Susceptible-exposed-infectious-removed Research Articles

Integrating socio-psychological factors in the SEIR model optimized by a genetic algorithm for COVID-19 trend analysis

The global spread of COVID-19 has profoundly affected health and economies, highlighting the need for precise epidemic trend predictions for effective interventions. In this study, we used infectious disease models to simulate and predict the trajectory of COVID-19. An SEIR (susceptible, exposed, infected, removed) model was established using Wuhan data to reflect the pandemic. We then trained a genetic algorithm-based SEIR (GA-SEIR) model using data from a specific U.S. region and focused on individual susceptibility and infection dynamics. By integrating socio-psychological factors, we achieved a significant enhancement to the GA-SEIR model, leading to the development of an optimized version. This refined GA-SEIR model significantly improved our ability to simulate the spread and control of the epidemic and to effectively track trends. Remarkably, it successfully predicted the resurgence of COVID-19 in mainland China in April 2023, demonstrating its robustness and reliability. The refined GA-SEIR model provides crucial insights for public health authorities, enabling them to design and implement proactive strategies for outbreak containment and mitigation. Its substantial contributions to epidemic modelling and public health planning are invaluable, particularly in managing and controlling respiratory infectious diseases such as COVID-19.

A Third-order Two Stage Numerical Scheme and Neural Network Simulations for SEIR Epidemic Model: A Numerical Study

This study focuses on the cutting-edge field of epidemic modeling, providing a comprehensive investigation of a third-order two-stage numerical approach combined with neural network simulations for the SEIR (Susceptible-Exposed-Infectious-Removed) epidemic model. An explicit numerical scheme is proposed in this work for dealing with both linear and nonlinear boundary value problems. The scheme is built on two grid points, or two time levels, and is third-order. The main advantage of the scheme is its order of accuracy in two stages. Third-order precision is not only not provided by most existing explicit numerical approaches in two phases, but it also necessitates the computation of an additional derivative of the dependent variable. The proposed scheme's consistency and stability are also examined and presented. Nonlinear SEIR (susceptible-exposed-infected-recovered) models are used to implement the scheme. The scheme is compared with the non-standard finite difference and forward Euler methods that are already in use. The graph shows that the plan is more accurate than non-standard finite difference and forward Euler methods that are already in use. The solution obtained is then looked at through the lens of the neural network. The neural network is trained using an optimization approach known as the Levenberg-Marquardt backpropagation (LMB) algorithm. The mean square error across the total number of iterations, error histograms, and regression plots are the various graphs that can be created from this process. This work conducts thorough evaluations to not only identify the strengths and weaknesses of the suggested approach but also to examine its implications for public health intervention. The results of this study make a valuable contribution to the continuously developing field of epidemic modeling. They emphasize the importance of employing modern numerical techniques and machine learning algorithms to enhance our capacity to predict and effectively control infectious diseases. Doi: 10.28991/ESJ-2024-08-01-023 Full Text: PDF

Hopf bifurcation analysis for a delayed nonlinear-SEIR epidemic model on networks

Using graph Laplacian diffusion, a delayed Susceptible–Exposed–Infected–Removed (SEIR) epidemic model with a non-linear incidence rate has been considered. This model incorporates a diffusion term that captures population mobility through a network. The local stability analysis for each steady state is demonstrated. Furthermore, we have explored the existence of Hopf bifurcation at the endemic equilibrium and addressed its direction using the Normal Form Theory and Center of Manifold Theorem. To visually illustrate our theoretical findings, we have performed computational experiments on a small-world Watts–Strogatz graph.

Modeling SARS coronavirus-2 omicron variant dynamic via novel fractional derivatives with immunization and memory trace effects

