Susceptible-exposed-infectious-recovered Model Research Articles

Infectious Disease Modeling

Infectious diseases pose a persistent challenge to public health worldwide. Recent global health crises, such as the COVID-19 pandemic and Ebola outbreaks, have underscored the vital role of infectious disease modeling in guiding public health policy and response. Infectious disease modeling is a critical tool for society, informing risk mitigation measures, prompting timely interventions, and aiding preparedness for healthcare delivery systems. This article synthesizes the current landscape of infectious disease modeling, emphasizing the integration of statistical methods in understanding and predicting the spread of infectious diseases. We begin by examining the historical context and the foundational models that have shaped the field, such as the SIR (susceptible, infectious, recovered) and SEIR (susceptible, exposed, infectious, recovered) models. Subsequently, we delve into the methodological innovations that have arisen, including stochastic modeling, network-based approaches, and the use of big data analytics. We also explore the integration of machine learning techniques in enhancing model accuracy and responsiveness. The review identifies the challenges of parameter estimation, model validation, and the incorporation of real-time data streams. Moreover, we discuss the ethical implications of modeling, such as privacy concerns and the communication of risk. The article concludes by discussing future directions for research, highlighting the need for data integration and interdisciplinary collaboration for advancing infectious disease modeling.

Design of a Simulation Model for the Diagnosis of Classical Swine Fever Virus in Ecuadorian Farms

Classical swine fever (CSF) is a disease that slows down animal production and international trade; therefore, its identification is key in pig farms to take the relevant health measures. Therefore, the objective of this research was to design a Susceptible-Exposed-Infected-Recovered (SEIR) simulation model to carry out epidemiological modeling for the identification of outbreaks of classical swine fever in the Sierra Region of Ecuador, using Python software and historical data on incidences of this disease in the provinces of the Ecuadorian highlands, considering the variables pig population, initial number of exposed pigs, initial number of infected, number of pigs removed, contagion rate (α), transmission rate (β), and recovery rate (γ). The results show that the SEIR model allowed us to determine that the population of susceptible (healthy) pigs decreases over time until reaching zero. This decrease in susceptibility occurred during the first 15 days, which shows that this is the time necessary to infect the entire population with an infected person. Therefore, the exposed population increases during the 15 days that the total infection process lasts and then decreases. It is also identified that throughout these five years of analysis of the past, it has been increasing from 2015 to 2019, which hurt the yields and productivity of pig farms in the Ecuadorian mountains.

Identification of Critical Nodes for Delay Propagation in Susceptible-Exposed-Infected-Recovered (SEIR) and Genetic Algorithm (GA) Route Networks

In response to the challenges associated with forecasting the trajectory of flight delay propagation, pinpointing pivotal nodes within the route network, and the substantial costs involved in enhancing operational efficiency, this study introduces an innovative approach to identifying critical nodes that influence delay propagation across route networks. The methodology commences by establishing a route network model for East China, leveraging the principles of complex network theory. It then incorporates the SEIR (Susceptible-Exposed-Infected-Recovered) model, typically used for analyzing the dynamics of infectious disease spread, to examine the propagation of delays between routes. Subsequently, the approach employs a GA to identify key nodes, which are then compared against those identified by network topology indices. The simulation outcomes demonstrate that the GA’s identification of key nodes offers superior insights into the overall network’s susceptibility to infection, thereby presenting operational managers with novel perspectives for analyzing the spread of flight delays.

Numerical Simulation of SEIR Model for COVID-19 Infection

One of the most basic models in epidemiology, the SEIR (Susceptible-Exposed-Infectious-Recovered) model explains how viral infections spread through communities. This study analyzes the SEIR model's differential equations to learn more about its dynamic behaviors. This study discusses the 2019 corona virus disease (COVID-19) epidemic model using numerical methods of susceptible exposed infected recovered (SEIR). A numerical description of the notion is provided using two numerical approaches, including forward Euler and RK-4 approaches. The subplots of SEIR model are drawn by ode 45 commands. The stability of disease free equilibrium and Endemic equilibrium points are depicted. The significance of comprehending the interaction between epidemiological variables and population dynamics in developing efficient public health treatments is brought to light in this study, which investigates the consequences of these equations on the transmission and management of infectious diseases. Insights into the dynamics of illness transmission and potential measures for mitigating its effects are presented through the use of mathematical analysis and computational simulations. Jagannath University Journal of Science, Volume 11, Number 1, June 2024, pp. 172−185

