SEIR Model Research Articles

A metapopulation model with exit screening measure for the 2014–2016 West Africa Ebola virus outbreak

We construct a new metapopulation model for the transmission dynamics and control of the Ebola Virus Disease (EVD) in an environment characterized by considerable migrations and travels of people. It is an extended SEIR model modified by the addition of Quarantine and Isolated compartments to account for travelers who undergo the exit screening. The model is well-fitted by using the reported cases from the neighboring countries Guinea, Liberia and Sierra Leone where the 2014–2016 Ebola outbreak simultaneously arose. We show that the unique disease-free equilibrium (DFE) of the model is unstable or locally asymptotically stable (LAS) depending on whether the control reproduction number is larger or less than unity. In the latter case, we prove that the DFE is globally asymptotically stable (GAS) provided that the exit screening is 100% negative. We also prove the GAS of the DFE by introducing more explicit thresholds, thanks to which the existence of at least one boundary equilibrium is established. We design two new nonstandard finite difference (NSFD) schemes, which preserve the dynamics of the continuous model. Numerical simulations that support the theory highlight that exit screening is useful to mitigate the infection. They also suggest that the disease is controlled or the explicit threshold is less than unity provided that the migration and the exit screening parameters are above a critical value.

Solutions to SIR/SEIR epidemic models with exponential series: Numerical and non numerical approaches

This study revisits the mathematical SIR/SEIR epidemic models, aiming to introduce novel exponential-type series solutions. Beyond standard non-dimensionalization, we implement a successful rescaling technique that reduces the parameter count in classical epidemiology. Consequently, solutions for the SIR model are determined solely by the basic reproduction number and initial infected fractions. Similarly, the SEIR model requires only the transmission-to-recovery ratio and initial exposed fractions. We present both numerical and non numerical solutions, alongside elucidating the limitations on the existence of exponential-type series solutions. Our analysis reveals that these solutions are valid under two key conditions: endemic situations and early epidemic stages, where the basic reproduction number is close to one. We graphically illustrate the range of physical parameters guaranteeing the existence of non numerical exponential series solutions. However, for epidemic/pandemic outbreaks with significantly higher reproduction numbers, achieving complete convergence of the exponential series across the entire physical domain becomes impossible. In such cases, we divide the exponential series solution into two zones: from initial time to peak time and from peak time to the final epidemic time. For the first zone, where convergence is slow, we successfully employ Padé approximants to accelerate the convergence of the series. This accelerated solution is then smoothly joined to the second zone solution once the peak time is identified within the first region. The presented non numerical solutions are envisioned to serve as valuable benchmarks for testing and enhancing other numerical approaches used to solve epidemic models and their variants.

Extended SEIR model of COVID-19 spread focusing on compartmental flow in England

Extended SEIR model of COVID-19 spread focusing on compartmental flow in England

The optimal spatially-dependent control measures to effectively and economically eliminate emerging infectious diseases.

Non-pharmaceutical interventions (NPIs) are effective in mitigating infections during the early stages of an infectious disease outbreak. However, these measures incur significant economic and livelihood costs. To address this, we developed an optimal control framework aimed at identifying strategies that minimize such costs while ensuring full control of a cross-regional outbreak of emerging infectious diseases. Our approach uses a spatial SEIR model with interventions for the epidemic process, and incorporates population flow in a gravity model dependent on gross domestic product (GDP) and geographical distance. We applied this framework to identify an optimal control strategy for the COVID-19 outbreak caused by the Delta variant in Xi'an City, Shaanxi, China, between December 2021 and January 2022. The model was parameterized by fitting it to daily case data from each district of Xi'an City. Our findings indicate that an increase in the basic reproduction number, the latent period or the infectious period leads to a prolonged outbreak and a larger final size. This indicates that diseases with greater transmissibility are more challenging and costly to control, and so it is important for governments to quickly identify cases and implement control strategies. Indeed, the optimal control strategy we identified suggests that more costly control measures should be implemented as soon as they are deemed necessary. Our results demonstrate that optimal control regimes exhibit spatial, economic, and population heterogeneity. More populated and economically developed regions require a robust regular surveillance mechanism to ensure timely detection and control of imported infections. Regions with higher GDP tend to experience larger-scale epidemics and, consequently, require higher control costs. Notably, our proposed optimal strategy significantly reduced costs compared to the actual expenditures for the Xi'an outbreak.