The objective of this paper is to recommend an adjusted Susceptible-Exposed-Infectious-Removed (SEIR) model that characterizes the temporal patterns of various individuals affected by the omicron variant in an epidemic. This model considers factors such as vaccination, asymptomatic cases, indoor and outdoor air, hospitalizations, and deaths, as well as the impact of immunization and memory trace. While many recent studies overlook the complexities of multiple strains, including their diverse transmission rates and reaction to vaccines, this study introduces a new fractional derivative model to examine the spread of the omicron variant of COVID-19 and the implementation of a vaccination campaign. A thorough theoretical analysis is conducted, and the critical factor (Rcrnz) is calculated using the model equations. It is demonstrated that when Rcrnz is less than 1, the disease-free state is globally asymptotically stable, meaning that the epidemic diminishes. Moreover, the stability of both global and local equilibrium points is examined. Numerical simulations are employed to demonstrate the alignment between the numerical findings and theoretical characteristics. The model is adjusted to experimental data that reflect the progression of the omicron variant of COVID-19 in Guangzhou, exhibiting a satisfactory performance in predicting the number of infected individuals, thereby suggesting its capability to accurately estimate asymptomatic cases. Furthermore, to emphasize the benefits of employing fractional differential equations, the paper provides examples related to memory trace and hereditary characteristics. Moreover, the examined models are expected to be applied and expanded upon in order to contribute to the formulation of policies for disease control during times of limited vaccine availability. To summarize, the model appears to be a sufficient tool for researching and managing infectious diseases. It is projected that as the Omicron variant's prevalence declines, there will be a reduced need for respiratory-focused precautions.

Modeling the Impact of Proportion, Sowing Date, and Architectural Traits of a Companion Crop on Foliar Fungal Pathogens of Wheat in Crop Mixtures.

Diversification of cropping systems is a lever for the management of epidemics. However, most research to date has focused on cultivar mixtures, especially for cereals, even though crop mixtures can also improve disease management. To investigate the benefits of crop mixtures, we studied the effect of different crop mixture characteristics (i.e., companion proportion, sowing date, and traits) on the protective effect of the mixture. We developed a SEIR (Susceptible, Exposed, Infectious, Removed) model of two damaging wheat diseases (Zymoseptoria tritici and Puccinia triticina), which were applied to different canopy components, ascribable to wheat and a theoretical companion crop. We used the model to study the sensitivity of disease intensity to the following parameters: wheat-versus-companion proportion, companion sowing date and growth, and architectural traits. For both pathogens, the companion proportion had the strongest effect, with 25% of companion reducing disease severity by 50%. However, changing companion growth and architectural traits also significantly improved the protective effect. The effect of companion characteristics was consistent across different weather conditions. After decomposing the dilution and barrier effects, the model suggested that the barrier effect is maximized for an intermediate proportion of companion crop. Our study thus supports crop mixtures as a promising strategy to improve disease management. Future studies should identify real species and determine the combination of host and companion traits to maximize the protective effect of the mixture. [Formula: see text] Copyright © 2023 The Author(s). This is an open access article distributed under the CC BY-NC-ND 4.0 International license.

Mathematical Model of the Spread of Hantavirus Infection.

A mathematical epidemiological model incorporating the mobility of rodents and human groups among zones of less or major contact between them is presented. The hantavirus infection dynamics is expressed using a model type SEIR (Susceptible-Exposed-Infectious-Removed), which incorporates the displacement of the rodent and the human, between the urban and rural sector, the latter being subdivided in populated and non-populated. The results show the impact that rodent or human displacement may have on the propagation of hantavirus infection. Human mobility is more significant than rodents in increasing the number of hantavirus infection cases. The results found may be used as a reference by the health authorities to develop more specific campaigns on the territorial dynamics of the rodent, attend to the mobility of humans in these territories, mainly agricultural and forestry workers, and strengthen control-prevention actions in the community, to prevent future outbreaks that are fatal.

Methods on COVID-19 Epidemic Curve Estimation During Emergency Based on Baidu Search Engine and ILI Traditional Surveillance in Beijing, China