Optimal control strategies for infectious disease management: Integrating differential game theory with the SEIR model

The rapid spread of infectious diseases poses a critical threat to global public health. Traditional frameworks, such as the Susceptible–Exposed–Infectious–Recovered (SEIR) model, have been crucial in elucidating disease dynamics. Nonetheless, these models frequently overlook the strategic interactions between public health authorities and individuals. This research extends the classic SEIR model by incorporating differential game theory to analyze optimal control strategies. By modeling the conflicting objectives of public health authorities aiming to minimize infection rates and intervention costs, and individuals seeking to reduce their infection risk and inconvenience, we derive a Nash equilibrium that provides a balanced approach to disease management. Using Picard’s iterative method, we solve the extended model to determine dynamic, optimal control strategies, revealing oscillatory behavior in public health interventions and individual preventive measures. This comprehensive approach offers valuable insights into the dynamic interactions essential for effective infectious disease control.

Modeling of Malware Propagation Under the Clustering Approach in Scale‐Free Networks

ABSTRACTIn this paper, we present an innovative malware propagation model that combines epidemic spread and clustering techniques, specifically designed for scale‐free networks. The proposed model builds upon the susceptible–exposed–infected–recovered (SEIR) framework, effectively simulating the dissemination of malware across the network. Our research demonstrates a notable reduction in the rate of malware transmission compared to the traditional SEIR model, with this improvement in containment being attributed to the incorporation of clustering methodologies. We also calculate the basic reproduction ratio (R0) for the proposed model, which offers valuable insights into the potential consequences of malware outbreaks within the network. By exploring variations in key parameters, we deepen our understanding of the model's behavior under different conditions. Furthermore, we evaluate the role of clustering in mitigating malware spread, highlighting its significant effectiveness in reducing the overall impact of infections.

Modeling the Spatial Dynamics and Human Mobility in Zika Virus Transmission: A Review

Spatial dynamics and human mobility significantly influence the transmission dynamics of vector-borne diseases like Zika virus. This paper reviews advancements in mathematical modeling that integrate spatial factors and human movement to enhance our understanding of disease transmission dynamics. Traditional SEIR (Susceptible-Exposed-Infectious-Recovered) models have been foundational but lack spatial heterogeneity and human mobility considerations. Recent studies have addressed these limitations by developing spatially explicit models that incorporate local interactions, environmental conditions, and human mobility patterns. By synthesizing findings from these studies, we identify strengths, limitations, and future research directions for improving predictive modeling of Zika virus transmission. Key insights include the amplifying effect of local interactions on disease spread and the critical role of human mobility networks in shaping transmission pathways. Addressing remaining challenges, such as refining spatial modeling techniques and integrating real-time data sources, will enhance the accuracy and applicability of spatial disease models in informing public health strategies.

Performance analysis of mathematical methods used to forecast the 2022 New York City Mpox outbreak.

In mid-2022, New York City (NYC) became the epicenter of the US mpox outbreak. We provided real-time mpox case forecasts to the NYC Department of Health and Mental Hygiene to aid in outbreak response. Forecasting methodologies evolved as the epidemic progressed. Initially, lacking knowledge of at-risk population size, we used exponential growth models to forecast cases. Once exponential growth slowed, we used a Susceptible-Exposed-Infectious-Recovered (SEIR) model. Retrospectively, we explored if forecasts could have been improved using an SEIR model in place of our early exponential growth model, with or without knowing the case detection rate. Early forecasts from exponential growth models performed poorly, as 2-week mean absolute error (MAE) grew from 53 cases/week (July 1-14)to 457 cases/week (July 15-28).However, when exponential growth slowed, providing insight into susceptible population size, an SEIR model was able to accurately predict the remainder of the outbreak (7-week MAE: 13.4 cases/week). Retrospectively, we found there was not enough known about the epidemiological characteristics of the outbreak to parameterize an SEIR model early on. However, if the at-risk population and case detection rate were known, an SEIR model could have improved accuracy over exponential growth models early in the outbreak.

