SEIR Model Research Articles

A Nonstandard Computational Investigation of SEIR Model with Fuzzy Transmission, Recovery and Death Rates

A Nonstandard Computational Investigation of SEIR Model with Fuzzy Transmission, Recovery and Death Rates

Age-specific contribution of contacts to transmission of SARS-CoV-2 in Germany

Current estimates of pandemic SARS-CoV-2 spread in Germany using infectious disease models often do not use age-specific infection parameters and are not always based on age-specific contact matrices of the population. They also do usually not include setting- or pandemic phase-based information from epidemiological studies of reported cases and do not account for age-specific underdetection of reported cases. Here, we report likely pandemic spread using an age-structured model to understand the age- and setting-specific contribution of contacts to transmission during different phases of the COVID-19 pandemic in Germany. We developed a deterministic SEIRS model using a pre-pandemic contact matrix. The model was optimized to fit age-specific SARS-CoV-2 incidences reported by the German National Public Health Institute (Robert Koch Institute), includes information on setting-specific reported cases in schools and integrates age- and pandemic period-specific parameters for underdetection of reported cases deduced from a large population-based seroprevalence studies. Taking age-specific underreporting into account, younger adults and teenagers were identified in the modeling study as relevant contributors to infections during the first three pandemic waves in Germany. For the fifth wave, the Delta to Omicron transition, only age-specific parametrization reproduces the observed relative and absolute increase in pediatric hospitalizations in Germany. Taking into account age-specific underdetection did not change considerably how much contacts in schools contributed to the total burden of infection in the population (up to 12% with open schools under hygiene measures in the third wave). Accounting for the pandemic phase and age-specific underreporting is important to correctly identify those groups of the population in which quarantine, testing, vaccination, and contact-reduction measures are likely to be most effective and efficient. Age-specific parametrization is also highly relevant to generate informative age-specific output for decision makers and resource planers.

Data-driven optimal control of a seir model for COVID-19

We present a data-driven optimal control approach which integrates the reported partial data with the epidemic dynamics for COVID-19. We use a basic Susceptible-Exposed-Infectious-Recovered (SEIR) model, the model parameters are time-varying and learned from the data. This approach serves to forecast the evolution of the outbreak over a relatively short time period and provide scheduled controls of the epidemic. We provide efficient numerical algorithms based on a generalized Pontryagin's Maximum Principle associated with the optimal control theory. Numerical experiments demonstrate the effective performance of the proposed model and its numerical approximations.

A bayesian non-parametric approach for estimating COVID-19's vaccine effectiveness in a stochastic epidemic model

ObjectivesThis paper proposes a new stochastic epidemic modeling approach to estimate the effectiveness of COVID-19 vaccinations based on individual vaccination status using only observational data. MethodsTo accomplish this goal, we modified the SEIR model to categorize individuals according to their vaccination status and utilized Bayesian data augmentation techniques to assess vaccine effectiveness with partially observed data. We also implemented a dynamic time warping algorithm to compare transmission probabilities between groups with different vaccination statuses. ResultsOur findings indicated that both the fully vaccinated and boosted groups experienced lowered transmission probabilities, with average reductions of 51% and 49% respectively. Interestingly, we also observed no significant difference between the boosted group and fully vaccinated group regarding re-susceptibility. ConclusionIn conclusion, this proposed stochastic epidemic modeling approach for estimating COVID-19 vaccine effectiveness has significant implications for public health policy and decision-making. It could lead to more precise assessments of vaccine effectiveness and validity tests for clinical trial estimates. Overall, this approach has the potential to be a valuable tool in evaluating vaccine effectiveness and the population impact of the vaccination process.

Effect of partially and fully vaccinated individuals in some regions of India: A mathematical study on COVID-19 outbreak

In this paper, we investigate the effect of partially vaccinated and fully vaccinated individuals in preventing the transmit of COVID-19, especially in the regions of Tamil Nadu, Maharashtra, West Bengal and Delhi. Here we construct an SEIR model and analyse the behaviour. We obtained R0 by using next generation matrix approach. Also, our system shows two types of equilibria, namely disease free and endemic equilibrium. For both disease free and endemic equilibrium, local and global stability is obtained here. Our disease-free equilibrium is locally asymptotically stable whenever R0 is less than one, whereas the endemic equilibrium is locally asymptotically stable whenever R0 is greater than one. Furthermore, the global stability of disease-free equilibrium has been proven by using Lyapunov function and the global stability of endemic equilibrium has been obtained by using Poincare Bendixson technique. Also, we enhance our analytic results by numerical simulation. At the end we have attempted to fit our proposed model with the real-world data.