Surveillance is an essential work on infectious diseases prevention and control. When the pandemic occurred, the inadequacy of traditional surveillance was exposed, but it also provided a valuable opportunity to explore new surveillance methods. This study aimed to estimate the transmission dynamics and epidemic curve of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) Omicron BF.7 in Beijing under the emergent situation using Baidu index and influenza-like illness (ILI) surveillance. A novel hybrid model (multiattention bidirectional gated recurrent unit (MABG)–susceptible–exposed–infected–removed (SEIR)) was developed, which leveraged a deep learning algorithm (MABG) to scrutinize the past records of ILI occurrences and the Baidu index of diverse symptoms such as fever, pyrexia, cough, sore throat, anti-fever medicine, and runny nose. By considering the current Baidu index and the correlation between ILI cases and coronavirus disease 2019 (COVID-19) cases, a transmission dynamics model (SEIR) was formulated to estimate the transmission dynamics and epidemic curve of SARS-CoV-2. During the COVID-19 pandemic, when conventional surveillance measures have been suspended temporarily, cases of ILI can serve as a useful indicator for estimating the epidemiological trends of COVID-19. In the specific case of Beijing, it has been ascertained that cumulative infection attack rate surpass 80.25% (95% confidence interval (95% CI): 77.51%–82.99%) since December 17, 2022, with the apex of the outbreak projected to transpire on December 12. The culmination of existing patients is expected to occur three days subsequent to this peak. Effective reproduction number (Rt) represents the average number of secondary infections generated from a single infected individual at a specific point in time during an epidemic, remained below 1 since December 17, 2022. The traditional disease surveillance systems should be complemented with information from modern surveillance data such as online data sources with advanced technical support. Modern surveillance channels should be used primarily in emerging infectious and disease outbreaks. Syndrome surveillance on COVID-19 should be established to following on the epidemic, clinical severity, and medical resource demand.

Analysis and prediction of improved SEIR transmission dynamics model: taking the second outbreak of COVID-19 in Italy as an example.

This study aimed to predict the transmission trajectory of the 2019 Corona Virus Disease (COVID-19) and analyze the impact of preventive measures on the spread of the epidemic. Considering that tracking a long-term epidemic trajectory requires explanatory modeling with more complexities than short-term predictions, an improved Susceptible-Exposed-Infected-Removed (SEIR) transmission dynamic model is established. The model depends on defining various parameters that describe both the virus and the population under study. However, it is likely that several of these parameters will exhibit significant variations among different states. Therefore, regression algorithms and heuristic algorithms were developed to effectively adapt the population-dependent parameters and ensure accurate fitting of the SEIR model to data for any specific state. In this study, we consider the second outbreak of COVID-19 in Italy as a case study, which occurred in August 2020. We divide the epidemic data from February to September of the same year into two distinct stages for analysis. The numerical results demonstrate that the improved SEIR model effectively simulates and predicts the transmission trajectories of the Italian epidemic during both periods before and after the second outbreak. By analyzing the impact of anti-epidemic measures on the spread of the disease, our findings emphasize the significance of implementing anti-epidemic preventive measures in COVID-19 modeling.

Epidemic propagation risk study with effective fractal dimension.

In this article, the risk of epidemic transmission on complex networks is studied from the perspective of effective fractal dimension. First, we introduce the method of calculating the effective fractal dimension of the network by taking a scale-free network as an example. Second, we propose the construction method of administrative fractal network and calculate the . using the classical susceptible exposed infectious removed (SEIR) infectious disease model, we simulate the virus propagation process on the administrative fractal network. The results show that the larger the is, the higher the risk of virus transmission is. Later, we proposed five parameters P, M, B, F, and D, where P denotes population mobility, M denotes geographical distance, B denotes GDP, F denotes , and D denotes population density. The new epidemic growth index formula was obtained by combining these five parameters, and the validity of I in epidemic transmission risk assessment was demonstrated by parameter sensitivity analysis and reliability analysis. Finally, we also confirmed the reliability of the SEIR dynamic transmission model in simulating early COVID-19 transmission trends and the ability of timely quarantine measures to effectively control the spread of the epidemic.

Recursive Stacked LeakyNet-Based Compartmental Model for Analysis of COVID-19 Transmission Dynamics

Mathematical models involving complex formulations are used for solving estimation problems across various disciplines. Epidemiological models like susceptible–infected–removed (SIR), and its variations like susceptible–exposed–infected–removed (SEIR) and others are traditionally used for estimating the progression of viral outbreaks. But, real-life situations adapt and respond to ever-changing surroundings and social norms in precise or random or in complex manners. The mathematical formulation-based compartmental models suffer from drawbacks that lead to inaccuracy in predictions. To address this gap, a deep learning (DL)-based hybrid architecture namely residual leaky network (LeakyNet) has been proposed for the first time to the best of authors’ knowledge. This DL-based hybrid architecture is capable of analysing various aspects of the pandemic by training on short-term data to generate probable future trends. Using this hybrid architecture as a building block, a DL-based epidemiological model namely vulnerable–contaminated–immuned (VCI) model has been formulated to analyse short-term historical data of COVID-19. The DL empowered compartmental model has been implemented on an ongoing real-life scenario and the results reveal that the proposed model performs reasonably well in comparison to the contemporary models. The predicted data have been observed to be in good agreement with the actual pandemic data. The prediction models considered in this study have been evaluated using mean absolute percentage error (MAPE).

