studies in flu and COVID-19

BackgroundUnder-reporting and, thus, uncertainty around the true incidence of health events is common in all public health reporting systems. While the problem of under-reporting is acknowledged in epidemiology, the guidance and methods available for assessing and correcting the resulting bias are obscure. ObjectiveWe aim to design a simple modification to the Susceptible – Infected – Removed (SIR) model for estimating the fraction or proportion of reported infection cases. MethodsThe suggested modification involves rescaling of the classical SIR model producing its mathematically equivalent version with explicit dependence on the reporting parameter (true proportion of cases reported). We justify the rescaling using the phase plane analysis of the SIR model system and show how this rescaling parameter can be estimated from the data along with the other model parameters. ResultsWe demonstrate how the proposed method is cross-validated using simulated data with known disease cases and then apply it to two empirical reported data sets to estimate the fraction of reported cases in Missoula County, Montana, USA, using: (1) flu data for 2016–2017 and (2) COVID-19 data for fall of 2020. ConclusionsWe establish with the simulated and COVID-19 data that when most of the disease cases are presumed reported, the value of the additional reporting parameter in the modified SIR model is close or equal to one, so that the original SIR model is appropriate for data analysis. Conversely, the flu example shows that when the reporting parameter is close to zero, the original SIR model is not accurately estimating the usual rate parameters, and the re-scaled SIR model should be used. This research demonstrates the role of under-reporting of disease data and the importance of accounting for under-reporting when modeling simulated, endemic, and pandemic disease data. Correctly reporting the “true” number of disease cases will have downstream impacts on predictions of disease dynamics. A simple parameter adjustment to the SIR modeling framework can help alleviate bias and uncertainty around crucial epidemiological metrics (e.g.: basic disease reproduction number) and public health decision making.

A Bayesian model calibration framework for stochastic compartmental models with both time-varying and time-invariant parameters

We consider state and parameter estimation for compartmental models having both time-varying and time-invariant parameters. In this manuscript, we first detail a general Bayesian computational framework as a continuation of our previous work. Subsequently, this framework is specifically tailored to the susceptible-infectious-removed (SIR) model which describes a basic mechanism for the spread of infectious diseases through a system of coupled nonlinear differential equations. The SIR model consists of three states, namely, the susceptible, infectious, and removed compartments. The coupling among these states is controlled by two parameters, the infection rate and the recovery rate. The simplicity of the SIR model and similar compartmental models make them applicable to many classes of infectious diseases. However, the combined assumption of a deterministic model and time-invariance among the model parameters are two significant impediments which critically limit their use for long-term predictions. The tendency of certain model parameters to vary in time due to seasonal trends, non-pharmaceutical interventions, and other random effects necessitates a model that structurally permits the incorporation of such time-varying effects. Complementary to this, is the need for a robust mechanism for the estimation of the parameters of the resulting model from data. To this end, we consider an augmented state vector, which appends the time-varying parameters to the original system states whereby the time evolution of the time-varying parameters are driven by an artificial noise process in a standard manner. Distinguishing between time-varying and time-invariant parameters in this fashion limits the introduction of artificial dynamics into the system, and provides a robust, fully Bayesian approach for estimating the time-invariant system parameters as well as the elements of the process noise covariance matrix. This computational framework is implemented by leveraging the robustness of the Markov chain Monte Carlo algorithm permits the estimation of time-invariant parameters while nested nonlinear filters concurrently perform the joint estimation of the system states and time-varying parameters. We demonstrate performance of the framework by first considering a series of examples using synthetic data, followed by an exposition on public health data collected in the province of Ontario.