Stability and persistence of a SEIRS model with multiple ages and delay

Stability and persistence of a SEIRS model with multiple ages and delay

An agent-based model of infectious disease considering regional characteristics and human flows

In this study we propose an agent-based SEIR model by taking agents’ heterogeneous mobilities into account. By using the actual human flow data between each district of Tokyo, we create behavior scenarios for every agent in the model. After calibrating the risk of infection in each region using DE (differential evolution), we were able to reproduce the realistic number of positive cases not only for the entire Tokyo metropolitan area but also for each of the 23 districts, with an NRMSD of less than 0.05.

Mathematical modeling of infectious diseases on the example of Astana city

Infectious diseases are caused by pathogens («microbes»), including viruses, bacteria, fungi and parasites, and are ranked by the World Health Organization as the second leading cause of death worldwide. These infections can cause temporary discomfort, severe tissue damage, or even death. Timely accumulation of complex information about the disease with the introduction of computer data processing into the system of the medical service will increase the level of information support for epidemiological surveillance. The paper considers the concepts and existing mathematical models of the spread of coronavirus infection COVID-19, based on SIR-type models. Variety of models of this type are most suitable for predicting, since the disease has a sufficiently long incubation period and the presence of asymptomatic carriers. A mathematical description of the SEIR model with thirteen variables is given.

Dynamics of a fractional-order COVID-19 model under the nonsingular kernel of Caputo-Fabrizio operator

For the sake of human health, it is crucial to investigate infectious diseases including HIV/AIDS, hepatitis, and others. Worldwide, the recently discovered new coronavirus (COVID-19) poses a serious threat. The experimental vaccination and different COVID-19 strains found around the world make the virus' spread unavoidable. In the current research, fractional order is used to study the dynamics of a nonlinear modified COVID-19 SEIR model in the framework of the Caputo-Fabrizio fractional operator with order b. Fixed point theory has been used to investigate the qualitative analysis of the solution respectively. The well-known Laplace transform method is used to determine the approximate solution of the proposed model. Using the COVID-19 data that is currently available, numerical simulations are run to validate the necessary scheme and examine the dynamic behavior of the various compartments of the model. In order to stop the pandemic from spreading, our findings highlight the significance of taking preventative steps and changing one's lifestyle.

Modeling of Mechanisms of Wave Formation for COVID-19 Epidemic

Two modifications with variable coefficients of the well-known SEIR model for epidemic development in the application to the modeling of the infection curves of COVID-19 are considered. The data for these models are information on the number of infections each day obtained from the Johns Hopkins Coronavirus Resource Center database. In our paper, we propose special methods based on Tikhonov regularization for models’ identification on the class of piecewise constant coefficients. In contrast to the model with constant coefficients, which cannot always accurately describe some of infection curves, the first model is able to approximate them for different countries with an accuracy of 2–8%. The second model considered in the article takes into account external sources of infection in the form of an inhomogeneous term in one of the model equations and is able to approximate the data with a slightly better accuracy of 2–4%. For the second model, we also consider the possibility of using other input data, namely the number of infected people per day. Such data are used to model infection curves for several waves of the COVID-19 epidemic, including part of the Omicron wave. Numerical experiments carried out for a number of countries show that the waves of external sources of infection found are ahead of the wave of infection by 10 or more days. At the same time, other piecewise constant coefficients of the model change relatively slowly. These models can be applied fairly reliably to approximate many waves of infection curves with high precision and can be used to identify external and hidden sources of infection. This is the advantage of our models.

Identification of COVID-19 spread mechanisms based on first-wave data, simulation models, and evolutionary algorithms.

The COVID-19 epidemic has shown that efficient prediction models are required, and the well-known SI, SIR, and SEIR models are not always capable of capturing the real dynamics. Modified models with novel structures could help identify unknown mechanisms of COVID-19 spread. Our objective is to provide additional insights into the COVID-19 spread mechanisms based on different models' parameterization which was performed using evolutionary algorithms and the first-wave data. Data from the Our World in Data COVID-19 database was analysed, and several models-SI, SIR, SEIR, SEIUR, and Bass diffusion-and their variations were considered for the first wave of the COVID-19 pandemic. The models' parameters were tuned with differential evolution optimization method L-SHADE to find the best fit. The algorithm for the automatic identification of the first wave was developed, and the differential evolution was applied to model parameterization. The reproduction rates (R0) for the first wave were calculated for 61 countries based on the best fits. The performed experiments showed that the Bass diffusion model-based modification could be superior compared to SI, SIR, SEIR and SEIUR due to the component responsible for spread from an external factor, which is not directly dependent on contact with infected individuals. The developed modified models containing this component were shown to perform better when fitting to the first-wave cumulative infections curve. In particular, the modified SEIR model was better fitted to the real-world data than the classical SEIR in 43 cases out of 61, based on Mann-Whitney U tests; the Bass diffusion model was better than SI for 57 countries. This showed the limitation of the classical models and indicated ways to improve them. By using the modified models, the mechanism of infection spread, which is not directly dependent on contacts, was identified, which significantly influences the dynamics of the spread of COVID-19.