Analysis of metapopulation models of the transmission of SARS-CoV-2 in the United States.

During the COVID-19 pandemic, renewal equation estimates of time-varying effective reproduction numbers were useful to policymakers in evaluating the need for and impact of mitigation measures. Our objective here is to illustrate the utility of mechanistic expressions for the basic and effective (or intrinsic and realized) reproduction numbers, [Formula: see text] and related quantities derived from a Susceptible-Exposed-Infectious-Removed (SEIR) model including features of COVID-19 that might affect transmission of SARS-CoV-2, including asymptomatic, pre-symptomatic, and symptomatic infections, with which people may be hospitalized. Expressions from homogeneous host population models can be analyzed to determine the effort needed to reduce [Formula: see text] from [Formula: see text] to 1 and contributions of modeled mitigation measures. Our model is stratified by age, 0-4, 5-9, …, 75+ years, and location, the 50 states plus District of Columbia. Expressions from such heterogeneous host population models include subpopulation reproduction numbers, contributions from the above-mentioned infectious states, metapopulation numbers, subpopulation contributions, and equilibrium prevalence. While the population-immunity at which [Formula: see text] has captured the popular imagination, the metapopulation [Formula: see text] could be attained in an infinite number of ways even if only one intervention (e.g., vaccination) were capable of reducing [Formula: see text] However, gradients of expressions derived from heterogeneous host population models,[Formula: see text] can be evaluated to identify optimal allocations of limited resources among subpopulations. We illustrate the utility of such analytical results by simulating two hypothetical vaccination strategies, one uniform and other indicated by [Formula: see text] as well as the actual program estimated from one of the CDC's nationwide seroprevalence surveys conducted from mid-summer 2020 through the end of 2021.

Multi-source dynamic ensemble prediction of infectious disease and application in COVID-19 case.

The development of an epidemic always exhibits multiwave oscillation owing to various anthropogenic sources of transmission. Particularly in populated areas, the large-scaled human mobility led to the transmission of the virus faster and more complex. The accurate prediction of the spread of infectious diseases remains a problem. To solve this problem, we propose a new method called the multi-source dynamic ensemble prediction (MDEP) method that incorporates a modified susceptible-exposed-infected-removed (SEIR) model to improve the accuracy of the prediction result. The modified SEIR model is based on the compartment model, which is suitable for local-scale and confined spaces, where human mobility on a large scale is not considered. Moreover, compartmental models cannot be used to predict multiwave epidemics. The proposed MDEP method can remedy defects in the compartment model. In this study, multi-source prediction was made on the development of coronavirus disease 2019 (COVID-19) and dynamically assembled to obtain the final integrated result. We used the real epidemic data of COVID-19 in three cities in China: Beijing, Lanzhou, and Beihai. Epidemiological data were collected from 17 April, 2022 to 12 August, 2022. Compared to the one-wave modified SEIR model, the MDEP method can depict the multiwave development of COVID-19. The MDEP method was applied to predict the number of cumulative cases of recent COVID-19 outbreaks in the aforementioned cities in China. The average accuracy rates in Beijing, Lanzhou, and Beihai were 89.15%, 91.74%, and 94.97%, respectively. The MDEP method improved the prediction accuracy of COVID-19. With further application to other infectious diseases, the MDEP method will provide accurate predictions of infectious diseases and aid governments make appropriate directives.

Threat Net: A Metagenomic Surveillance Network for Biothreat Detection and Early Warning.

