Susceptible-exposed-infectious-recovered Model Research Articles

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.

Simulating the impact of optimized prevention and control measures on the transmission of monkeypox in the United States: A model-based study.

This study aimed to develop a modified susceptible-exposed-infected-recovered (SEIR) model to evaluate monkeypox epidemics in the United States and explore more optimized prevention and control measures. To further assess the impact of public health measures on the transmission of monkeypox, different intervention scenarios were developed based on the classic SEIR model, considering reducing contact, enhancing vaccination, diagnosis delay, and environmental transmission risk, respectively. We evaluated the impact of different measures by simulating their spread in different scenarios. During the simulation period, 8709 people were infected with monkeypox. The simulation analysis showed that: (1) the most effective measures to control monkeypox transmission during the early stage of the epidemic were reducing contact and enhancing vaccination, with cumulative infections at 51.20% and 41.90% of baseline levels, respectively; (2) shortening diagnosis time would delay the peak time of the epidemic by 96 days; and (3) the risk of environmental transmission of monkeypox virus was relatively low. This study indirectly proved the effectiveness of the prevention and control measures, such as reducing contact, enhancing vaccination, shortening diagnosis time, and low risk of environmental transmission, which also provided an important reference and containment experience for nonepidemic countries.

Exploring of Homotopy Perturbation Method (HPM) for Solving Spread of COVID-19

This article discusses the solution to the non-linear differential equation system for the spread of COVID19 with SEIR (Susceptible, Exposed, Infected, Recovered) model using the Homotopy Perturbation Method. Specifically, this article examines the impact of moving the recovered subpopulation back to the susceptible subpopulation on the spread of COVID-19 in the city of Medan. The data used is real data for the city of Medan in 2021. The results of constructing a model for the spread of COVID-19 were analyzed to obtain a disease-free critical point. By using the Next Generation Matrix method, the Basic Reproduction number R0 = 4.61 is obtained, this indicates that COVID-19 is still possible to spread in Medan City. Simulations using the Homotopy Perturbation Method numerical approach and the results compared with the Runge Kutte Order 4 method show results that accurately describe the dynamics of the spread of COVID-19 in Medan City. The very small error indicates that the Homotopy Perturbation Method is very suitable for use in solving non-linear differential equation systems, especially in the SEIRS model of the spread of COVID-19. The simulation results show that the impact of the movement of recovered sub-populations to susceptible sub-populations results in accelerated transmission of COVID-19. The greater the number of movements higher the rate of spread of COVID-19.

Topic and Trend Analysis of Weibo Discussions About COVID-19 Medications Before and After China's Exit from the Zero-COVID Policy: Retrospective Infoveillance Study.

After 3 years of its zero-COVID policy, China lifted its stringent pandemic control measures with the announcement of the 10 new measures on December 7, 2022. Existing estimates suggest 90%-97% of the total population was infected during December. This change created a massive demand for COVID-19 medications and treatments, either modern medicines or traditional Chinese medicine (TCM). This study aimed to explore (1) how China's exit from the zero-COVID policy impacted media and the public's attention to COVID-19 medications; (2) how social COVID-19 medication discussions were related to existing model estimates of daily cases during that period; (3) what the diversified themes and topics were and how they changed and developed from November 1 to December 31, 2022; and (4) which topics about COVID-19 medications were focused on by mainstream and self-media accounts during the exit. The answers to these questions could help us better understand the consequences of exit strategies and explore the utilities of Sina Weibo data for future infoveillance studies. Using a scrapper for data retrieval and the structural topic modeling (STM) algorithm for analysis, this study built 3 topic models (all data, before a policy change, and after a policy change) of relevant discussions on the Chinese social media platform Weibo. We compared topic distributions against existing estimates of daily cases and between models before and after the change. We also compared proportions of weibos published by mainstream versus self-media accounts over time on different topics. We found that Weibo discussions shifted sharply from concerns of social risks (case tracking, governmental regulations, etc) to those of personal risks (symptoms, purchases, etc) surrounding COVID-19 infection after the exit from the zero-COVID policy. Weibo topics of "symptom sharing" and "purchase and shortage" of modern medicines correlated more strongly with existing susceptible-exposed-infected-recovered (SEIR) model estimates compared to "TCM formulae" and other topics. During the exit, mainstream accounts showed efforts to specifically engage in topics related to worldwide pandemic control policy comparison and regulations about import and reimbursement of medications. The exit from the zero-COVID policy in China was accompanied by a sudden increase in social media discussions about COVID-19 medications, the demand for which substantially increased after the exit. A large proportion of Weibo discussions were emotional and expressed increased risk concerns over medication shortage, unavailability, and delay in delivery. Topic keywords showed that self-medication was sometimes practiced alone or with unprofessional help from others, while mainstream accounts also tried to provide certain medication instructions. Of the 16 topics identified in all 3 STM models, only "symptom sharing" and "purchase and shortage" showed a considerable correlation with SEIR model estimates of daily cases. Future studies could consider topic exploration before conducting predictive infoveillance analysis, even with narrowly defined search criteria with Weibo data.