A clustered-LPSEIRS malware propagation model in complex networks

In this paper, we present a new malware propagation model that integrates epidemic spread, clustering, and link prediction techniques, tailored for complex network networks. Our model is based on the clustered-link prediction-susceptible-exposed-infected-recovered (clustered-LPSEIRS) epidemic model, which simulates malware dissemination within the network. Our findings reveal a significant decrease in the rate of malware spread compared to the traditional SEIR model, with this enhancement in containment attributed to the integration of clustering and link prediction methods. We also compute the basic reproduction ratio (R0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R_{0}$$\\end{document}) for our model, providing insights into the potential ramifications of malware within the network. By examining parameter variations, we enhance our understanding of the model's behavior under diverse scenarios. Additionally, we assess the influence of clustering and link prediction on mitigating malware spread, emphasizing its effectiveness in diminishing the overall impact.

A Stochastic Approach in the Analysis of Compartmental Models in Epidemiology

The spread of infectious diseases is a significant public health issue. Mathematical modeling is being used to find appropriate answers to this question. In this paper we propose a stochastic approach to compartmental models. A new model allows to rely on the fokker-planck equation with a SEIR model, with constant rates, to take into account the random environment in the propagation of a disease, markov and kolmogorov properties have been used in the modeling of the process. We have also determined the basic reproduction rate R0 of our new stochastic model using the new generation matrix.

Bifurcation Analysis and Optimal Control of an SEIR Model with Limited Medical Resources and Media Impact on Heterogeneous Networks

The spread of epidemic diseases is often considered to be bound up with human behavior. Both treatment and awareness-raising are seen as important preventive measures during an outbreak. In this paper, an SEIR model on heterogeneous network containing saturated treatment function with media information variable is constructed. Through mathematical analysis, the basic reproduction number and equilibriums of the system are derived. The global stability of disease-free equilibrium is further proved based on LaSalle’s invariant principle. It is also found that with a gradual increase of the delayed treatment parameter, the system exhibits a transition from forward bifurcation to backward bifurcation with the variation of the basic reproduction number. Finally, an optimal control problem is formulated with both treatment rate and media information dissemination rate as control variables and solved using the Pontryagin’s maximum principle. All the above results are verified by numerical experiments.

Sensitivity stability and feasibility analysis of epidemic measles using mathematical SEIR model

Sensitivity stability and feasibility analysis of epidemic measles using mathematical SEIR model

A delay differential equation model on covid-19 with vaccination strategy

In this paper, we have extended SEIR model of COVID-19. The model incorporates two vital aspects in the form of vaccine compartment and constant time delay. The vaccination and time delay provide the information about immune protection and actual existence of the infection among the individuals, respectively. The model is analysed numerically and numerical simulation are executed for three different initial histories and constant time delays which affirm the biological relevance of the system. The analysis includes disease-free equilibrium (DFE), endemic equilibrium, and the basic reproduction number. The stability analysis is performed which reveal the asymptotic stability of the DFE when the basic reproduction number R0 < 1. The study addresses the boundedness and positivity of the solution as the time delay approaches zero. In addition, sensitivity analysis and contour plots for R0 with different parameters offer deeper insights into the model. The impact of vaccination and vaccine inefficacy on the model dynamics is explored.