Early detection of novel pathogens can prevent or substantially mitigate biological incidents, including pandemics. Metagenomic next-generation sequencing (mNGS) of symptomatic clinical samples may enable detection early enough to contain outbreaks, limit international spread, and expedite countermeasure development. In this article, we propose a clinical mNGS architecture we call "Threat Net," which focuses on the hospital emergency department as a high-yield surveillance location. We develop a susceptible-exposed-infected-removed (SEIR) simulation model to estimate the effectiveness of Threat Net in detecting novel respiratory pathogen outbreaks. Our analysis serves to quantify the value of routine clinical mNGS for respiratory pandemic detection by estimating the cost and epidemiological effectiveness at differing degrees of hospital coverage across the United States. We estimate that a biological threat detection network such as Threat Net could be deployed across hospitals covering 30% of the population in the United States. Threat Net would cost between $400 million and $800 million annually and have a 95% chance of detecting a novel respiratory pathogen with traits of SARS-CoV-2 after 10 emergency department presentations and 79 infections across the United States. Our analyses suggest that implementing Threat Net could help prevent or substantially mitigate the spread of a respiratory pandemic pathogen in the United States.

Nonintegrability of the SEIR epidemic model

We prove the nonintegrability of the susceptible–exposed–infected–removed (SEIR) epidemic model in the Bogoyavlenskij sense. This property of the SEIR model is different from the more fundamental susceptible–infected–removed (SIR) model, which is Bogoyavlenskij-integrable. Our basic tool for the proof is an extension of the Morales–Ramis theory due to Ayoul and Zung. Moreover, we introduce three new state variables and extend the system to a six-dimensional system to treat transcendental first integrals and commutative vector fields. We also use the fact that the incomplete gamma function Γ(α,x) is not elementary for α⁄∈N, of which a proof is included.

Modified SEIR epidemic model including asymptomatic and hospitalized cases with correct demographic evolution

The aim of this study is to propose a modified Susceptible-Exposed-Infectious-Removed (SEIR) model that describes the time behaviour of symptomatic, asymptomatic and hospitalized patients in an epidemic, taking into account the effect of the demographic evolution. Unlike most of the recent studies where a constant ratio of new individuals is considered, we consider a more correct assumption that the growth ratio is proportional to the total population, following a Logistic law, as is usual in population growth studies for humans and animals. An exhaustive theoretical study is carried out and the basic reproduction number R0 is computed from the model equations. It is proved that if R0<1 then the disease-free manifold is globally asymptotically stable, that is, the epidemics remits. Global and local stability of the equilibrium points is also studied. Numerical simulations are used to show the agreement between numerical results and theoretical properties. The model is fitted to experimental data corresponding to the pandemic evolution of COVID-19 in the Republic of Cuba, showing a proper behaviour of infected cases which let us think that can provide a correct estimation of asymptomatic cases. In conclusion, the model seems to be an adequate tool for the study and control of infectious diseases.

Pandemic lockdown, isolation, and exit policies based on machine learning predictions.

The widespread lockdowns imposed in many countries at the beginning of the COVID‐19 pandemic elevated the importance of research on pandemic management when medical solutions such as vaccines are unavailable. We present a framework that combines a standard epidemiological SEIR (susceptible–exposed–infected–removed) model with an equally standard machine learning classification model for clinical severity risk, defined as an individual's risk of needing intensive care unit (ICU) treatment if infected. Using COVID‐19–related data and estimates for France as of spring 2020, we then simulate isolation and exit policies. Our simulations show that policies considering clinical risk predictions could relax isolation restrictions for millions of the lowest risk population months earlier while consistently abiding by ICU capacity restrictions. Exit policies without risk predictions, meanwhile, would considerably exceed ICU capacity or require the isolation of a substantial portion of population for over a year in order to not overwhelm the medical system. Sensitivity analyses further decompose the impact of various elements of our models on the observed effects. Our work indicates that predictive modeling based on machine learning and artificial intelligence could bring significant value to managing pandemics. Such a strategy, however, requires governments to develop policies and invest in infrastructure to operationalize personalized isolation and exit policies based on risk predictions at scale. This includes health data policies to train predictive models and apply them to all residents, as well as policies for targeted resource allocation to maintain strict isolation for high‐risk individuals.