Understanding How Parasites from Farmed Fish May Influence Wild Fish Declines Using Epidemiological Modelling

Beside various fields of its applications, in this study epidemiological modelling was used to understand how parasites from farmed fish may cause wild fish declines. Two separate strategic models were constructed addressing the transmission of micro-parasites and macro-parasites between farmed and wild fish: A SIR (Susceptible-Infective-Removed) model for micro-parasite infections and a compartmental density-dependent model for macro-parasite infestations. The results indicated that parasites originated in wild fish populations, after infecting farmed fish can cause epizootics. Subsequently, these parasites can be transmitted from farmed to wild fish and might have negative impact on the dynamics of wild fish populations. Sensitivity analysis of the basic model parameters in both models showed that model parameters, which are influenced by abiotic factors and allow passive manipulation, such as pathogen specific transmission rate (β), pathogen specific transmission rate between infected farmed and susceptible wild fish (δ), the rate of production of infective stages by an adult parasite (λ) and transmission rate between host and parasite infective stages (β) are more sensitive compared to model parameters which encompass chemical control and fallowing. This emphasizes the importance of the preventive medicine rather than intervention procedures in aquaculture aiming at eradicating epizootics caused by parasites and protecting wild fish stocks.

Solving a Predictive Model of Infectious Disease in Epidemiology and Epizootiology by Assigning Scores to Individuals

Every mathematical solution to a problem corresponds to a model that more or less corresponds to reality. One of the many possibilities is the solution to epidemiological problems (processes) using the susceptible-infected-removed (SIR) model. Like any model, this model also has its advantages and benefits that allow us to close such a complicated reality as the origin and course of the epidemic into simple differential equations (DE) and through the model’s parameters modify it and compare it with reality. This is possible only in the case of a comprehensive understanding of reality in all its breadth and depth. This study focuses on another solution to the epidemiological or epizootiological processes based on the newly designed simulation, which assigns individuals a certain score in time intervals. In this case, the score from the simulation has a normal probability distribution with certain parameters N (µ, σ) in given time intervals. This score level also divides the given individuals into certain groups based on the given (selected) critical level. This determines whether individuals are with manifestations of the disease or without signs of the disease. In the study, the epidemic curve (EC) simulation results could be used to solve the current pandemic caused by COVID-19. It can be stated that the newly proposed model could be more suitable because it permanently confirms the agreement of experimental and expected frequencies.

A SIR-UC EPIDEMIC MODEL: THE ANALYSIS OF SUSCEPTIBLE-INFECTED-REMOVED (SIR) EPIDEMIC MODEL WITH THE COVERAGE OF HEALTH INSURANCE (UNCOVERED AND COVERED INDIVIDUALS)

Susceptible-Infected-Removed (SIR) model is a widely used epidemic model that simulates the spread of infectious diseases within a population. It classifies individuals into susceptible, infected, and removed states, with the number of individuals in each state being time-dependent variables denoted by S(t), I(t), and R(t), respectively. The model considers direct contact transmission between infected and susceptible individuals. In developed countries, some people cannot afford medical treatment. In contrary, the recovery rate of infected individual in the population is directly proportional to the number of people receiving medical treatment. Affordable health insurance increases the number of people receiving medical treatment thus insurance should be considered aspect in epidemic model. The main purpose of this research is to analyze the effect of insurance on the SIR epidemic model. This research classifies individuals in both S(t) and I(t) based on their insurance coverage status. This model assumes permanent immunity for R(t), thus it is unnecessary to classify individuals in this state based on their insurance coverage status because they do not spread the disease nor have potential to be re-infected. Numerical simulation is organized to find the effect of insurance in SIR model by analyzing the equilibrium point. The result based on the equilibrium point suggests that the insurance in SIR epidemic model: (1) decrease the I(t) because it accelerate the recovery rate; (2) decrease theR(t) because there is less infected people for recovery; (3) increase the S(t) because there is less infected people to transmit the disease, compared to the SIR model without the insurance.

