SEIR Epidemic Model Research Articles

Near-optimal control of a stochastic partial differential equation SEIR epidemic model under economic constraints

The outbreak of a disease has negative effects on the economy, and economic activities affect the spread of a disease. In this paper, based on the relationship between economic activities and infectious diseases, we establish a SEIRG (susceptible-exposure-infective-recovered-economic) model. Applying the near-maximum condition of a Hamiltonian function, we provide sufficient and necessary conditions for the near optimal control problem of the SEIRG system. In addition, we obtain the optimal control function of the research system. Finally, we develop an algorithm for a near optimal control problem and use numerical simulations to illustrate the effects of vaccination and treatment.

Sensitivity Analysis of SEIRS Model with Quarantine on the Spread of Covid-19

Since the Covid-19 pandemic, various mathematical models have been developed to describe its spread using the compartment model. The purpose of this research was to construct a new model of Covid-19. This formulated model is an application of SEIRS epidemic model by Zhang & Teng (2007) and a modification of the Covid-19 model by Chatterjee et al. (2020) by adding variations of quarantine. The model is analyzed by determining the disease-free fixed point and basic reproduction number 〖(R〗_0) through the next generation matrix method. The next step is to analyze the sensitivity to find out the parameters that have the most influence on the spread of Covid-19. The disease will not spread in the population if the value of R_0<1, while the disease will spread if the value of R_0>1. The result of the sensitivity analysis stated the parameters that can be controlled and have the most significant effect, respectively, are the transmission rate from symptomatic infected individuals (β_2 ),transmission rates from asymptomatic infected individuals (β_1 ), quarantine rates for symptomatic infected individuals (θ_3), and quarantine rates for asymptomatic infected individuals (θ_2). Parameters β_2 and β_1 have a negative index, while θ_3 and θ_2 have a negative index. It means decreasing the transmission rate from infected individuals and increasing the quarantine rate for infected individuals can decrease the spread of Covid-19. Therefore there will not be an outbreak in the long term.

COVID-19 outbreak: a predictive mathematical study incorporating shedding effect.

In this paper, a modified SEIR epidemic model incorporating shedding effect is proposed to analyze transmission dynamics of the COVID-19 virus among different individuals’ classes. The direct impact of pathogen concentration over susceptible populations through the shedding of COVID-19 virus into the environment is investigated. Moreover, the threshold value of shedding parameters is computed which gives information about their significance in decreasing the impact of the disease. The basic reproduction number (R_{0}) is calculated using the next-generation matrix method, taking shedding as a new infection. In the absence of disease, the condition for the equilibrium point to be locally and globally asymptotically stable with R_{0}<1 are established. It has been shown that the unique endemic equilibrium point is globally asymptotically stable under the condition R_{0}>1. Bifurcation theory and center manifold theorem imply that the system exhibit backward bifurcation at R_{0}=1. The sensitivity indices of R_{0} are computed to investigate the robustness of model parameters. The numerical simulation is demonstrated to illustrate the results.

Bifurcation analysis and optimal control of COVID-19 with exogenous reinfection and media coverages

In this paper, a SEIR epidemic model related to media coverage and exogenous reinfections is established to explore the transmission dynamics of COVID-19. The basic reproduction number is calculated using the next generation matrix method. First, the existence of equilibrium points is investigated, and different kinds of equilibrium points indicate that the disease may disappear, or exist that result in different quantity of susceptible individuals, pre-symptomatic infected individuals and symptomatic infected individuals. The stability of the equilibria is discussed by a geometric approach, and it is found that controlling reproduction number to be lower than 1 is not sufficient for eradication of COVID-19. Second, transcritical bifurcation is explored, and it is found that improving the ratio of exogenous reinfection may lead to backward bifurcation under poor medical conditions, which indicates that two endemic equilibrium points appear. Third, to investigate the influence of parameters on the basic reproduction, sensitivity analysis is done to choose relatively sensitive parameters, and the parameters for treatment and media coverage are selected. An optimal control model is established to balance the treatment and media awareness. By exploring the existence and the uniqueness of the optimal control solution, the optimal control strategies are given. Finally, we run numerical simulations to verify the theoretical analysis on actual data of China, and the data from the four different states of India is used for forecasting the situation of infected individuals in a short period. It is found by the simulation that the co-function of treatment and media coverage results in the reduced number of infectious individuals.

