scholarly journals Bifurcation Analysis of an SIR Epidemic Model with the Contact Transmission Function

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Guihua Li ◽  
Gaofeng Li
Keyword(s):  
Theoretical Basis ◽  
Prevention And Control ◽  
Transmission Function ◽  
Threshold Value ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Contact Transmission ◽  
Disease Spreading ◽  
Intervention Policy ◽  
And Control

We consider an SIR endemic model in which the contact transmission function is related to the number of infected population. By theoretical analysis, it is shown that the model exhibits the bistability and undergoes saddle-node bifurcation, the Hopf bifurcation, and the Bogdanov-Takens bifurcation. Furthermore, we find that the threshold value of disease spreading will be increased, when the half-saturation coefficient is more than zero, which means that it is an effective intervention policy adopted for disease spreading. However, when the endemic equilibria exist, we find that the disease can be controlled as long as we let the initial values lie in the certain range by intervention policy. This will provide a theoretical basis for the prevention and control of disease.

scholarly journals Stability and Hopf Bifurcation for a Delayed SIR Epidemic Model with Logistic Growth

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yakui Xue ◽  
Tiantian Li
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Threshold Value ◽  
Endemic Equilibrium ◽  
Logistic Growth ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Sir Epidemic Model ◽  
Globally Asymptotically Stable ◽  
Sir Epidemic

We study a delayed SIR epidemic model and get the threshold value which determines the global dynamics and outcome of the disease. First of all, for anyτ, we show that the disease-free equilibrium is globally asymptotically stable; whenR0<1, the disease will die out. Directly afterwards, we prove that the endemic equilibrium is locally asymptotically stable for anyτ=0; whenR0>1, the disease will persist. However, for anyτ≠0, the existence conditions for Hopf bifurcations at the endemic equilibrium are obtained. Besides, we compare the delayed SIR epidemic model with nonlinear incidence rate to the one with bilinear incidence rate. At last, numerical simulations are performed to illustrate and verify the conclusions.

scholarly journals Optimal Control of an SIR Model with Delay in State and Control Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Mohamed Elhia ◽  
Mostafa Rachik ◽  
Elhabib Benlahmar
Keyword(s):  
Optimal Control ◽  
Influenza A ◽  
Optimization Strategy ◽  
Sir Epidemic Model ◽  
Optimal Control Strategy ◽  
Control Variables ◽  
Sir Epidemic ◽  
Influenza A H1n1 ◽  
Using Data ◽  
And Control

We will investigate the optimal control strategy of an SIR epidemic model with time delay in state and control variables. We use a vaccination program to minimize the number of susceptible and infected individuals and to maximize the number of recovered individuals. Existence for the optimal control is established; Pontryagin’s maximum principle is used to characterize this optimal control, and the optimality system is solved by a discretization method based on the forward and backward difference approximations. The numerical simulation is carried out using data regarding the course of influenza A (H1N1) in Morocco. The obtained results confirm the performance of the optimization strategy.

scholarly journals Stability Analysis of an Age-Structured SIR Epidemic Model with a Reduction Method to ODEs

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 147 ◽  
Author(s):  
Toshikazu Kuniya
Keyword(s):  
Stability Analysis ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Transmission Function ◽  
Endemic Equilibrium ◽  
Dimensional System ◽  
Relevant Parameter ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Age Structured

In this paper, we are concerned with the asymptotic stability of the nontrivial endemic equilibrium of an age-structured susceptible-infective-recovered (SIR) epidemic model. For a special form of the disease transmission function, we perform the reduction of the model into a four-dimensional system of ordinary differential equations (ODEs). We show that the unique endemic equilibrium of the reduced system exists if the basic reproduction number for the original system is greater than unity. Furthermore, we perform the stability analysis of the endemic equilibrium and obtain a fourth-order characteristic equation. By using the Routh–Hurwitz criterion, we numerically show that the endemic equilibrium is asymptotically stable in some epidemiologically relevant parameter settings.

scholarly journals Forecasting Confirmed Cases, Deaths, and Recoveries from COVID-19 in China during the Early Stage

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
Lianyi Liu ◽  
Yan Chen ◽  
Lifeng Wu
Keyword(s):  
Theoretical Basis ◽  
Prevention And Control ◽  
Early Stage ◽  
Grey Model ◽  
Disease Spread ◽  
Forecasting Accuracy ◽  
And Control