Feedback control of the COVID-19 outbreak based on active disturbance rejection control

The outbreak of COVID-19 causes a serious threat to human health and life around the world and puts enormous pressure on the healthcare system. The lockdown policy has effectively reduced the number of cases and suppressed the spread of the COVID-19 epidemic, but it also requires high social and economic costs. In this paper, we aim to use feedback control to help decision-makers establish lockdown policies, which can effectively constrain the spread of the COVID-19 pandemic with minimal financial loss. The time-dependent susceptible-infected-removed (SIR) model is used for the dynamics of the COVID-19 pandemic. The feedback control is based on a modified nonlinear active disturbance rejection controller (ADRC) that includes modified nonlinear extended state and nonlinear state error feedback with parameters tuned by particle swarm optimization, and the performances are compared with a well-known proportional-–integral–-derivative (PID) controller. The final simulation results show that the modified nonlinear ADRC has better performances and is more robust against uncertainties in the parameters of the epidemiological model.

Approaching epidemiological dynamics of COVID-19 with physics-informed neural networks

A physics-informed neural network (PINN) embedded with the susceptible–infected–removed (SIR) model is devised to understand the temporal evolution dynamics of infectious diseases. Firstly, the effectiveness of this approach is demonstrated on synthetic data as generated from the numerical solution of the susceptible–asymptomatic–infected–recovered–dead (SAIRD) model. Then, the method is applied to COVID-19 data reported for Germany and shows that it can accurately identify and predict virus spread trends. The results indicate that an incomplete physics-informed model can approach more complicated dynamics efficiently. Thus, the present work demonstrates the high potential of using machine learning methods, e.g., PINNs, to study and predict epidemic dynamics in combination with compartmental models.

The Identification of Influential Nodes Based on Neighborhood Information in Asymmetric Networks

Identifying influential nodes, with pivotal roles in practical domains like epidemic management, social information dissemination optimization, and transportation network security enhancement, is a critical research focus in complex network analysis. Researchers have long strived for rapid and precise identification approaches for these influential nodes that are significantly shaping network structures and functions. The recently developed SPON (sum of proportion of neighbors) method integrates information from the three-hop neighborhood of each node, proving more efficient and accurate in identifying influential nodes than traditional methods. However, SPON overlooks the heterogeneity of neighbor information, derived from the asymmetry properties of natural networks, leading to its lower accuracy in identifying essential nodes. To sustain the efficiency of the SPON method pertaining to the local method, as opposed to global approaches, we propose an improved local approach, called the SSPN (sum of the structural proportion of neighbors), adapted from the SPON method. The SSPN method classifies neighbors based on the h-index values of nodes, emphasizing the diversity of asymmetric neighbor structure information by considering the local clustering coefficient and addressing the accuracy limitations of the SPON method. To test the performance of the SSPN, we conducted simulation experiments on six real networks using the Susceptible–Infected–Removed (SIR) model. Our method demonstrates superior monotonicity, ranking accuracy, and robustness compared to seven benchmarks. These findings are valuable for developing effective methods to discover and safeguard influential nodes within complex networked systems.

The probability of epidemic burnout in the stochastic SIR model with vital dynamics

We present an approach to computing the probability of epidemic "burnout," i.e., the probability that a newly emergent pathogen will go extinct after a major epidemic. Our analysis is based on the standard stochastic formulation of the Susceptible-Infectious-Removed (SIR) epidemic model including host demography (births and deaths) and corresponds to the standard SIR ordinary differential equations (ODEs) in the infinite population limit. Exploiting a boundary layer approximation to the ODEs and a birth-death process approximation to the stochastic dynamics within the boundary layer, we derive convenient, fully analytical approximations for the burnout probability. We demonstrate-by comparing with computationally demanding individual-based stochastic simulations and with semi-analytical approximations derived previously-that our fully analytical approximations are highly accurate for biologically plausible parameters. We show that the probability of burnout always decreases with increased mean infectious period. However, for typical biological parameters, there is a relevant local minimum in the probability of persistence as a function of the basic reproduction number [Formula: see text]. For the shortest infectious periods, persistence is least likely if [Formula: see text]; for longer infectious periods, the minimum point decreases to [Formula: see text]. For typical acute immunizing infections in human populations of realistic size, our analysis of the SIR model shows that burnout is almost certain in a well-mixed population, implying that susceptible recruitment through births is insufficient on its own to explain disease persistence.