Study of Fractional Order SEIR Epidemic Model and Effect of Vaccination on the Spread of COVID-19.

In this manuscript, a fractional order SEIR model with vaccination has been proposed. The positivity and boundedness of the solutions have been verified. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at disease-free equilibrium point {E}_{0} when {mathfrak{R}}_{0}< 1 and at epidemic equilibrium {E}_{1} when {mathfrak{R}}_{0}> 1. It has been found that introduction of the vaccination parameter eta reduces the reproduction number {mathfrak{R}}_{0}. The parameters are identified using real-time data from COVID-19 cases in India. To numerically solve the SEIR model with vaccination, the Adam-Bashforth-Moulton technique is used. We employed MATLAB Software (Version 2018a) for graphical presentations and numerical simulations.. It has been observed that the SEIR model with fractional order derivatives of the dynamical variables is much more effective in studying the effect of vaccination than the integral model.

Study on the Global Stability for a Generalized SEIR Epidemic Model.

In the current study, a generalized SEIR epidemic model is studied. The generalized fractional-order SEIR model (susceptible-infected-recovered (SIR) epidemic) model differentiated the population into susceptible population, exposure population, infected population, and rehabilitation population and has fundamental mentoring importance for the forecast of the probable outburst of infectious ailments. The fundamental duplicated quantity R0 is inferred. When R0 < 1, the disease-free equilibrium (DFE) is particular and tending towards stability. When R0 > 1, the endemic equilibrium is sole. In addition, certain circumstances are set up to make sure the local progressive stability of disease-free and endemic equilibrium. Considering the influence of the individual behavior, a broader SEIR epidemic model is raised, which classified the population into susceptible, exposure, infected, and rehabilitation. What is more, the basic reproduction number, that regulates whether the infection will die out or not, is obtained by the spectral radius of the next-generation matrix; moreover, the global stability of DFE and endemic equilibrium are analyzed by a geometry method.

Study and Analysis of Corona-Virus Transfer Dynamics using Enhanced SEIR Epidemic Model with Vaccination Effect

Corona Virus Syndrome (COVID-19) is a contagious disease and it is considered one of the deadliest viruses ever known to humanity. In this work, the transmission dynamics of the COVID- 19 has been studied using an enhanced SEIR epidemic compartmental model with a vaccination compartment. This model divides the whole population into five categories: susceptible (S), exposed (E), infectious (I), recovered (R), and vaccinated (V). Firstly, Positivity, Existence and Uniqueness of solution are illustrated. Secondly, a mathematical analysis is done to study the equilibrium points of the model and the basic reproduction number has been computed using Next Generation Matrix method. Thirdly, by using analytical computation the Stability of disease free equilibrium (DFE) point of the model is discussed and the Existence, and uniqueness of the endemic equilibrium are proved. Finally, Bifurcation coefficient is computed using the available data and Simulations are made to illustrate the effect of the transmission rate and vaccination rate on the value of the basic reproduction number.

Global attractivity of the equilibria of the diffusive SIR and SEIR epidemic models with multiple parallel infectious stages and nonlinear incidence mechanism

In this paper, we are concerned with the diffusive SIR and SEIR epidemic models with multiple parallel infectious stages and nonlinear incidence mechanism. We first establish a priori L∞-norm estimates for the solutions to the epidemic models, and then derive the global attractivity of disease-free equilibrium and endemic equilibrium for the two models in terms of the basic reproduction number. Our results show that the diversity of infectious stages, the infection mechanism and the diffusion do not affect the global dynamics of the infectious disease.

On a Novel Dynamics of SEIR Epidemic Models with a Potential Application to COVID-19

In this paper, we study a type of disease that unknowingly spreads for a long time, but by default, spreads only to a minimal population. This disease is not usually fatal and often goes unnoticed. We propose and derive a novel epidemic mathematical model to describe such a disease, utilizing a fractional differential system under the Atangana–Baleanu–Caputo derivative. This model deals with the transmission between susceptible, exposed, infected, and recovered classes. After formulating the model, equilibrium points as well as stability and feasibility analyses are stated. Then, we present results concerning the existence of positivity in the solutions and a sensitivity analysis. Consequently, computational experiments are conducted and discussed via proper criteria. From our experimental results, we find that the loss and regain of immunity result in the gain and loss of infections. Epidemic models can be linked to symmetry and asymmetry from distinct points of view. By using our novel approach, much research may be expected in epidemiology and other areas, particularly concerning COVID-19, to state how immunity develops after being infected by this virus.