Global stability analysis, stabilization and synchronization of an SEIR epidemic model

In this paper, we investigate an SEIR epidemic model in which recruitment is assumed to be regulated by a constant function. The SEIR model is a widely-used epidemiological framework that categorises the population into four distinct groups: Susceptible, Exposed, Infectious, and Removed. It employs a system of differential equations to describe the transitions of individuals among these groups, making it a valuable tool for understanding and modelling the dynamics of infectious diseases. Mathematical analysis is used to study the dynamic behaviour of this model. We first determine the basic reproduction number, denoted as R 0 , which governs the dynamics of the SEIR model. Our findings reveal that when R 0 is less than 1, the unique disease-free equilibrium is asymptotically stable, and there is no endemic equilibrium. However, when R 0 exceeds 1, the disease-free equilibrium becomes unstable, and a unique, asymptotically stable endemic equilibrium emerges. Furthermore, by constructing appropriate Lyapunov functions, we have studied the global asymptotic stability of the two equilibrium points. On the other hand, we have used the backstepping method to design a control law that stabilises the SEIR model towards the disease-free equilibrium, which means the eradication of the disease from the target population. Next, we have used the same method to synchronise the SEIR drive system and the SEIR response system. This method is used to stabilise the synchronisation error dynamics arising from the mismatch between the drive and response systems. Finally, we presented numerical simulations to illustrate the theoretical results.

Stochastic modeling of influenza transmission: Insights into disease dynamics and epidemic management

The stochastic SEIR model was employed to investigate the dynamics of influenza transmission. By incorporating transmission rates and prevalence ratios, this model provides the most comprehensive explanation of the virus’s unpredictable dissemination. To simulate the stochastic components of influenza transmission, we implemented conventional Brownian motions and stochastic differential equations. The investigation examines the uniqueness and presence of the solutions to demonstrate the conditions needed for eliminating the infection under random disturbances. The transmission rate coefficient (β) strongly impacts disease transmission speed. as demonstrated by the simulation results.Thus, the proper usage of safe transmission control methods is another decisive factor that determines the outcome of epidemics. Actual data of the Kingdom of Saudi Arabia was used. The results highlighted practicality of stochastic models and their usefulness to address and formulate and even execute the public health related policies. Regarding this, this study sets a high bar for other studies on modeling viral diseases on the grounds that stochastic and dynamic factors are also very important. These subsequent improvements in the model shall enable us to pinpoint the best strategies for the prevention and eradication of influenza and any other subsequent epidemic diseases, with reference to epidemic, epidemiology and public health.

Construction of effective reproduction number of infectious disease individuals based on spatiotemporal discriminant search model: take hand-foot-mouth disease as an example

ObjectiveIn order to facilitate the tracing of infectious diseases in a small area and to effectively carry out disease control and epidemiological investigations, this research proposes a novel spatiotemporal model to estimate effective reproduction number(Re)for infectious diseases, based on the fundamental concept of contact tracing.MethodsThis study utilizes the incidence of hand, foot, and mouth disease (HFMD) among children in Bishan District, Chongqing, China from 2015 to 2019. The study incorporates the epidemiological characteristics of HFMD and aims to construct a Spatiotemporal Correlation Discrimination of HFMD. Utilizing ARC ENGINE and C# programming for the creation of a spatio-temporal database dedicated to HFMD to facilitate data collection and analysis. The scientific validity of the proposed method was verified by comparing the effective reproduction number obtained by the traditional SEIR model.ResultsWe have ascertained the optimal search radius for the spatiotemporal search model to be 1.5 km. Upon analyzing the resulting Re values, which range from 1.14 to 4.75, we observe a skewed distribution pattern from 2015 to 2019. The median and quartile Re value recorded is 2.42 (1.98, 2.72). Except for 2018, the similarity coefficient r of the years 2015, 2016, 2017, and 2019 were all close to 1, and p <0.05 in the comparison of the two models, indicating that the Re values obtained by using the search model and the traditional SEIR model are correlated and closely related. The results exhibited similarity between the Re curves of both models and the epidemiological characteristics of HFMD. Finally, we illustrated the regional distribution of Re values obtained by the search model at various time intervals on Geographic Information System (GIS) maps which highlighted variations in the incidence of diseases across different communities, neighborhoods, and even smaller areas.ConclusionThe model comprehensively considers both temporal variation and spatial heterogeneity in disease transmission and accounts for each individual's distinct time of onset and spatial location. This proposed method differs significantly from existing mathematical models used for estimating Re in that it is founded on reasonable scientific assumptions and computer algorithms programming that take into account real-world spatiotemporal factors. It is particularly well-suited for estimating the Re of infectious diseases in relatively stable mobile populations within small geographical areas.