Evaluation of the Canadian government policies on controlling the COVID-19 outbreaks

In this paper, we investigate the COVID-19 pandemic in Canada and evaluate the Canadian government policies on controlling COVID-19 outbreaks. The first case of COVID-19 was reported in Ontario on 25 January 2020. Since then, there have been over million cases by now. During this time period, the federal, provincial and local governments have implemented regulations and policies in order to control the pandemic. To evaluate these government policies, which may be done by analysing the infection rate, infection period and reproductive number of COVID-19, we approach the problem by introducing an extended susceptible-exposed-infectious-removed (SEIR) model and conduct the model inference by using the iterated filter ensemble adjustment Kalman filter (IF-EAKF) algorithm. We first divide the time period into phases according to the policy intensities in each province by segmenting the time period from 4 March 2020 to 31 October 2020 into three time phases: the exploding phase, the strict policy implementation phase, and the provincial reopening phase. We then use IF-EAKF algorithm to obtain the estimates of the model parameters. We show that the infection rate in the second phase is lower than that in both first and third phases. We also discuss the number of new COVID-19 cases under different policy intensities and different policy durations in the third wave of the pandemic.

A novel complex social network rumor stochastic model: Convergence in distribution to a final rumor size

We introduce a chain-binomial model in a heterogeneous complex social network (HCSN) to investigate the spread of a rumor. A novel formulation of the state of the Markov chain (MC) for the SEIR (susceptible-exposed-infected-removed) rumor epidemic model is obtained, where two discrete time measures represent individuals in their disease states both instantaneously, and also the total time duration in each state. The general MC is characterized in the HCSN, for both the mean-field and global levels of the network rumor epidemic dynamics. The convergence in distribution of the MC to the final size of the rumor epidemic random variable is fully characterized. Moreover, the algorithm to obtain the expected final number of nodes that ever hear the rumor is given. An example to demonstrate the algorithm is presented.

Analyzing COVID-19 data in the Canadian province of Manitoba: A new approach

The basic homogeneous SEIR (susceptible–exposed–infected–removed) model is a commonly used compartmental model for analysing infectious diseases such as influenza and COVID-19. However, in the homogeneous SEIR model, it is assumed that the population of study is homogeneous and, one cannot incorporate individual-level information (e.g., location of infected people, distance between susceptible and infected individuals, vaccination status) which may be important in predicting new disease cases. Recently, a geographically-dependent individual-level model (GD-ILM) within an SEIR framework was developed for when both regional and individual-level spatial data are available. In this paper, we propose to use an SEIR GD-ILM for each health region of Manitoba (central Canadian province) population to analyse the COVID-19 data. As different health regions of the population under study may act differently, we assume that each health region has its own corresponding parameters determined by a homogeneous SEIR model (such as contact rate, latent period, infectious period). A Monte Carlo Expectation Conditional Maximization (MCECM) algorithm is used for inference. Using estimated parameters we predict the infection rate at each health region of Manitoba over time to identify highly risk local geographical areas. Performance of the proposed approach is also evaluated through simulation studies.

Assessment of 2021/22 influenza epidemic scenarios in Italy during SARS-CoV-2 outbreak.

Global mitigation strategies to tackle the threat posed by SARS-CoV-2 have produced a significant decrease of the severity of 2020/21 seasonal influenza, which might result in a reduced population natural immunity for the upcoming 2021/22 influenza season. To predict the spread of influenza virus in Italy and the impact of prevention and control measures, we present an age-structured Susceptible-Exposed-Infectious-Removed (SEIR) model including the role of social mixing patterns and the impact of age-stratified vaccination strategies and Non-Pharmaceutical Interventions (NPIs) such as school closures, partial lockdown, as well as the adoption of personal protective equipment and the practice of hand hygiene. We find that vaccination campaigns with standard coverage would produce a remarkable mitigation of the spread of the disease in moderate influenza seasons, making the adoption of NPIs unnecessary. However, in case of severe seasonal epidemics, a standard vaccination coverage would not be sufficiently effective in fighting the epidemic, thus implying that a combination with the adoption of NPIs is necessary to contain the disease. Alternatively, our results show that the enhancement of the vaccination coverage would reduce the need to adopt NPIs, thus limiting the economic and social impacts that NPIs might produce. Our results highlight the need to respond to the influenza epidemic by strengthening the vaccination coverage.