Investigating The Behaviourial Analysis Of Disease Transmission Coefficient In SEIRS Epidemic Model With Disease Induced Death

An extensive behaviourial study and analysis of disease transmission coefficient in a SEIRS epidemic model with disease induced death was carried out in this study. The simulation of the system of linear differential equations was obtained using an effective hybrid block method. The results obtained conforms with the objectives of study.

Assessing the Impact of Continuous Vaccination and Voluntary Isolation on the Dynamics of COVID-19: A Mathematical Optimal Control of SEIR Epidemic Model.

In order to study the impact of continuous vaccination and voluntary isolation for the COVID-19, a susceptible-exposed-infected-recovered-quarantine-vaccines (SEIR-QV) model is proposed. A basic regeneration number R0 is defined to determine the extinction or persistence of the disease. We numerically analyze the impact of key parameters based on actual parameters of COVID-19, such as the vaccination rate, population importation rate, and natural (or causal) mortality transmission rate on the dynamics of disease transmission. Then we obtain sensitivity indices of some parameters on R0 by sensitivity analysis. Finally, the stability of the system and the effectiveness of the optimal control strategy are verified by numerical simulation.

Modeling and analysis of SEIRS epidemic models using homotopy perturbation method: A special outlook to 2019-nCoV in India

Considering the prevailing situations, the mathematical modeling and dynamics of novel coronavirus (2019-nCoV) particularly in India are studied in this paper. The goal of this work is to create an effective SEIRS model to study about the epidemic. Four different SEIRS models are considered and solved in this paper using an efficient homotopy perturbation method. A clear picture of disease spreading can be obtained from the solutions derived using this method. We parametrized the model by considering the number of infection cases from 1 April 2020 to 30 June 2020. Finally, numerical analysis and graphical representations are provided to interpret the spread of virus.

Optimization of Site Selection for Emergency Medical Facilities considering the SEIR Model.

Since the outbreak of COVID-19, the rapid construction and operation of Wuhan Vulcan Mountain Hospital and Raytheon Hospital have attracted positive responses from local and international observers. At the same time, it has also highlighted the urgency for the construction of emergency medical facilities for public health emergencies. Before construction, the practical location of medical facilities is the basis for improving the city's emergency management ability. Based on the classic susceptible, exposed, infected, and recovered (SEIR) epidemic model and epidemic data in Guangzhou, we established a multi-stage time-delay SEIR epidemic model that is suitable for epidemic research in Guangzhou. According to the results of the model, the five areas with the highest number of infected patients were identified, which included Baiyun District, Panyu District, Haizhu District, Tianhe District, and Zengcheng District. We then centralized infected individuals at five demand points. Based on the distribution of these points and by combining the characteristics of the emergency medical facilities, we built and solved the set covering location decision model, and considered the economy, society, and environment as the starting points to optimize the site location. Finally, based on simulations, we concluded that appropriate site selection can increase the time required to reach the maximum number of patients and reduce the proportion of infected and exposed people by 11.3% and 1.11%, respectively. This is indicative of the effectiveness of the site selection model and the rational selection of facility points in this study. It solves the optimization problem of the location decision of emergency medical facilities for public health emergencies in China, and also provides some valuable references for site selection decisions of emergency medical facilities in other areas.

Stability analysis of an SEIRS epidemic model with relapse, immune and general incidence rates

Stability analysis of an SEIRS epidemic model with relapse, immune and general incidence rates

Conceptual Investigation of the Disease Transmission Coefficient in Seir Epidemic Model Using Laplace Adomian Decomposition Method (LADM)

In this paper, the impact of disease transmission coefficient on a SEIR epidemic model using Laplace Adomian Decomposition Method (LADM) towards disease eradication is presented. Numerical Simulations which show the effect of transmission coefficient are shown with the use of Maple 18 and the results discussed extensively. The simulation results show that disease transmission coefficient plays vital role in disease eradication.

