In this paper, we study a kind of the delayed SEIQR infectious disease model with the quarantine and latent, and get the threshold value which determines the global dynamics and the outcome of the disease. The model h...In this paper, we study a kind of the delayed SEIQR infectious disease model with the quarantine and latent, and get the threshold value which determines the global dynamics and the outcome of the disease. The model has a disease-free equilibrium which is unstable when the basic reproduction number is greater than unity. At the same time, it has a unique endemic equilibrium when the basic reproduction number is greater than unity. According to the mathematical dynamics analysis, we show that disease-free equilibrium and endemic equilibrium are locally asymptotically stable by using Hurwitz criterion and they are globally asymptotically stable by using suitable Lyapunov functions for any Besides, the SEIQR model with nonlinear incidence rate is studied, and the that the basic reproduction number is a unity can be found out. Finally, numerical simulations are performed to illustrate and verify the conclusions that will be useful for us to control the spread of infectious diseases. Meanwhile, the will effect changing trends of in system (1), which is obvious in simulations. Here, we take as an example to explain that.展开更多
This article attempts to establish a mathematical epidemic model for the outbreak of the new COVID-19 coronavirus.A new consideration for evaluating and controlling the COVID-19 outbreak will be constructed based on t...This article attempts to establish a mathematical epidemic model for the outbreak of the new COVID-19 coronavirus.A new consideration for evaluating and controlling the COVID-19 outbreak will be constructed based on the SEIQR Pandemic Model.In this paper,the real data of COVID-19 spread in Saudi Arabia has been used for the mathematical model and dynamic analyses.Including the new reproductive number and detailed stability analysis,the dynamics of the proposed SEIQR model have been applied.The local sensitivity of the reproduction number has been analyzed.The domain of solution and equilibrium based on the SEIQR model have been proved using a Jacobian linearization process.The state of equilibrium and its significance have been proved,and a study of the integrity of the disease-free equilibrium has been carried out.The Lyapunov stability theorem demonstrated the global stability of the current model equilibrium.The SEIQR model has been numerically validated and projected by contrasting the results from the SEIQR model with the actual COVID-19 spread data in Saudi Arabia.The result of this paper shows that the SEIQR model is a model that is effective in analyzing epidemic spread,such as COVID-19.At the end of the study,we have implemented the protocol which helped the Saudi population to stop the spread of COVID-19 rapidly.展开更多
由于二次感染及“复阳”问题的出现,以及隔离人群变量的增加,本文在SEIR传染病模型基础上,建立含有隔离人群的SEIRS模型。使用香港第五波新冠疫情数据,通过最小二乘法求得含有隔离人群的SEIRS模型中各参数最优解,并使用Python软件模拟...由于二次感染及“复阳”问题的出现,以及隔离人群变量的增加,本文在SEIR传染病模型基础上,建立含有隔离人群的SEIRS模型。使用香港第五波新冠疫情数据,通过最小二乘法求得含有隔离人群的SEIRS模型中各参数最优解,并使用Python软件模拟得到新冠病毒传播趋势。结果显示:含有隔离人群的SEIRS模型与香港新冠肺炎的实际传播走势较为一致。表明增加有效的隔离手段,如建立方舱医院等方式,能提升隔离率,使感染人群数量不断下降,从而以最大力量保护人民生命安全。Due to the emergence of secondary infection and “re-infection”, as well as the increase of quaran-tined population variables, a SEIRS model was established based on the SEIR epidemic model with quarantined population. Using the data of the fifth wave of COVID-19 in Hong Kong, the least square method was used to obtain the optimal solution of each parameter in the SEIRS model containing the quarantined population, and the spread trend of COVID-19 was simulated by Python software. The result shows: the SEIRS model containing quarantined population is consistent with the actual transmission trend of COVID-19 in Hong Kong. It shows that increasing effective isolation methods, such as the establishment of mobile cabin hospitals, can improve the isolation rate, reduce the number of infected people, so as to protect people's lives as much as possible.展开更多
文摘In this paper, we study a kind of the delayed SEIQR infectious disease model with the quarantine and latent, and get the threshold value which determines the global dynamics and the outcome of the disease. The model has a disease-free equilibrium which is unstable when the basic reproduction number is greater than unity. At the same time, it has a unique endemic equilibrium when the basic reproduction number is greater than unity. According to the mathematical dynamics analysis, we show that disease-free equilibrium and endemic equilibrium are locally asymptotically stable by using Hurwitz criterion and they are globally asymptotically stable by using suitable Lyapunov functions for any Besides, the SEIQR model with nonlinear incidence rate is studied, and the that the basic reproduction number is a unity can be found out. Finally, numerical simulations are performed to illustrate and verify the conclusions that will be useful for us to control the spread of infectious diseases. Meanwhile, the will effect changing trends of in system (1), which is obvious in simulations. Here, we take as an example to explain that.
基金The authors are grateful and thank the Research and Development Grants Program for National Research Institutions and Centres(GRANTS),Target Research Program,Infectious Diseases Research Grant Program,King Abdulaziz City for Science and Technology(KACST)Kingdom of Saudi Arabia,for funding this project and this work with grant number(5-20-01-007-0002).
文摘This article attempts to establish a mathematical epidemic model for the outbreak of the new COVID-19 coronavirus.A new consideration for evaluating and controlling the COVID-19 outbreak will be constructed based on the SEIQR Pandemic Model.In this paper,the real data of COVID-19 spread in Saudi Arabia has been used for the mathematical model and dynamic analyses.Including the new reproductive number and detailed stability analysis,the dynamics of the proposed SEIQR model have been applied.The local sensitivity of the reproduction number has been analyzed.The domain of solution and equilibrium based on the SEIQR model have been proved using a Jacobian linearization process.The state of equilibrium and its significance have been proved,and a study of the integrity of the disease-free equilibrium has been carried out.The Lyapunov stability theorem demonstrated the global stability of the current model equilibrium.The SEIQR model has been numerically validated and projected by contrasting the results from the SEIQR model with the actual COVID-19 spread data in Saudi Arabia.The result of this paper shows that the SEIQR model is a model that is effective in analyzing epidemic spread,such as COVID-19.At the end of the study,we have implemented the protocol which helped the Saudi population to stop the spread of COVID-19 rapidly.
文摘由于二次感染及“复阳”问题的出现,以及隔离人群变量的增加,本文在SEIR传染病模型基础上,建立含有隔离人群的SEIRS模型。使用香港第五波新冠疫情数据,通过最小二乘法求得含有隔离人群的SEIRS模型中各参数最优解,并使用Python软件模拟得到新冠病毒传播趋势。结果显示:含有隔离人群的SEIRS模型与香港新冠肺炎的实际传播走势较为一致。表明增加有效的隔离手段,如建立方舱医院等方式,能提升隔离率,使感染人群数量不断下降,从而以最大力量保护人民生命安全。Due to the emergence of secondary infection and “re-infection”, as well as the increase of quaran-tined population variables, a SEIRS model was established based on the SEIR epidemic model with quarantined population. Using the data of the fifth wave of COVID-19 in Hong Kong, the least square method was used to obtain the optimal solution of each parameter in the SEIRS model containing the quarantined population, and the spread trend of COVID-19 was simulated by Python software. The result shows: the SEIRS model containing quarantined population is consistent with the actual transmission trend of COVID-19 in Hong Kong. It shows that increasing effective isolation methods, such as the establishment of mobile cabin hospitals, can improve the isolation rate, reduce the number of infected people, so as to protect people's lives as much as possible.