How to correctly fit an SIR model to data from an SEIR model?

In epidemiology, realistic disease dynamics often require Susceptible-Exposed-Infected-Recovered (SEIR)-like models because they account for incubation periods before individuals become infectious. However, for the sake of analytical tractability, simpler Susceptible-Infected-Recovered (SIR) models are commonly used, despite their lack of biological realism. Bridging these models is crucial for accurately estimating parameters and fitting models to observed data, particularly in population-level studies of infectious diseases.This paper investigates stochastic versions of the SEIR and SIR frameworks and demonstrates that the SEIR model can be effectively approximated by a SIR model with time-dependent infection and recovery rates. The validity of this approximation is supported by the derivation of a large-population Functional Law of Large Numbers (FLLN) limit and a finite-population concentration inequality.To apply this approximation in practice, the paper introduces a parameter inference methodology based on the Dynamic Survival Analysis (DSA) survival analysis framework. This method enables the fitting of the SIR model to data simulated from the more complex SEIR dynamics, as illustrated through simulated experiments.

A cost-effectiveness analysis of reduced viral transmission with baloxavir marboxil versus oseltamivir or no treatment for seasonal and pandemic influenza management in the United Kingdom

ABSTRACT Background Baloxavir marboxil is an oral, single-dose, cap-dependent endonuclease inhibitor that reduces the duration of influenza symptoms and rapidly stops viral shedding. We developed a susceptible, exposed, infected, recovered (SEIR) model to inform a cost-effectiveness model (CEM) of baloxavir versus oseltamivir or no antiviral treatment in the UK. Research design and methods The SEIR model estimated the attack rates among otherwise healthy and high-risk individuals in seasonal and pandemic settings. The CEM assumed that a proportion of infected patients would receive antiviral treatment. Results were reported at the population level (per 10,000 at risk of infection). Results The SEIR model estimated greater reductions in infections with baloxavir. In a seasonal setting, baloxavir provided incremental cost-effectiveness ratios (ICERs) of £1884 per quality-adjusted life-year (QALY) gained versus oseltamivir and a dominant cost-effectiveness position versus no antiviral treatment in the total population; ICERs of £2574/QALY versus oseltamivir and £128/QALY versus no antiviral treatment were seen in the high-risk population. Baloxavir was also cost-effective versus oseltamivir or no antiviral treatment and reduced population-level health system occupancy concerns during a pandemic. Conclusion Baloxavir treatment resulted in the fewest influenza cases and was cost-effective versus oseltamivir or no antiviral treatment from a UK National Health Service perspective.

Global dynamics and threshold behavior of an SEIR epidemic model with nonlocal diffusion

This paper studies the global dynamics of an SEIR (Susceptible–Exposed–Infectious–Recovered) model with nonlocal diffusion. We show the model’s well-posedness, proving the solutions’ existence, uniqueness, and positivity, along with a disease-free equilibrium. Next, we prove that the model admits the global threshold dynamics in terms of the basic reproduction number R0, defined as the spectral radius of the next-generation operator. We show that the solution map has a global compact attractor, offering insights into long-term dynamics. In particular, the analysis shows that for R0<1, the disease-free equilibrium is globally stable. Using the persistence theory, we show that there is an endemic equilibrium point for R0>1. Moreover, by constructing an appropriate Lyapunov function, we establish the global stability of the unique endemic equilibrium in two distinct scenarios.

Evaluating the Public Health and Health Economic Impacts of Baloxavir Marboxil and Oseltamivir for Influenza Pandemic Control in China: A Cost-Effectiveness Analysis Using a Linked Dynamic Transmission-Economic Evaluation Model.