Automatic Calibration of Sociotechnical Systems Simulation Models on The Example of The Infection Spread Model

Predicting the spread of infectious diseases is an urgent task, since it allows for an assessment of the current situation and making informed decisions on the disease stemming measures to be taken. However, predictive models need constant adjustment and validation of the data obtained according to current data on infection spread dynamics. The present research aims to select and integrate a calibration method for the epidemiological Kermak-McKendrick SEIR model with additional factors. This paper provides an overview and analysis of calibration algorithms for the required parameters of the epidemiological model, as well as numerical experiments comparing the accuracy of the results. The resulting calibration method is the least squares method, since it allows considering boundary values and searching for a local minimum, spending the least amount of time compared to other algorithms.Automatic calibration of the model parameters allows for up-to-date predictions on the spread of infectious diseases with minimal time resources in response to changes in disease data and various quarantine measures. The developed solution can be tailored to other infection spread models.

Epidemic threshold and ergodicity of an SEIR model with vertical transmission under the telegraph noise

An SEIR epidemic model incorporating both environmental and genetic factors is developed to investigate the impact of Markovian switching on the transmission dynamics of infectious diseases. Probabilistically, we show first that the basic reproduction number R0 is a sharp threshold for the disease transmission: when R0<1, the disease dies out almost surely; when R0>1, the disease is persistent. We then obtain that the Markov process derived from the model is positive Harris recurrence if R0>1, followed by the global attractivity of the Ω-limit set and the ergodicity of the Markov process. The theoretical results are applied to study the dynamics of rubella in China. This work has significantly simplified the analysis process in the existing literature. This research concludes that multiple waves of infections may be driven by the randomly environmental switching.

Modelling Cyclic Fluctuations of SEIR Epidemic Diseases

Seasonality of infectious disease is an important factor in disease incidence, outbreaks, control and prevention. Many mathematical models that incorporate seasonality in the transmission were formulated and analyzed. In this essay a qualitative analysis is given in terms of the effective reproduction number R0, the existence and stability of the disease-free equilibrium and endemic equilibrium of both the SEIR model and seasonal SEIR model. We perform numerical simulations to validate the model formulation.

Parameters Sensitivity Analysis of COVID-19 Based on the SCEIR Prediction Model

At the end of 2019, COVID-19 outbreaks occurred one after another in countries worldwide. Managing the outbreak efficiently and stably is an essential public health issue facing countries worldwide. In this paper, based on the SEIR model, we propose a SCEIR model that incorporates close contacts (C) and self-protectors (P). Firstly, the epidemic data of China, the USA, and Italy are predicted and compared with the actual data. Secondly, sensitivity analysis of each parameter in the SCEIR model was conducted using Anylogic. The study shows that the SCEIR model established in this paper has a certain validity. The infection rate in contact with E (𝛽) etc., has positive effects on the basic regeneration number (R0); the self-isolation rate (φ) etc., has a negative effect on the basic regeneration number (R0). Emergency management measures are proposed according to the influencing factors corresponding to the model parameters. These can provide theoretical guidance for developing effective epidemic prevention and control measures in areas where the epidemic has not yet been controlled. It also provides some reference for formulating prevention and control policies for similar epidemics that may occur in the future.

Unpredictability in seasonal infectious diseases spread

In this work, we study the unpredictability of seasonal infectious diseases considering a SEIRS model with seasonal forcing. To investigate the dynamical behaviour, we compute bifurcation diagrams type hysteresis and their respective Lyapunov exponents. Our results from bifurcations and the largest Lyapunov exponent show bistable dynamics for all the parameters of the model. Choosing the inverse of latent period as control parameter, over 70% of the interval comprises the coexistence of periodic and chaotic attractors, bistable dynamics. Despite the competition between these attractors, the chaotic ones are preferred. The bistability occurs in two wide regions. One of these regions is limited by periodic attractors, while periodic and chaotic attractors bound the other. As the boundary of the second bistable region is composed of periodic and chaotic attractors, it is possible to interpret these critical points as tipping points. In other words, depending on the latent period, a periodic attractor (predictability) can evolve to a chaotic attractor (unpredictability). Therefore, we show that unpredictability is associated with bistable dynamics preferably chaotic, and, furthermore, there is a tipping point associated with unpredictable dynamics.