A COVID-19 vaccine effectiveness model using the susceptible-exposed-infectious-recovered model

Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) caused the start of the COVID-19 outbreak in the world, including Malaysia and Thailand. This study identifies the trend of the COVID-19 outbreak before and after the vaccination campaign by using the Susceptible-Exposed-Infectious-Recovered (SEIR) and Susceptible-Exposed-Infectious-Recovered-Vaccinated (SEIRV) models. Moreover, we predict the daily reported death and recovery cases using the SEIR model and Holt's linear trend method and then evaluate their performance. The data used in this study is real data from Malaysia and Thailand. The SEIRV model provides a comprehensive view of the efficacy of COVID-19 vaccinations in curbing the COVID-19 outbreak. This research reveals that the SEIR model outperforms Holt's linear trend method in predicting daily reported cases.

Optimal logistics scheduling with dynamic information in emergency response: Case studies for humanitarian objectives

The mathematical model of infectious disease is a typical problem in mathematical modeling, and the common infectious disease models include the susceptible-infected (SI) model, the susceptible-infected-recovered model (SIR), the susceptible-infected-recovered-susceptible model (SIRS) and the susceptible-exposed-infected-recovered (SEIR) model. These models can be used to predict the impact of regional return to work after the epidemic. In this paper, we use the SEIR model to solve the dynamic medicine demand information in humanitarian relief phase. A multistage mixed integer programming model for the humanitarian logistics and transport resource is proposed. The objective functions of the model include delay cost and minimum running time in the time-space network. The model describes that how to distribute and deliver medicine resources from supply locations to demand locations with an efficient and lower-cost way through a transportation network. The linear programming problem is solved by the proposed Benders decomposition algorithm. Finally, we use two cases to calculate model and algorithm. The results of the case prove the validity of the model and algorithm.

Susceptible exposed infectious recovered-machine learning for COVID-19 prediction in Saudi Arabia

<span lang="EN-US">Susceptible exposed infectious recovered (SEIR) is among the epidemiological models used in forecasting the spread of disease in large populations. SEIR is a fitting model for coronavirus disease (COVID-19) spread prediction. Somehow, in its original form, SEIR could not measure the impact of lockdowns. So, in the SEIR equations system utilized in this study, a variable was included to evaluate the impact of varying levels of social distance on the transmission of COVID-19. Additionally, we applied artificial intelligence utilizing the deep neural network machine learning (ML) technique. On the initial spread data for Saudi Arabia that were available up to June 25<sup>th</sup>, 2021, this improved SEIR model was used. The study shows possible infection to around 3.1 million persons without lockdown in Saudi Arabia at the peak of spread, which lasts for about 3 months beginning from the lockdown date (March 21<sup>st</sup>). On the other hand, the Kingdom's current partial lockdown policy was estimated to cut the estimated number of infections to 0.5 million over nine months. The data shows that stricter lockdowns may successfully flatten the COVID-19 graph curve in Saudi Arabia. We successfully predicted the COVID-19 epidemic's peaks and sizes using our modified deep neural network (DNN) and SEIR model.</span>

NLSI: An innovative method to locate epidemic sources on the SEIR propagation model.