Pandemic influenza poses a recurring threat to public health. Antiviral drugs are vital in combating influenza pandemics. Baloxavir marboxil (BXM) is a novel agent that provides clinical and public health benefits in influenza treatment. We constructed a linked dynamic transmission-economic evaluation model combining a modified susceptible-exposed-infected-recovered (SEIR) model and a decision tree model to evaluate the cost-effectiveness of adding BXM to oseltamivir in China's influenza pandemic scenario. The cost-effectiveness was evaluated for the general population from the Chinese healthcare system perspective, although the users of BXM and oseltamivir were influenza-infected persons. The SEIR model simulated the transmission dynamics, dividing the population into four compartments: susceptible, exposed, infected, and recovered, while the decision tree model assessed disease severity and costs. We utilized data from clinical trials and observational studies in the literature to parameterize the models. Costs were based on 2021 CN¥ and not discounted due to a short time-frame of one year in the model. One-way, two-way, and probabilistic sensitivity analyses were also conducted. The integrated model demonstrated that adding BXM to treatment choices reduced the cumulative incidence of infection from 49.49% to 43.26% and increased quality-adjusted life years (QALYs) by 0.00021 per person compared with oseltamivir alone in the base-case scenario. The intervention also amounted to a positive net monetary benefit of CN¥77.85 per person at the willingness to pay of CN¥80,976 per QALY. Sensitivity analysis confirmed the robustness of these findings, with consistent results across varied key parameters and assumptions. Adding BXM to treatment choices instead of only treating with oseltamivir for influenza pandemic control in China appears to be cost-effective compared with oseltamivir alone. The dual-agent strategy not only enhances population health outcomes and conserves resources, but also mitigates influenza transmission and alleviates healthcare burden.

Comparison of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) for Estimating the Susceptible-Exposed-Infected-Recovered (SEIR) Model Parameter Values

Background: The most commonly used mathematical model for analyzing disease spread is the Susceptible-Exposed-Infected-Recovered (SEIR) model. Moreover, the dynamics of the SEIR model depend on several factors, such as the parameter values. Objective: This study aimed to compare two optimization methods, namely genetic algorithm (GA) and particle swarm optimization (PSO), in estimating the SEIR model parameter values, such as the infection, transition, recovery, and death rates. Methods: GA and PSO algorithms were compared to estimate parameter values of the SEIR model. The fitness value was calculated from the error between the actual data of cumulative positive COVID-19 cases and the numerical data of cases from the solution of the SEIR COVID-19 model. Furthermore, the numerical solution of the COVID-19 model was calculated using the fourth-order Runge-Kutta algorithm (RK-4), while the actual data were obtained from the cumulative dataset of positive COVID-19 cases in the province of Jakarta, Indonesia. Two datasets were then used to compare the success of each algorithm, namely, Dataset 1, representing the initial interval for the spread of COVID-19, and Dataset 2, representing an interval where there was a high increase in COVID-19 cases. Results: Four parameters were estimated, namely the infection rate, transition rate, recovery rate, and death rate, due to disease. In Dataset 1, the smallest error of GA method, namely 8.9%, occurred when the value of , while the numerical error of PSO was 7.5%. In Dataset 2, the smallest error of GA method, namely 31.21%, occurred when , while the numerical error of PSO was 3.46%. Conclusion: Based on the parameter estimation results for Datasets 1 and 2, PSO had better fitting results than GA. This showed PSO was more robust to the provided datasets and could better adapt to the trends of the COVID-19 epidemic. Keywords: Genetic algorithm, Particle swarm optimization, SEIR model, COVID-19, Parameter estimation.

Nonrepresentativeness of Human Mobility Data and its Impact on Modeling Dynamics of the COVID-19 Pandemic: Systematic Evaluation.

