scholarly journals Dynamic Analysis of an SEIR Model with Distinct Incidence for Exposed and Infectives

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Junhong Li ◽  
Ning Cui
Keyword(s):  
Matrix Theory ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Vaccination Strategy ◽  
Invariant Set ◽  
Incidence Rates ◽  
Seir Model ◽  
Asymptotical Stable ◽  
Compound Matrix ◽  
Disease Free

An SEIR model with vaccination strategy that incorporates distinct incidence rates for the exposed and the infected populations is studied. By means of Lyapunov function and LaSalle’s invariant set theorem, we proved the global asymptotical stable results of the disease-free equilibrium. The sufficient conditions for the global stability of the endemic equilibrium are obtained using the compound matrix theory. Furthermore, the method of direct numerical simulation of the system shows that there is a periodic solution, when the system has three equilibrium points.

Dynamics Analysis of an SEIQS Model with a Nonlinear Incidence Rate

2012 ◽  
Vol 157-158 ◽  
pp. 1220-1223
Author(s):  
Ning Cui ◽  
Jun Hong Li ◽  
Jiao Qu ◽  
Hong Dan Xue
Keyword(s):  
Lyapunov Function ◽  
Incidence Rate ◽  
Matrix Theory ◽  
Invariant Set ◽  
Dynamics Analysis ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Asymptotical Stable ◽  
Compound Matrix ◽  
Disease Free

This paper considers an SEIQS model with nonlinear incidence rate. By means of Lyapunov function and LaSalle’s invariant set theorem, we proved the global asymptotical stable results of the disease-free equilibrium. It is then obtained the sufficent conditions for the global stability of the endemic equilibrium by the compound matrix theory. In addition, we also study the phenomena of limit cycle of the systems with the numerical simulations.

A stochastic vaccinated epidemic model incorporating Lévy processes with a general awareness-induced incidence

2021 ◽  
pp. 2150044
Author(s):  
Khadija Akdim ◽  
Adil Ez-Zetouni ◽  
Mehdi Zahid
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Dynamic Behavior ◽  
Epidemic Model ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Lévy Noise ◽  
Global Positive Solution ◽  
Levy Noise ◽  
Disease Free

In this paper, we investigate a stochastic vaccinated epidemic model with a general awareness-induced incidence perturbed by Lévy noise. First, we show that this model has a unique global positive solution. Therefore, we establish the dynamic behavior of the solution around both disease-free and endemic equilibrium points. Furthermore, when [Formula: see text], we give sufficient conditions for the existence of an ergodic stationary distribution to the model when the jump part in the Lévy noise is null. Finally, we present some examples to illustrate the analytical results by numerical simulations.

scholarly journals Mathematical Analysis of a Cholera Model with Vaccination

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Jing'an Cui ◽  
Zhanmin Wu ◽  
Xueyong Zhou
Keyword(s):  
Disease Transmission ◽  
Reproduction Number ◽  
Sufficient Conditions ◽  
Endemic Equilibrium ◽  
Disease Spread ◽  
Relative Importance ◽  
Globally Asymptotically Stable ◽  
Perform Sensitivity Analysis ◽  
Compound Matrix ◽  
Disease Free

We consider aSVR-Bcholera model with imperfect vaccination. By analyzing the corresponding characteristic equations, the local stability of a disease-free equilibrium and an endemic equilibrium is established. We calculate the certain threshold known as the control reproduction numberℛv. Ifℛv<1, we obtain sufficient conditions for the global asymptotic stability of the disease-free equilibrium; the diseases will be eliminated from the community. By comparison of arguments, it is proved that ifℛv>1, the disease persists and the unique endemic equilibrium is globally asymptotically stable, which is obtained by the second compound matrix techniques and autonomous convergence theorems. We perform sensitivity analysis ofℛvon the parameters in order to determine their relative importance to disease transmission and show that an imperfect vaccine is always beneficial in reducing disease spread within the community.

scholarly journals Mathematical Model for MERS-COV Disease Transmission with Medical Mask Usage and Vaccination

2019 ◽  
Vol 1 (2) ◽  
Author(s):  
Muhammad Manaqib ◽  
Irma Fauziah ◽  
Mujiyanti Mujiyanti
Keyword(s):  
Equilibrium Point ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Local Equilibrium ◽  
Preventive Measure ◽  
Simulation Models ◽  
Seir Model ◽  
Model Stability ◽  
Disease Free