Epidemics pose a significant threat to societal development. Accurately and swiftly identifying the source of an outbreak is crucial for controlling the spread of an epidemic and minimizing its impact. However, existing research on locating epidemic sources often overlooks the fact that epidemics have an incubation period and fails to consider social behaviors like self-isolation during the spread of the epidemic. In this study, we first take into account isolation behavior and introduce the Susceptible-Exposed-Infected-Recovered (SEIR) propagation model to simulate the spread of epidemics. As the epidemic reaches a certain threshold, government agencies or hospitals will report the IDs of some infected individuals and the time when symptoms first appear. The reported individuals, along with their first and second-order neighbors, are then isolated. Using the moment of symptom onset reported by the isolated individuals, we propose a node-level classification method and subsequently develop the node-level-based source identification (NLSI) algorithm. Extensive experiments demonstrate that the NLSI algorithm is capable of solving the source identification problem for single and multiple sources under the SEIR propagation model. We find that the source identification accuracy is higher when the infection rate is lower, and a sparse network structure is beneficial to source localization. Furthermore, we discover that the length of the isolation period has little impact on source localization, while the length of the incubation period significantly affects the accuracy of source localization. This research offers a novel approach for identifying the origin of the epidemic associated with our defined SEIR model.

An algebraic formula, deep learning and a novel SEIR-type model for the COVID-19 pandemic.

The most extensively used mathematical models in epidemiology are the susceptible-exposed-infectious-recovered (SEIR) type models with constant coefficients. For the first wave of the COVID-19 epidemic, such models predict that at large times equilibrium is reached exponentially. However, epidemiological data from Europe suggest that this approach is algebraic. Indeed, accurate long-term predictions have been obtained via a forecasting model only if it uses an algebraic as opposed to the standard exponential formula. In this work, by allowing those parameters of the SEIR model that reflect behavioural aspects (e.g. spatial distancing) to vary nonlinearly with the extent of the epidemic, we construct a model which exhibits asymptoticly algebraic behaviour. Interestingly, the emerging power law is consistent with the typical dynamics observed in various social settings. In addition, using reliable epidemiological data, we solve in a numerically robust way the inverse problem of determining all model parameters characterizing our novel model. Finally, using deep learning, we demonstrate that the algebraic forecasting model used earlier is optimal.

Computation of the Exact Forms of Waves for a Set of Differential Equations Associated with the SEIR Model of Epidemics

We studied obtaining exact solutions to a set of equations related to the SEIR (Susceptible-Exposed-Infectious-Recovered) model of epidemic spread. These solutions may be used to model epidemic waves. We transformed the SEIR model into a differential equation that contained an exponential nonlinearity. This equation was then approximated by a set of differential equations which contained polynomial nonlinearities. We solved several equations from the set using the Simple Equations Method (SEsM). In doing so, we obtained many new exact solutions to the corresponding equations. Several of these solutions can describe the evolution of epidemic waves that affect a small percentage of individuals in the population. Such waves have frequently been observed in the COVID-19 pandemic in recent years. The discussion shows that SEsM is an effective methodology for computing exact solutions to nonlinear differential equations. The exact solutions obtained can help us to understand the evolution of various processes in the modeled systems. In the specific case of the SEIR model, some of the exact solutions can help us to better understand the evolution of the quantities connected to the epidemic waves.

Analytical solution of l-i SEIR model-Comparison of l-i SEIR model with conventional SEIR model in simulation of epidemic curves.

The Susceptible-Exposed-Infectious-Recovered (SEIR) epidemic model has been commonly used to analyze the spread of infectious diseases. This 4-compartment (S, E, I and R) model uses an approximation of temporal homogeneity of individuals in these compartments to calculate the transfer rates of the individuals from compartment E to I to R. Although this SEIR model has been generally adopted, the calculation errors caused by temporal homogeneity approximation have not been quantitatively examined. In this study, a 4-compartment l-i SEIR model considering temporal heterogeneity was developed from a previous epidemic model (Liu X., Results Phys. 2021; 20:103712), and a closed-form solution of the l-i SEIR model was derived. Here, l represents the latent period and i represents the infectious period. Comparing l-i SEIR model with the conventional SEIR model, we are able to examine how individuals move through each corresponding compartment in the two SEIR models to find what information may be missed by the conventional SEIR model and what calculation errors may be introduced by using the temporal homogeneity approximation. Simulations showed that l-i SEIR model could generate propagated curves of infectious cases under the condition of l>i. Similar propagated epidemic curves were reported in literature, but the conventional SEIR model could not generate propagated curves under the same conditions. The theoretical analysis showed that the conventional SEIR model overestimates or underestimates the rate at which individuals move from compartment E to I to R in the rising or falling phase of the number of infectious individuals, respectively. Increasing the rate of change in the number of infectious individuals leads to larger calculation errors in the conventional SEIR model. Simulations from the two SEIR models with assumed parameters or with reported daily COVID-19 cases in the United States and in New York further confirmed the conclusions of the theoretical analysis.

