STABILITY AND BIFURCATION ANALYSIS OF A STAGE-STRUCTURED SIR MODEL WITH TIME DELAYS

2010 ◽  
Vol 03 (03) ◽  
pp. 337-350
Author(s):  
ZHICHAO JIANG ◽  
CHUNJIANG HE ◽  
GUANGTAO CHENG
Keyword(s):  
Infectious Disease ◽  
Time Delays ◽  
Disease Model ◽  
Sir Model ◽  
Constant Time Delay ◽  
Boundedness Of Solutions ◽  
Infectious Disease Model ◽  
Stability And Bifurcation Analysis ◽  
Two Stages ◽  
Positivity And Boundedness

In this paper, we considered an SIR infectious disease model with two stages, immature and mature, with the time to maturity represented by a constant time delay. We obtain positivity and boundedness of solutions and analyze the equilibria and their stability properties.

Stability and Bifurcation Analysis of a Stage-Structured SIR Model with Time Delays

2012 ◽  
Vol 468-471 ◽  
pp. 1070-1073
Author(s):  
Shan Wen Yan ◽  
Li Zhang
Keyword(s):  
Infectious Disease ◽  
Time Delays ◽  
Disease Model ◽  
Sufficient Conditions ◽  
Sir Model ◽  
Constant Time Delay ◽  
Infectious Disease Model ◽  
Stability And Bifurcation Analysis ◽  
The Stability ◽  
Two Stages

In this paper, we considered a SIR infectious disease model with two stages, immature and mature, with the time to maturity represented by a constant time delay. Positivity and boundness of solutions and sufficient conditions of the stability of equilibria are obtained.

scholarly journals Analysis of Response to the Wild Hornet Crisis Based on the SIR Model

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Aihua Gu ◽  
Mengmeng Li ◽  
Yue Ran ◽  
Zhenzhuo Wang ◽  
Shujun Li ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Disease Model ◽  
Least Square Method ◽  
Theoretical Models ◽  
Sir Model ◽  
Least Square ◽  
Grey System ◽  
Local Conditions ◽  
Infectious Disease Model ◽  
Very High

In this paper, we propose 4 theoretical models to deal with the wild hornet crisis. First, we use ORIGIN to visualize the distribution of wild wasps. Using the least square method and the grey system GM (1, 1), we establish a theoretical model to predict the propagation of wild wasps over time and analyze the accuracy of the model. However, the accuracy of our model is not very high, which results from the influence of many factors such as climate and human. Secondly, we use convolution neural network to recognize the images. With the increase of network depth, the accuracy rate reaches a bottleneck, which can help predict mistaken classification. We also use the SIR infectious disease model based on the dataset file provided. In the model, we mark the confirmed giant hornet as the infected state I (infected), mark the nonwild wasp as the removed state R (removed, refractory, or recovered), and mark the unclassified and unverified wild wasp as the susceptible state S (susceptible). A model to predict the possibility of misclassification was established by considering the normal death of wild wasp. Thirdly, by analogy with the SIR model, when the epidemic occurs, people pay more attention to the infected person. Thus, the SIR model will lead to the most likely positive sightings. Then, in order to ensure the timeliness and accuracy, the model must be updated once a year by changing or adding parameter according to local conditions. Finally, by establishing an optimized SIR infectious disease model, we added the factor of the Washington state’s control of wild wasps. The analysis shows that the number of infected I (i.e., wild wasps) has tended to zero after 250 days, so it can be proved that the Washington state has eliminated the pest.

scholarly journals DNA Epidemic Model Construction and Dynamics Optimization

2020 ◽  
Vol 14 (3) ◽  
pp. 97-117
Author(s):  
Yinglian Zhou
Keyword(s):  
Infectious Disease ◽  
Disease Transmission ◽  
Optimization Problems ◽  
Disease Model ◽  
Sir Model ◽  
Test Results ◽  
Infectious Disease Model ◽  
Exchange Information ◽  
Complex Optimization ◽  
Dna Algorithm

In order to solve some complex optimization problems, the SIR-DNA algorithm was constructed based on the DNA-based SIR (susceptible-infectious-recovered) infectious disease model. Since infectious diseases attack a very small part of the individual's genes, the number of variables per treatment is small; thus, the natural dimensionality reduction of the algorithm is achieved. Based on the DNA-SIR infectious disease model, different infections can be distinguished in the pathogenesis of viruses. The mechanisms of disease transmission are described by the SIR model, and these are used to construct operators such as SS, SI, II, IR, RR, and RS, so that individuals can naturally exchange information naturally through disease transmission. The test results show that the algorithm has the characteristics of strong search ability and has a high convergence speed for solving complex optimization problems.

scholarly journals Obesity as an "infectious" disease

2021 ◽  
Vol 11 (9) ◽  
pp. 534-537
Author(s):  
Daria Żuraw ◽  
Paulina Oleksa ◽  
Mateusz Sobczyk
Keyword(s):  
Infectious Disease ◽  
Disease Model ◽  
Living Environment ◽  
Social Contagion ◽  
Social Discrimination ◽  
Obese People ◽  
Obesity Epidemic ◽  
Global Epidemic ◽  
Infectious Disease Model ◽  
The One

Introduction: Obesity has been recognized as a global epidemic by the WHO, followed by a wealth of empirical evidence supporting its contagiousness. However, the dynamics of the spread of obesity between individuals are rarely studied.  A distinguishing feature of the obesity epidemic is that it is driven by a process of social contagion that cannot be perfectly described by the infectious disease model. There is also social discrimination in the obesity epidemic. Social discrimination against obese people plays quite different roles in two cases: on the one hand, when obesity cannot be eliminated, social discrimination can reduce the number of obese people; on the other hand, when obesity is eradicable, social discrimination can cause it to explode.(1)   Materiał and methods: A literature analysis on obesity epidemic was carried out within the Pubmed, Google scholar and Research Gate platform. The following keywords were used in serach: obesity, epidemy, children, body max index.    Purpose of the work: The aim of the following analysis is to present an obesity as an infectious disease. The steadily increasing percentage of obese people, including children, shows that there is an obesity epidemic. This is the phenomenon of social contagion, which partially explains the concept of homophily, which involves the grouping of people with similar characteristics. Potential explanations are also provided by sharing a living environment with similar access to certain foods and similar opportunities for physical activity, which defines the occurrence of analogous health habits

Improving Computational Models and Practices

2012 ◽  
pp. 432-455
Author(s):  
Iain Barrass ◽  
Joanna Leng
Keyword(s):  
Public Health ◽  
Infectious Disease ◽  
Computational Models ◽  
Disease Model ◽  
Significant Risk ◽  
Epidemiological Studies ◽  
Health Interventions ◽  
Computational Steering ◽  
Infectious Disease Model

Since infectious diseases pose a significant risk to human health many countries aim to control their spread. Public health bodies faced with a disease threat must understand the disease’s progression and its transmission process. From this understanding it is possible to evaluate public health interventions intended to decrease impacts on the population. Commonly, contingency planning has been achieved through epidemiological studies and the use of relatively simple models. However, computational methods increasingly allow more complex, and potentially more realistic, simulations of various scenarios of the control of the spread of disease. However, understanding computational results from more sophisticated models can pose considerable challenges. A case study of a system combining a complex infectious disease model with interactive visualization and computational steering tools shows some of the opportunities this approach offers to infectious disease control.

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