AbstractThis study developed a model of the spread of MERS-CoV disease using the SEIR model which was added by a health mask and vaccination factor as a preventive measure. The population is divided into six subpopulations namely susceptible subpopulations not using health masks and using health masks, exposed subpopulations, infected subpopulations not using health masks and using health masks, and recovering subpopulations. The results are obtained two equilibrium points, namely disease-free equilibrium points and endemic equilibrium points. Analysis of the stability of the disease-free equilibrium point using linearization around the equilibrium point. As a result, the asymptotic stable disease-free local equilibrium point if the base reproduction number is less than one. Numerical simulation models for MERS-CoV disease are carried out in line with the analysis of model behavior.Keywords: MERS-CoV, SEIR Model, Stability Equilibrium Point, Basic Reproduction Number. AbstrakPenelitian ini mengembangkan model penyebaran penyakit MERS-CoV menggunakan model SEIR yang ditambahkan faktor masker kesehatan dan vaksinasi sebagai upaya pencegahan. Populasi dibagi menjadi enam subpopulasi yaitu subpopulasi rentan tidak menggunakan masker kesehatan dan menggunakan masker kesehatan, subpopulasi laten, subpopulasi terinfeksi tidak menggunakan masker kesehatan dan menggunakan masker kesehatan, serta subpopulasi sembuh. Hasilnya diperoleh dua titik ekuilibrium yaitu titik ekulibrium bebas penyakit dan endemik. Analisis kestabilan titik ekuilibrium bebas penyakit menggunakan linearisasi disekitar titik ekuilibrium. Hasilnya, titik ekuilibrium bebas penyakit stabil asimtotik lokal jika bilangan reproduksi dasar kurang dari satu. Simulasi numerik model untuk penyakit MERS-CoV yang dilakukan sejalan dengan analisis perilaku model.Kata kunci: MERS-CoV, Model SEIR, Kestabilan Titik Ekuilibrium, Bilangan Reproduksi Dasar.

scholarly journals Analisis Kestabilan Model SEIR Penyebaran Penyakit Campak dengan Pengaruh Imunisasi dan Vaksin MR

2019 ◽  
Vol 16 (1) ◽  
pp. 107
Author(s):  
Willyam Daniel Sihotang ◽  
Ceria Clara Simbolon ◽  
July Hartiny ◽  
Desrinawati Tindaon ◽  
Lasker Pangarapan Sinaga
Keyword(s):  
Infectious Disease ◽  
Equilibrium Point ◽  
Numerical Solutions ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Seir Model ◽  
Rate Of Spread ◽  
The Stability ◽  
Disease Free

Measles is a contagious infectious disease caused by a virus and has the potential to cause an outbreak. Immunization and vaccination are carried out as an effort to prevent the spread of measles. This study aims to analyze and determine the stability of the SEIR model on the spread of measles with the influence of immunization and MR vaccines. The results obtained from model analysis, namely there are two disease free and endemic equilibrium points. If the conditions are met, the measles-free equilibrium point will be asymptotically stable and the measles endemic equilibrium point will be stable. Numerical solutions show a decrease in the rate of spread of measles due to the effect of immunization and the addition of MR vaccines.

scholarly journals Forecast analysis of the epidemics trend of COVID-19 in the United States by a generalized fractional-order SEIR model

2020 ◽  
Author(s):  
Conghui Xu ◽  
Yongguang Yu ◽  
YangQuan Chen ◽  
Zhenzhen Lu
Keyword(s):  
United States ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Equilibrium Points ◽  
The United States ◽  
Endemic Equilibrium ◽  
Qualitative Properties ◽  
Prediction Ability ◽  
Seir Model ◽  
Disease Free

AbstractIn this paper, a generalized fractional-order SEIR model is proposed, denoted by SEIQRP model, which has a basic guiding significance for the prediction of the possible outbreak of infectious diseases like COVID-19 and other insect diseases in the future. Firstly, some qualitative properties of the model are analyzed. The basic reproduction number R0 is derived. When R0 < 1, the disease-free equilibrium point is unique and locally asymptotically stable. When R0 > 1, the endemic equilibrium point is also unique. Furthermore, some conditions are established to ensure the local asymptotic stability of disease-free and endemic equilibrium points. The trend of COVID-19 spread in the United States is predicted. Considering the influence of the individual behavior and government mitigation measurement, a modified SEIQRP model is proposed, defined as SEIQRPD model. According to the real data of the United States, it is found that our improved model has a better prediction ability for the epidemic trend in the next two weeks. Hence, the epidemic trend of the United States in the next two weeks is investigated, and the peak of isolated cases are predicted. The modified SEIQRP model successfully capture the development process of COVID-19, which provides an important reference for understanding the trend of the outbreak.

scholarly journals Protection after Quarantine: Insights from a Q-SEIR Model with Nonlinear Incidence Rates Applied to COVID-19

2020 ◽  
Author(s):  
Jose Marie Antonio Minoza ◽  
Jesus Emmanuel Sevilleja ◽  
Romulo de Castro ◽  
Salvador E. Caoili ◽  
Vena Pearl Bongolan
Keyword(s):  
Reproduction Number ◽  
Incidence Rates ◽  
Health Promoting Behaviors ◽  
Strict Adherence ◽  
Seir Model ◽  
Nonlinear Incidence ◽  
Nonlinear Incidence Rates ◽  
Health Promoting ◽  
Two Parameters ◽  
Disease Free