In recent years, a range of novel smartphone-derived data streams about human mobility have become available on a near-real-time basis. These data have been used, for example, to perform traffic forecasting and epidemic modeling. During the COVID-19 pandemic in particular, human travel behavior has been considered a key component of epidemiological modeling to provide more reliable estimates about the volumes of the pandemic's importation and transmission routes, or to identify hot spots. However, nearly universally in the literature, the representativeness of these data, how they relate to the underlying real-world human mobility, has been overlooked. This disconnect between data and reality is especially relevant in the case of socially disadvantaged minorities. The objective of this study is to illustrate the nonrepresentativeness of data on human mobility and the impact of this nonrepresentativeness on modeling dynamics of the epidemic. This study systematically evaluates how real-world travel flows differ from census-based estimations, especially in the case of socially disadvantaged minorities, such as older adults and women, and further measures biases introduced by this difference in epidemiological studies. To understand the demographic composition of population movements, a nationwide mobility data set from 318 million mobile phone users in China from January 1 to February 29, 2020, was curated. Specifically, we quantified the disparity in the population composition between actual migrations and resident composition according to census data, and shows how this nonrepresentativeness impacts epidemiological modeling by constructing an age-structured SEIR (Susceptible-Exposed-Infected- Recovered) model of COVID-19 transmission. We found a significant difference in the demographic composition between those who travel and the overall population. In the population flows, 59% (n=20,067,526) of travelers are young and 36% (n=12,210,565) of them are middle-aged (P<.001), which is completely different from the overall adult population composition of China (where 36% of individuals are young and 40% of them are middle-aged). This difference would introduce a striking bias in epidemiological studies: the estimation of maximum daily infections differs nearly 3 times, and the peak time has a large gap of 46 days. The difference between actual migrations and resident composition strongly impacts outcomes of epidemiological forecasts, which typically assume that flows represent underlying demographics. Our findings imply that it is necessary to measure and quantify the inherent biases related to nonrepresentativeness for accurate epidemiological surveillance and forecasting.

Dynamic analysis and optimal control of knowledge diffusion model in regional innovation ecosystem under digitalization

Knowledge diffusion in regional innovation ecosystems is an important factor that influences the regional innovation efficiency. In regional innovation ecosystems under digital empowerment, the knowledge diffusion enables the optimal allocation of innovation resources and promotes the sustainable development and ecological evolution of regional innovation ecosystems. In this paper, a SEIR (Susceptible–Exposed–Infected–Recovered) model is proposed for knowledge diffusion in regional innovation ecosystems under digitization. The basic reproduction number of the proposed model is calculated and its stability is validated. Finally, the expressions for the optimal control system and the optimal control parameters are presented. According to the research conclusions of this paper, the knowledge-diffusion ability of innovation agents in an innovation ecosystem affects the knowledge diffusion in a system; the contact rate between innovation agents affects the efficiency of knowledge diffusion in the system and the structure of the system; the digital transmission ability of innovation agents affects the breadth of knowledge diffusion in the system; and the self-learning ability of innovation agents affects the efficiency of knowledge diffusion in the system.The digital technologies help heterogeneous innovation agents in regional innovation ecosystems to break down the knowledge silos. At the same time, the digital technologies enhance the ability of innovation agents to absorb and learn knowledge in regional innovation ecosystems under digitization, thereby increasing the infection rate of knowledge diffusion in such systems.These conclusions extend the theoretical boundaries of innovation ecosystems and knowledge diffusion and offer management implications for enterprises and governments in decision-making.

A Novel Extended Susceptible, Exposed, Infected, and Recovered Model with Surveys for Analysis of COVID-19 Pandemic in Rajasthan.

The impact of COVID-19 on human life has been catastrophic. It is the greatest crisis that humankind has ever faced. It already caused over 21 million confirmed cases and 758,000 deaths as of July 2021. Modeling frameworks, underlying assumptions, available datasets, and the region/time frame being modeled, predictions are possible, but the projections might vary widely, making it difficult to rely on one model universally way. This article presents the prediction and forecasting technique for COVID-19, using the widely adopted susceptible-exposed-infected-recovered (SEIR) model. The modified SEIR model is presented to model the pandemic to represent an open system where the mass movement of the population is considered. Spreading patterns of the pandemic over time, in actual and as per the model, are compared to check the authenticity of the model.