To provide a theoretical basis for the prevention and control of COVID-19 in China, confirmed cases, deaths, and recoveries from COVID-19 in China were predicted using a fractional grey model. The results indicated that the grey model has high forecasting accuracy in the prediction of disease spread.

scholarly journals Modelling, Simulations and Analysis of the First and Second COVID-19 Epidemics in Beijing

2021 ◽  
Author(s):  
Lequan Min
Keyword(s):  
Numerical Simulations ◽  
Prevention And Control ◽  
Control Strategies ◽  
Equation Model ◽  
Control Measures ◽  
Disease Spreading ◽  
Prevention And Control Measures ◽  
Asymptomatic Individuals ◽  
Reported Data ◽  
And Control

AbstractTo date, over 130 million people on infected with COVID-19. It causes more 2.8 millions deaths. This paper introduces a symptomatic-asymptomatic-recoverer-dead differential equation model (SARDDE). It gives the conditions of the asymptotical stability on the disease-free equilibrium of SARDDE. It proposes the necessary conditions of disease spreading for the SARDDE. Based on the reported data of the first and the second COVID-19 epidemics in Beijing and simulations, it determines the parameters of SARDDE, respectively. Numerical simulations of SARDDE describe well the outcomes of current symptomatic and asymptomatic individuals, recovered symptomatic and asymptomatic individuals, and died individuals, respectively. The numerical simulations suggest that both symptomatic and asymptomatic individuals cause lesser asymptomatic spread than symptomatic spread; blocking rate of about 90% cannot prevent the spread of the COVID19 epidemic in Beijing; the strict prevention and control strategies implemented by Beijing government is not only very effective but also completely necessary. The numerical simulations suggest also that using the data from the beginning to the day after about two weeks at the turning point can estimate well or approximately the following outcomes of the two COVID-19 academics, respectively. It is expected that the research can provide better understanding, explaining, and dominating for epidemic spreads, prevention and control measures.

scholarly journals Analysis of a Delayed SIR Model with Nonlinear Incidence Rate

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
Author(s):  
Jin-Zhu Zhang ◽  
Zhen Jin ◽  
Quan-Xing Liu ◽  
Zhi-Yu Zhang
Keyword(s):  
Time Delay ◽  
Incidence Rate ◽  
Incubation Time ◽  
Complex Dynamics ◽  
Threshold Value ◽  
Global Dynamics ◽  
Sir Epidemic Model ◽  
Globally Asymptotically Stable ◽  
Sir Epidemic ◽  
Saturated Form

An SIR epidemic model with incubation time and saturated incidence rate is formulated, where the susceptibles are assumed to satisfy the logistic equation and the incidence term is of saturated form with the susceptible. The threshold valueℜ0determining whether the disease dies out is found. The results obtained show that the global dynamics are completely determined by the values of the threshold valueℜ0and time delay (i.e., incubation time length). Ifℜ0is less than one, the disease-free equilibrium is globally asymptotically stable and the disease always dies out, while if it exceeds one there will be an endemic. By using the time delay as a bifurcation parameter, the local stability for the endemic equilibrium is investigated, and the conditions with respect to the system to be absolutely stable and conditionally stable are derived. Numerical results demonstrate that the system with time delay exhibits rich complex dynamics, such as quasiperiodic and chaotic patterns.

Monitoring of Campylobacter jejuni Contamination in Different Links of Broiler Production Chain in Qingdao

2015 ◽  
Vol 713-715 ◽  
pp. 548-551
Author(s):  
Hai Hua Zhai ◽  
Wei Shan Chang ◽  
Jun Wei Wang ◽  
Juan Wang
Keyword(s):  
Campylobacter Jejuni ◽  
Theoretical Basis ◽  
Prevention And Control ◽  
Scientific Management ◽  
Production Chain ◽  
Microbial Monitoring ◽  
Animal Diseases ◽  
Broiler Production ◽  
Genotyping Method ◽  
And Control