AbstractCommunity quarantine has been resorted to by various governments to address the current COVID-19 pandemic; however, this is not the only non-therapeutic method of effectively controlling the spread of the infection. We study an SEIR model with nonlinear incidence rates, and introduce two parameters, α and ε, which mimics the effect of quarantine (Q). We compare this with the Q-SEIR model, recently developed, and demonstrate the control of COVID-19 without the stringent conditions of community quarantine. We analyzed the sensitivity and elasticity indices of the parameters with respect to the reproduction number. Results suggest that a control strategy that involves maximizing α and ε is likely to be successful, although quarantine is still more effective in limiting the spread of the virus. Release from quarantine depends on continuance and strict adherence to recommended social and health promoting behaviors. Furthermore, maximizing α and ε is equivalent to a 50% successful quarantine in disease-free equilibrium (DFE). This model reduced the infectious in Quezon City by 3.45% and Iloilo Province by 3.88%; however, earlier peaking by nine and 17 days, respectively, when compared with the results of Q-SEIR.

scholarly journals A Mathematical Study of a Generalized SEIR Model of COVID-19

2020 ◽  
Vol 2 ◽  
pp. 30-67
Author(s):  
Abdelkader Intissar
Keyword(s):  
Control Strategies ◽  
Nonlinear Dynamical System ◽  
Globally Asymptotically Stable ◽  
Seir Model ◽  
Nonlinear Dynamical ◽  
Compound Matrices ◽  
Compound Matrix ◽  
The Stability ◽  
Additive Compound ◽  
Disease Free

In this work (Part I), we reinvestigate the study of the stability of the Covid-19 mathematical model constructed by Shah et al. (2020) [1]. In their paper, the transmission of the virus under different control strategies is modeled thanks to a generalized SEIR model. This model is characterized by a five dimensional nonlinear dynamical system, where the basic reproduction number can be established by using the next generation matrix method. In this work (Part I), it is established that the disease free equilibrium point is locally as well as globally asymptotically stable when . When , the local and global asymptotic stability of the equilibrium are determined employing the second additive compound matrix approach and the Li-Wang’s (1998) stability criterion  for real matrices [2]. In the second paper (Part II), some control parameters with uncertainties will be added to stabilize the five-dimensional Covid-19 system studied here, in order to force the trajectories to go to the equilibria. The stability of the Covid-19 system with these new parameters will also be assessed in Intissar (2020) [3] applying the Li-Wang criterion and compound matrices theory. All sophisticated technical calculations including those in part I will be provided in appendices of the part II.

scholarly journals Modeling the Dynamics of an Epidemic under Vaccination in Two Interacting Populations

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Ibrahim H. I. Ahmed ◽  
Peter J. Witbooi ◽  
Kailash Patidar
Keyword(s):  
Optimal Control Theory ◽  
Equilibrium Points ◽  
Vaccination Strategy ◽  
Kutta Method ◽  
Sir Epidemic ◽  
Runge Kutta Method ◽  
Interacting Populations ◽  
Group Population ◽  
The Stability ◽  
Disease Free

We present a model for an SIR epidemic in a population consisting of two components—locals and migrants. We identify three equilibrium points and we analyse the stability of the disease free equilibrium. Then we apply optimal control theory to find an optimal vaccination strategy for this 2-group population in a very simple form. Finally we support our analysis by numerical simulation using the fourth order Runge-Kutta method.

scholarly journals Analysis of a Multiscale Model of Ebola Virus Disease

2020 ◽  
pp. 53-69
Author(s):  
Duncan O. Oganga ◽  
George O. Lawi ◽  
Colleta A. Okaka
Keyword(s):  
Ebola Virus ◽  
Reproduction Number ◽  
Virus Disease ◽  
Equilibrium Points ◽  
Vaccination Strategy ◽  
Multiscale Model ◽  
Ebola Virus Disease ◽  
Disease Spread ◽  
The Impact ◽  
Disease Free

Multiscale models are ones that link the epidemiological processes dealing with the transmission between hosts and the immunological processes dealing with the dynamics within one host. In this study, a multiscale model of Ebola Virus Disease linking epidemiological and immunological processes has been developed and analysed. The model has considered two infectious classes ; the exposed and the infected individuals. Local and global stability analyses of the Disease Free Equilibrium and the Endemic Equilibrium points of the model show that the disease dies out if the basic reproduction number Rc0 < 1 and persists in the population when Rc0 > 1 respectively. Sensitivity analysis shows that the rate of vaccination, v , is the most sensitive parameter. This indicates that effort should be directed towards implementing an effective vaccination strategy to control the spread of the disease. It has also been established that when treatment efficacy is scaled up, the viral load goes down and consequently, the transmission between hosts is also reduced. The impact of treatment on the disease spread has also been established through the coupling function (L∗) . The study indicates that a higher percentage of the exposed and the infected individuals should be treated to control the spread of the disease within the population.

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