Dynamics and Transmission of COVID-19 Epidemic in Malaysia: Atangana-Baleanu Fractional Model

The purpose of this artical is to specify the passage and mathematical model of COVID-19. This infectious disease COVID-19 originated in China and has affected the whole world. In the present study, we have considered, SEIR model to evaluate the spread of COVID-19 in Malaysia. In this article, we have explored the gesture of COVID-19 accurately by applying the newly advanced fractional operator of Atangana-Baleanu on the classical SEIR model. Based on (WHO) reported data in this study, we discussed the corona virus's behavior in Malaysia. We have taken the available infection cases from 1st May 2020 to 14th May 2020. We have matched our problem to Malaysia's actual data, which shows a firm agreement with the actual data. From the information collected from WHO, we have found the basic reproduction number . Moreover, stability analysis at DFE (Disease Free Equilibrium) and EE (Endemic Equilibrium) is accomplished for the given model to detect the model's gesture and transportation. The given fractional model has been solved numerically using MATLAB software. The influence of many parameters specifically has been shown graphically and discussed in detail. It is to be noted that in the present study, we have approximated the escalation of disease for the up-coming 300 days.

Tiered social distancing policies and epidemic control

Tiered social distancing policies have been adopted by many governments to mitigate the harmful consequences of COVID-19. Such policies have a number of well-established features, i.e. they are short-term, adaptive (to the changing epidemiological conditions), and based on a multiplicity of indicators of the prevailing epidemic activity. Here, we use ideas from Behavioural Epidemiology to represent tiered policies in an SEIRS model by using a composite information index including multiple indicators of current and past epidemic activity mimicking those used by governments during the COVID-19 pandemic, such as transmission intensity, infection incidence and hospitals’ occupancy. In its turn, the dynamics of the information index is assumed to endogenously inform the governmental social distancing interventions. The resulting model is described by a hereditary system showing a noteworthy property, i.e. a dependency of the endemic levels of epidemiological variables from initial conditions. This is a consequence of the need to normalize the different indicators to pool them into a single index. Simulations suggest a rich spectrum of possible results. These include policy suggestions and identify pitfalls and undesired outcomes, such as a worsening of epidemic control, that can arise following such types of approaches to epidemic responses.

Modelling the impact of school reopening and contact tracing strategies on Covid-19 dynamics in different epidemiologic settings in Brazil.

We simulate the impact of school reopening during the COVID-19 pandemic in three major urban centers in Brazil to identify the epidemiological indicators and the best timing for the return of in-school activities and the effect of contact tracing as a mitigation measure. Our goal is to offer guidelines for evidence-based policymaking. We implement an extended SEIR model stratified by age and considering contact networks in different settings - school, home, work, and community, in which the infection transmission rate is affected by various intervention measures. After fitting epidemiological and demographic data, we simulate scenarios with increasing school transmission due to school reopening, and also estimate the number of hospitalization and deaths averted by the implementation of contact tracing. Reopening schools results in a non-linear increase in reported COVID-19 cases and deaths, which is highly dependent on infection and disease incidence at the time of reopening. When contact tracing and quarantining are restricted to school and home settings, a large number of daily tests is required to produce significant effects in reducing the total number of hospitalizations and deaths. Policymakers should carefully consider the epidemiological context and timing regarding the implementation of school closure and return of in-person school activities. While contact tracing strategies prevent new infections within school environments, they alone are not sufficient to avoid significant impacts on community transmission.

A modified SEIR model with a jump in the transmission parameter applied to COVID-19 data on Wuhan.

In December 2019, Wuhan, the capital of Hubei Province, was struck by an outbreak of COVID-19. Numerous studies have been conducted to fit COVID-19 data and make statistical inferences. In applications, functions of the parameters in the model are usually used to assess severity of the outbreak. Because of the strategies applied during the struggle against the pandemic, the trend of the parameters changes abruptly. However, time-varying parameters with a jump have received scant attention in the literature. In this study, a modified SEIR model is proposed to fit the actual situation of the COVID-19 epidemic. In the proposed model, the dynamic propagation system is modified because of the high infectivity during incubation, and a time-varying parametric strategy is suggested to account for the utility of the intervention. A corresponding model selection algorithm based on the information criterion is also suggested to detect the jump in the transmission parameter. A real data analysis based on the COVID-19 epidemic in Wuhan and a simulation study demonstrate the plausibility and validity of the proposed method.