On quasi-linear reaction diffusion systems arising from compartmental SEIR models

The global existence and boundedness of solutions to quasi-linear reaction-diffusion systems are investigated. The system arises from compartmental models describing the spread of infectious diseases proposed in Viguerie et al. (Appl Math Lett 111:106617, 2021); Viguerie et al. (Comput Mech 66(5):1131–1152, 2020), where the diffusion rate is assumed to depend on the total population, leading to quasilinear diffusion with possible degeneracy. The mathematical analysis of this model has been addressed recently in Auricchio et al. (Math Methods Appl Sci 46:12529–12548, 2023) where it was essentially assumed that all sub-populations diffuse at the same rate, which yields a positive lower bound of the total population, thus removing the degeneracy. In this work, we remove this assumption completely and show the global existence and boundedness of solutions by exploiting a recently developed Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p$$\\end{document}-energy method. Our approach is applicable to a larger class of systems and is sufficiently robust to allow model variants and different boundary conditions.

Assessing marginal effects of non-pharmaceutical interventions on the transmission of SARS-CoV-2 across Africa: a hybrid modeling study.

Since 2019, a new strain of coronavirus has challenged global health systems. Due its fragile healthcare systems, Africa was predicted to be the most affected continent. However, past experiences of African countries with epidemics and other factors, including actions taken by governments, have contributed to reducing the spread of SARS-CoV-2. This study aims to assess the marginal impact of non-pharmaceutical interventions in fifteen African countries during the pre-vaccination period. To describe the transmission dynamics and control of SARS-CoV-2 spread, an extended time-dependent SEIR model was used. The transmission rate of each infectious stage was obtained using a logistic model with NPI intensity as a covariate. The results revealed that the effects of NPIs varied between countries. Overall, restrictive measures related to assembly had, in most countries, the largest reducing effects on the pre-symptomatic and mild transmission, while the transmission by severe individuals is influenced by privacy measures (more than $10\%$). Countries should develop efficient alternatives to assembly restrictions to preserve the economic sector. This involves e.g. training in digital tools and strengthening digital infrastructures.

Analysis of a fractional endemic SEIR model with vaccination and time delay

Analysis of a fractional endemic SEIR model with vaccination and time delay

The importance of the incubation time distribution in compartmental epidemiological models

This study investigates the utilization of various mathematical models for comprehending and managing outbreaks of infectious diseases, with a specific focus on how different distributions of incubation times influence predictions regarding epidemics. Two methodologies are examined: a compartmental SEnIR ODE model, which represents an enhanced version of the mean-field SEIR model, and a stochastic agent-based complex network model. Our findings demonstrate that the selection of diverse incubation time distributions can result in noteworthy discrepancies in critical epidemic forecasts, highlighting the crucial role of precise modeling in shaping effective public health interventions. The research underscores the necessity of integrating authentic distribution patterns into epidemic modeling to increase its reliability and applicability.

SEIR MODEL OF DISSEMINATION FALSE INFORMATION ON FACEBOOK

Dissemination of false information on social media has become a major problem in creating a peaceful community and led to many outrageous behaviours such as racial discrimination and interpersonal discord. Allegations against individuals, misinterpretation of ideologies, and misrepresentation of the conduct of specific individuals are among the various manifestations of false information that have proliferated extensively on the Facebook platform. Thus, this study aims to analyze the dissemination of false information on Facebook using the SEIR model. The data obtained from the selected postings in August 2023 from Info Berita Semasa, Berita Hari Ini Official and Malaysia Buat Apa Hari Ini. The postings have been classified and filtered to ensure the false information being studied. The results show that the false information was viral, and its posting was received by more than half of the group members and only few numbers of group members have realized that the information is fake. Therefore, the administrator in the group should play a vital part in controlling the dissemination of false information. This study will benefit social media controlling association like Malaysian Criminology and Correctional Association to back-pedal the dissemination of false information on Facebook.