Multivariate time series short term forecasting using cumulative data of coronavirus.

Coronavirus emerged as a highly contagious, pathogenic virus that severely affects the respiratory system of humans. The epidemic-related data is collected regularly, which machine learning algorithms can employ to comprehend and estimate valuable information. The analysis of the gathered data through time series approaches may assist in developing more accurate forecasting models and strategies to combat the disease. This paper focuses on short-term forecasting of cumulative reported incidences and mortality. Forecasting is conducted utilizing state-of-the-art mathematical and deep learning models for multivariate time series forecasting, including extended susceptible-exposed-infected-recovered (SEIR), long-short-term memory (LSTM), and vector autoregression (VAR). The SEIR model has been extended by integrating additional information such as hospitalization, mortality, vaccination, and quarantine incidences. Extensive experiments have been conducted to compare deep learning and mathematical models that enable us to estimate fatalities and incidences more precisely based on mortality in the eight most affected nations during the time of this research. The metrics like mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) are employed to gauge the model's effectiveness. The deep learning model LSTM outperformed all others in terms of forecasting accuracy. Additionally, the study explores the impact of vaccination on reported epidemics and deaths worldwide. Furthermore, the detrimental effects of ambient temperature and relative humidity on pathogenic virus dissemination have been analyzed.

Decision-Dependent Distributionally Robust Markov Decision Process Method in Dynamic Epidemic Control

In this paper, we present a Distributionally Robust Markov Decision Process (DRMDP) approach for addressing the dynamic epidemic control problem. The Susceptible-Exposed-Infectious-Recovered (SEIR) model is widely used to represent the stochastic spread of infectious diseases, such as COVID-19. While Markov Decision Processes (MDP) offers a mathematical framework for identifying optimal actions, such as vaccination and transmission-reducing intervention, to combat disease spreading according to the SEIR model. However, uncertainties in these scenarios demand a more robust approach that is less reliant on error-prone assumptions. The primary objective of our study is to introduce a new DRMDP framework that allows for an ambiguous distribution of transition dynamics. Specifically, we consider the worst-case distribution of these transition probabilities within a decision-dependent ambiguity set. To overcome the computational complexities associated with policy determination, we propose an efficient Real-Time Dynamic Programming (RTDP) algorithm that is capable of computing optimal policies based on the reformulated DRMDP model in an accurate, timely, and scalable manner. Comparative analysis against the classic MDP model demonstrates that the DRMDP achieves a lower proportion of infections and susceptibilities at a reduced cost.

An SEIR model with modified saturated incidence rate and Holling type II treatment function

Abstract In this article, the behavior of an susceptible exposed infected recovered (SEIR) epidemic model with nonlinear incidence rate and Holling type II treatment function is presented and analyzed. Reproduction number of the model is calculated. Equilibrium points are determined. Disease-free equilibrium exists when R0 is below 1. Behavior of disease-free equilibrium is examined at R0 = 1. Endemic equilibrium exists when R0 crosses 1. Stability of both equilibrium points is investigated locally and globally. Simulation is provided to support the result.

Mathematical Models Used to Assess the COVID-19 Outbreak and Preventive Measures

Background: Mathematical modelling is one of the most powerful methods for exploring the diverse range of intervention strategies, determining the fundamental reproduction rate, and forecasting disease spread. This paper reviews the mathematical models that were utilized to investigate coronavirus disease 2019 (COVID-19) transmission dynamics. Methods: We looked through four electronic databases for research that evaluated the transmission dynamics of COVID-19 using a mathematical modeling strategy based on compartmental models. Research describing COVID-19 transmission utilizing compartmental models and published in English in preprints and peer-reviewed publications between December 30, 2019 and May 25, 2020 was eligible for inclusion. This limitation period of time was chosen because it’s when the disease emerged and peaked in many countries worldwide. Results: A total of 46 studies that used compartmental models to explain COVID-19 transmission were included in the review. Six studies employed the age-structured SEIR model, making up the majority of studies’ (37/46) use of the Susceptible-Exposed-Infected-Recovered (SEIR) framework. In one of the eight investigations that used SIR, an age-structured model was used. One study evaluated COVID-19 transmission using the generalized SIRS model. To anticipate the onset of the disease, 36 of the 46 studies calculated the basic reproduction number, and 5 estimated the effective reproduction number. Conclusion: Modelling studies applied generalised and age-structure models to assess the transmission and control of the COVID-19, suggesting that combined mitigations have a substantial impact on disease transmission