A Simplified Fractional Seir Epidemic Model and Unique Inversion of the Fractional Order

A simplified linear time-fractional SEIR epidemic system is set forth, and an inverse problem of determining the fractional order is discussed by using the measurement at one given time. By the Laplace transform the solution to the forward problem is obtained, by which the inverse problem is transformed to a nonlinear algebraic equation. By choosing suitable model parameters and the measured time, the nonlinear equation has a unique solution by the monotonicity of the Mittag-Lellfer function. Theoretical testification is presented to demonstrate the unique solvability of the inverse problem.

Effect of two vaccine doses in the SEIR epidemic model using a stochastic cellular automaton

In this work, to support decision making of immunisation strategies, we propose the inclusion of two vaccination doses in the SEIR model considering a stochastic cellular automaton. We analyse three different scenarios of vaccination: (i) unlimited doses, (ii) limited doses into susceptible individuals, and (iii) limited doses randomly distributed overall individuals. Our results suggest that the number of vaccinations and time to start the vaccination is more relevant than the vaccine efficacy, delay between the first and second doses, and delay between vaccinated groups. The scenario (i) shows that the solution can converge early to a disease-free equilibrium for a fraction of individuals vaccinated with the first dose. In the scenario (ii), few two vaccination doses divided into a small number of applications reduce the number of infected people more than into many applications. In addition, there is a low waste of doses for the first application and an increase of the waste in the second dose. The scenario (iii) presents an increase in the waste of doses from the first to second applications more than the scenario (ii). In the scenario (iii), the total of wasted doses increases linearly with the number of applications. Furthermore, the number of effective doses in the application of consecutive groups decays exponentially overtime.

Mathematical Analysis of a SEIR Model with Nonlinear Incidence Rate for COVID-19 Dynamics

In this paper, an SEIR epidemic model with nonlinear incidence is considered. First, we formulate the model and obtain its basic properties. Then, we find the equilibrium points of the model, the disease-free and the endemic equilibrium. The stability of disease-free and endemic equilibrium is associated with the basic reproduction number R. If the basic reproduction number \(\mathcal{R}\) &lt; 1, the disease-free equilibrium \(\mathcal{E}\) is locally as well as globally asymptotically stable. Moreover, if the basic reproduction number \(\mathcal{R}\) &gt; 1, the disease is uniformly persistent and the unique endemic equilibrium \(\mathcal{E}\) * of the system is locally as well as globally asymptotically stable under certain conditions. Finally, the numerical results justify the analytical results.

Sensitivity analysis of SEIR epidemic model of Covid 19 spread in Indonesia

Epidemiological models may provide public health practitioners with some fundamental guidelines, allowing for the examination of issues that may influence disease prevention and treatment techniques. On establish the relative impact of the model parameters to disease transmission, a sensitivity analysis of the epidemiological model is undertaken. A sensitivity analysis of the Susceptible, Exposed, Infectious, and Recovered (SEIR) model of corona virus 2019 (COVID 19) was undertaken to determine the parameters’ influence on the basic reproduction number and endemic equilibrium. The rate of contact between susceptible individual and exposed individuals and rate of exposed to infected individuals are the most impactful parameters on the basic reproduction number and the number of infectious individuals, according to our findings. Furthermore, the number of people who have been exposed is affected by the rate at which they proceed from exposed to infect. The findings show that if infectious people recover faster, the number of contagious people will decrease.

Analysis and Parametrical Estimation with Real COVID-19 Data of a New Extended SEIR Epidemic Model with Quarantined Individuals

During the recent COVID-19 pandemic, quarantine and testing policies have been of vital importance since the causative agent has been a novel virus and no vaccine was developed at the time. In this work, a new epidemiological deterministic model is proposed, analyzed, and discussed. Such a model includes quarantine periods of people with symptoms that have been tested positive, and it will trigger a trace of their close contact, who will be also tested and put in quarantine if the result is positive. Moreover, how the model parameters affect its stability is analyzed with the basic reproduction number R0. Since the COVID-19 outbreak in Spain (approximately 13/03/2020) until 25/04/2021, different restrictions have been applied. For discussion of a real case study, data have been gathered and used from the Spanish Autonomous Community of Cantabria to estimate the parameters and to see how the restrictions have affected their values. In the parameter estimation process, it has been assumed that the constructed model follows the structure of an ARX model. Finally, by considering that the gathered data are subject to certain errors, the paper discusses how to adequate the model usefulness for its use in fitting and processing data through an estimation mechanism involving the provided daily total and positive performed tests.