A parsimonious Bayesian predictive model for forecasting new reported cases of West Nile disease

Upon researching predictive models related to West Nile virus disease, it is discovered that there are numerous parameters and extensive information in most models, thus contributing to unnecessary complexity. Another challenge frequently encountered is the lead time, which refers to the period for which predictions are made and often is too short. This paper addresses these issues by introducing a parsimonious method based on ICC curves, offering a logistic distribution model derived from the vector-borne SEIR model. Unlike existing models relying on diverse environmental data, our approach exclusively utilizes historical and present infected human cases (number of new cases). With a year-long lead time, the predictions extend throughout the 12 months, gaining precision as new data emerge. Theoretical conditions are derived to minimize Bayesian loss, enhancing predictive precision. We construct a Bayesian forecasting probability density function using carefully selected prior distributions. Applying these functions, we predict month-specific infections nationwide, rigorously evaluating accuracy with probabilistic metrics. Additionally, HPD credible intervals at 90%, 95%, and 99% levels is performed. Precision assessment is conducted for HPD intervals, measuring the proportion of intervals that does not include actual reported cases for 2020–2022.

A simple approach for studying stability properties of an SEIRS epidemic model

Abstract In this work, we study stability properties of a well-known integer-order SEIRS model with nonlinear incidence and vertical transmission. Firstly, we introduce a simple approach to the analysis of global asymptotic stability (GAS) of the integer-order model. This approach is based on general quadratic Lyapunov functions and characteristic of quadratic forms associated with real matrices. The result is that the GAS of disease-free and disease-endemic equilibrium points is completely established. This provides an important improvement for results constructed in two previous works. Secondly, we generalize the integer-order SEIRS model by considering it in the context of the Caputo fractional-order derivative. After that, the present approach is utilized to investigate the GAS of the proposed fractional-order model. As an important consequence, not only the GAS but also the uniform stability of the fractional-order model are determined fully. Therefore, the applicability of the approach is shown. Finally, a series of numerical experiments is conducted to illustrate and support the theoretical findings.

Simulating the spread of COVID-19 with cellular automata: A new approach

Between the years 2020 and 2022, the world was hit by the pandemic of COVID-19 giving rise to an extremely grave situation. Many people suffered and died from this disease. Also, the global economy was badly hurt due to the consequences of various intervention strategies (like social distancing, lockdown) which were applied by different countries to control this pandemic. There are multiple speculations that humanity will again face such pandemics in the future. Thus, it is very important to learn and gain knowledge about the spread of such infectious diseases and the various factors which are responsible for it. In this study, we have extended our previous work [S. Chowdhury, S. Roychowdhury and I. Chaudhuri, Eur. Phys. J. Spec. Top. 231, 3619 (2022), doi:10.1140/epjs/s11734-022-00619-1] on the probabilistic cellular automata (CA) model to reproduce the spread of COVID-19 in several countries by modifying its earlier used neighborhood criteria. This modification gives us the liberty to adopt the effect of different restrictions like lockdown and social distancing in our model. We have done some theoretical analysis for initial infection and simulations to gain insights into our model. We have also studied the data from eight countries for COVID-19 in a window of 876 days and compared it with our model. We have developed a proper framework to fit our model on the data for confirmed cases of COVID-19 and have also re-checked the goodness of the fit with the data of the deceased cases for this pandemic. Our model is compared with other well-known CA models and the ODE-based SEIR model. This model fits well with different peaks of COVID-19 data for all the eight countries and can be possibly generalized for a global prediction. Our study shows that the rate of disease spread depends both on infectivity of a disease and social restrictions. Also, it shows an overall decrement in mortality rate with time due to COVID-19 as more and more people get infected as well as vaccinated. Our minimal model with modified neighborhood condition can easily quantify the degree of social restrictions. It is statistically concluded that the overall degree of social restrictions is above the mean when we considered all eight countries. Finally to conclude, this study has given us various important insights about this pandemic which can help in preparing for combating epidemics in future situations.