scholarly journals Global Stability of a Mumps Transmission Model with Quarantine Measure

2021 ◽  
Vol 37 (4) ◽  
pp. 665-672
Author(s):  
Yu-zhen Bai ◽  
Xiao-jing Wang ◽  
Song-bai Guo
2017 ◽  
Vol 10 (06) ◽  
pp. 1750081 ◽  
Author(s):  
Zhiting Xu ◽  
Cuihua Ai

In this paper, we derive a time-delayed and diffusive echinococcosis transmission model. We first address the well-posedness to the initial-value problem for the model and give the basic reproduction number [Formula: see text]. In the case of a bounded spatial domain, we establish the local stability as well as the global stability of the disease-free and disease equilibria of the model. The methods to prove the local and the global stability are to analyze the corresponding characteristic equations and construct Lyapunov functionals, respectively. In the case of an unbounded spatial domain, by applying Schauder’s fixed point theorem and the limiting arguments, we show that when [Formula: see text], there exists a constant [Formula: see text] such that the model admits positive traveling wave solutions connecting the disease-free and endemic equilibrium for [Formula: see text], and when [Formula: see text] and [Formula: see text], the model has no positive traveling wave solutions connecting them.


2015 ◽  
Vol 2015 ◽  
pp. 1-4 ◽  
Author(s):  
Anwar Zeb ◽  
Gul Zaman

We show the erroneous assumptions and reasoning by introducing the migration effect of individuals in the transmission model of Hepatitis B virus. First, some false results related to the eigenvalues and reproductive number in the recent literature in mathematical biology will be presented. Then, it will be proved that the product of the matrices in the next generation method to obtain the reproductive numberR0is not correct and the local and global stability results based on the reproductive numberR0are considered false.


2021 ◽  
Author(s):  
Wen Cao ◽  
Haoran Dai ◽  
Xiaochong Tong ◽  
Jingwen Zhu ◽  
Yuzhen Tian ◽  
...  

Abstract Background: The outbreak of COVID-19 posed a serious threat to human health, economic development, and social stability worldwide, and many countries had taken different interventions to control the deterioration of the epidemic. Although many studies have evaluated the effectiveness of these interventions, there were few reasonable explanations for the practical geographic significance of the model parameters. Our aim was to evaluate the potential of different interventions to mitigate the spread of the epidemic, including discussion about the different time and intensity of implementation, and map parameters of model to the practical application meanings of the special interventions.Methods: In this study, a COVID-19 spread model based on the discrete grid was proposed from perspective of geography. A multi-level grid was introduced to describe the quarantine status and intensity in different spaces, which also combined with the model of medical reception-cured and self-protection, and the spatiotemporal evolution process of early COVID-19 spread was simulated based on the spatial correlation, finally, the effect of interventions was quantitatively analyzed by the dynamic transmission model of COVID-19.Results: Quarantine measure were the most effective interventions, which could effectively reduce the peak value of infection, advance the arrival time of the peak, and shorten the duration of the epidemic, but it only played a role under sufficient intensity; the medical reception-cured and self-protection measure could effectively fatten the infection curve and slowed the spread of the epidemic in the early stage, which could provide more buffer time for the relevant government departments, but the practical effect was not obvious because of the limitation of actually invested resources. The role of the medical reception-cured measure was more reflected in the reduction of the number of deaths, and the effect of the self-protection measure could be reduced in strict quarantine measure.Conclusions: Results of the study indicated that the quarantine, medical reception-cured and self-protection measures were effective, and mitigating the spread of COVID-19 by achieving strong interventions was necessary. Strict quarantine should be implementing as soon as possible in countries with serious development of COVID-19.


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