Neuro-computational intelligence for numerical treatment of multiple delays SEIR model of worms propagation in wireless sensor networks

In this study, the dynamics of a nonlinear multiple delays susceptible, exposed, infected, recovered (SEIR) model for worms propagation in wireless sensor networks (WSNs) i.e, (SEIR-WSNs) is analyzed via the design of intelligent numerical computing paradigm by exploiting the neural networks (NNs) backpropagation with the Bayesian-Regularization technique (BBRT) i.e., (NNs-BBRT). The model SEIR-WSNs is mathematically governed with ODEs system that represents the nodes as susceptible, exposed, infectious, and recovered (SEIR) nodes for the description of wireless sensor networks (WSNs). Reference outcomes are produced for the nonlinear SEIR-WSNs system using the Adams method for different scenarios based on the variation in the delays for the latent period, time taken by the antivirus to remove the worms and temporary immunization period. The reference data is used for the execution procedure of NNs-BBRT by segmenting samples into the training and testing sets to approximate the solution for nonlinear SEIR-WSNs system. The precision/accuracy and convergence of designed NNs-BBRT are validated based on the acquired accuracy through the effective fitness attainment on mean squared error (MSE), exhaustive regression analysis and sufficient error histogram illustrations.

Developing a Video Game as an Awareness and Research Tool Based on SARS-CoV-2 Epidemiological Dynamics and Motivational Perspectives

In mid-2020, the University of Liège (ULiège, Belgium) commissioned the ULiège Video Game Research Laboratory (Liège Game Lab) and the AR/VR Lab of the HEC-Management School of ULiège to create a serious game to raise awareness of preventive measures for its university community. This project has its origins in two objectives of the institutional policy of ULiège in response to the crisis caused by SARS-CoV-2 to raise awareness among community members of various preventive actions that can reduce the spread of the virus and to inform about the emergence and progression of a pandemic. After almost two years of design, the project resulted in the creation of SARS Wars, a decision-making management game for browsers and smartphones. This article presents the creative process of the game, specifically the integration of an adapted SEIR (susceptible-exposed-infectious-recovered) model, as well as the modeling of intercompartmental circulation dynamics in the game’s algorithm, and the various limitations observed regarding the game’s original missions and possibilities for future work. The SARS-CoV-2 video game project may be considered an innovative way to translate epidemiology into a language that can be used in the scope of citizen sciences. On the one hand, it provides an engaging tool and encourages active participation of the audience. On the other hand, it allows us to have a better understanding of the dynamic changes of a pandemic or an epidemic (crisis preparedness, monitoring, and control) and to anticipate potential consequences in the given parameters at set time (emerging risk identification), while offering insights for impact on some parameters on motivation (social science aspect).

SEIR models in the light of Critical Realism – A critique of exaggerated claims about the effectiveness of Covid 19 vaccinations

In a recent modeling study Watson et al. (Lancet Infect Dis 2022;3099:1-10) claim that Covid-19 vaccinations have helped to prevent roughly 14–20 million deaths in 2021. This conclusion is based on an epidemiological susceptible-exposed-infectious-recovered (SEIR) model trained on partially simulated data and yielding a reproduction number distribution which was then applied to a counterfactual scenario in which the efficacy of vaccinations was removed. Drawing on the meta-theory of Critical Realism, we point out several caveats of this model and caution against believing in its predictions. We argue that the absence of vaccinations would have significantly changed the causal tendencies of the system being modelled, yielding a different reproduction number than obtained from training the model on actually observed data. Furthermore, the model omits many important causal factors. Therefore this model, similar to many previous SEIR models, has oversimplified the complex interplay between biomedical, social and cultural dimensions of health and should not be used to guide public health policy. In order to predict the future in epidemic situations more accurately, continuously optimized dynamic causal models which can include the not directly tangible, yet real causal mechanisms affecting public health appear to be a promising alternative to SEIR-type models.