Microbial monitoring of broiler production can provide an important theoretical basis for the prevention and control of animal diseases and reduce the pollution of the environment. In order to investigate the contamination and spread of Campylobacter jejuni in broiler production chain, we collected samples from the broiler farms, slaughterhouse and market of a big production chain in Qingdao, isolated and identified of Campylobacter jejuni. Then we used genotyping method to subtype the isolates. The result showed that C.jejuni were widespread in broiler pruduction chain, and the strains can spread during the production chain, so strengthen the scientific management of the production chain must be implemented. Control in the feeding, processing and preparation before eating of chicken are the important measures in reducing the Campylobacter jejuni infections caused by chicken.

scholarly journals Shortages of hospital beds exacerbate severity of COVID-19 outbreaks

2020 ◽  
Author(s):  
Weike Zhou ◽  
Aili Wang ◽  
Xia Wang ◽  
Robert A Cheke ◽  
Sanyi Tang
Keyword(s):  
Prevention And Control ◽  
Reproduction Number ◽  
Control Strategies ◽  
Threshold Value ◽  
Control Measures ◽  
Unknown Parameters ◽  
Health Authorities ◽  
Hospital Beds ◽  
And Control ◽  
The Impact

Abstract Background: The global outbreak of COVID-19 has caused worrying concern amongst the public and health authorities. The first and foremost problem that many countries face is a shortage of medical resources. The experience of Wuhan, China, in fighting against COVID-19 provides a model for other countries to learn from. Methods: We formulated a piecewise smooth model to describe the limitation of hospital beds, based on the transmission progression of COVID-19, and the strengthening prevention and control strategies implemented in Wuhan, China. We used data of the cumulative numbers of confirmed cases, cured cases and deaths in Wuhan city from 10 January to 20 March, 2020 to estimate unknown parameters and the effective reproduction number. Sensitivity analysis was conducted to investigate the impact of a shortage of hospital beds on the COVID-19 outbreak. Results: Even with strong prevention and control measures in Wuhan, slowing down of the supply rate, reducing the maximum capacity and delaying the intervention time of supplementing hospital beds aggravated the outbreak severity by magnifying the cumulative numbers of confirmed cases and deaths, prolonging the period of the outbreak in Wuhan, enlarging the value of the effective reproduction number during the outbreak and postponing the time when the threshold value is reduced to 1. Conclusions: The quick establishment of the Huoshenshan and Leishenshan Hospitals in a short time and the deployment of mobile cabin hospitals played important roles in containing the COVID-19 outbreak in Wuhan, providing a model for other countries to provide more hospital beds for COVID-19 patients faster and earlier.

scholarly journals Rich dynamics of an SIR epidemic model

2010 ◽  
Vol 15 (1) ◽  
pp. 71-81 ◽  
Author(s):  
S. Pathak ◽  
A. Maiti ◽  
G. P. Samanta
Keyword(s):  
Numerical Simulations ◽  
Epidemic Model ◽  
Transmission Function ◽  
Endemic Equilibrium ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
The Stability ◽  
Disease Free

This paper aims to study an SIR epidemic model with an asymptotically homogeneous transmission function. The stability of the disease-free and the endemic equilibrium is addressed. Numerical simulations are carried out. Implications of our analytical and numerical findings are discussed critically.

scholarly journals Risk factors analyses and preventive measures of immersed tunnel engineering

2021 ◽  
Vol 236 ◽  
pp. 02025
Author(s):  
Jiao Zhang ◽  
Sainan Fu ◽  
Jianping Zhu ◽  
Jiancheng Wang
Keyword(s):  
Risk Factors ◽  
Risk Management ◽  
Theoretical Basis ◽  
Prevention And Control ◽  
Preventive Measures ◽  
Control Measures ◽  
Tunnel Engineering ◽  
Immersed Tunnel ◽  
Prevention And Control Measures ◽  
And Control

Based on the comprehensive analyses of many risk factors leading to accidents in immersed tunnel engineering, it is concluded that the risk factors leading to accidents in immersed tunnel engineering are very large and must be paid attention to in all aspects at all stages of the project. This paper classifies and identifies the risk factors in immersed tunnel engineering by investigating and visiting the relevant investigation, design and construction units of immersed tunnel, and then puts forward prevention and control measures to provide theoretical basis for the prevention of risk factors in Immersed Tunnel Engineering in the future and the risk management of the whole project.

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