Simulations for the Susceptible-Exposed-Infected-Recovered (SEIR) Model in the Forecast of Epidemic Outbreak

Mathematical modelling based on the compartmental Susceptible – Exposed – Infected - Recovered (SEIR) model is proposed in this paper to study the pandemic outbreak. In addition, simulations from both the deterministic approach as well as the stochastic approach are implemented to validate the present study. Among each state, the transitions between different categories are simulated by using various graph models including the complete graph, the steady Erdos-Renyi graph, as well as the varying Erdos-Renyi graph. The related parameters for the SEIR model are chosen from available literature and the effect of some other factors such as the inflow or outflow of travellers in a city as well as the impact of vaccination rate is explored. Furthermore, the difference between the simulation results coming from the deterministic SEIR model and the stochastic SEIR one is examined to check the availability of the present simulation. It is found that, the stochastic simulation based on the complete graph is more consistent with the deterministic SEIR model.

Multi-feature SEIR model for epidemic analysis and vaccine prioritization.

The SEIR (susceptible-exposed-infected-recovered) model has become a valuable tool for studying infectious disease dynamics and predicting the spread of diseases, particularly concerning the COVID pandemic. However, existing models often oversimplify population characteristics and fail to account for differences in disease sensitivity and social contact rates that can vary significantly among individuals. To address these limitations, we have developed a new multi-feature SEIR model that considers the heterogeneity of health conditions (disease sensitivity) and social activity levels (contact rates) among populations affected by infectious diseases. Our model has been validated using the data of the confirmed COVID cases in Allegheny County (Pennsylvania, USA) and Hamilton County (Ohio, USA). The results demonstrate that our model outperforms traditional SEIR models regarding predictive accuracy. In addition, we have used our multi-feature SEIR model to propose and evaluate different vaccine prioritization strategies tailored to the characteristics of heterogeneous populations. We have formulated optimization problems to determine effective vaccine distribution strategies. We have designed extensive numerical simulations to compare vaccine distribution strategies in different scenarios. Overall, our multi-feature SEIR model enhances the existing models and provides a more accurate picture of disease dynamics. It can help to inform public health interventions during pandemics/epidemics.

Estimation of the Impact of Vaccination Intervention on Recovered Coronavirus Patients

This work estimated the impact of vaccination intervention on coronavirus patients who have recovered from the disease and the vulnerability index of the recovered population due to the impact of vaccine was also investigated. This work adopted a numerical solution to study the continuous dynamical system of linear first order differential equations describing a SEIR (Susceptible, Exposed, Infected, Recovered) model on the spread of Coronavirus Disease – 2019 (COVID-19). To tackle this problem, MATLAB ordinary differential equation of order 45 (ODE45) numerical method was adopted for the analysis. The vulnerability index of the recovered population was low due to the impact of vaccine meaning that the recovered population will gain immunity and they will not be re-infected. The study recommended that coronavirus patients who have recovered from the disease should ensure that they have vaccination administered to them to avoid re-occurrence of the virus attack as an intervention strategy.

COVID-19 in Saudi Arabia: Real Data and Simulation for Impact Prediction - A Case Study

The start of the COVID-19 pandemic in early 2020 has caused trouble all over the world. This contagious disease is mostly spread by people, and it spreads much faster than other flu viruses that have been found before. Although vaccines have been discovered and are functional, it will still be the greatest challenge to conquer this disease. To effectively respond to this unprecedented crisis and save human lives from other infectious diseases in the future, it is crucial to better understand how the virus is transmitted from one host to another and how future zones of contagion can be anticipated. Several waves of infection have hit nations worldwide for almost the last four years, and governments have implemented necessary measures to tackle the spread of the virus. However, mathematical modeling has emerged as a powerful tool to inform decision-making, allowing for the prediction of COVID-19’s effects. In this research article, we investigate the impact of COVID-19 in Saudi Arabia using the three most commonly used mathematical models: the classic SIR (Susceptible-Infected-Recovered) model, the extended SEIR (Susceptible-Exposed-Infected-Recovered) model, and the advanced fractional-order models using freely available real recorded data for research. By incorporating actual data from Saudi Arabia and utilizing three simulation techniques, we strive to provide valuable insights into the dynamics of the pandemic and aid in the formulation of effective strategies to control its spread in Saudi Arabia.