This paper investigates a new SEIQR(susceptible–exposed–infected–quarantined–recovered) epidemic model with quarantine mechanism on heterogeneous complex networks. Firstly, the nonlinear SEIQR epidemic spreading d...This paper investigates a new SEIQR(susceptible–exposed–infected–quarantined–recovered) epidemic model with quarantine mechanism on heterogeneous complex networks. Firstly, the nonlinear SEIQR epidemic spreading dynamic differential coupling model is proposed. Then, by using mean-field theory and the next-generation matrix method, the equilibriums and basic reproduction number are derived. Theoretical results indicate that the basic reproduction number significantly relies on model parameters and topology of the underlying networks. In addition, the globally asymptotic stability of equilibrium and the permanence of the disease are proved in detail by the Routh–Hurwitz criterion, Lyapunov method and La Salle's invariance principle. Furthermore, we find that the quarantine mechanism, that is the quarantine rate(γ1, γ2), has a significant effect on epidemic spreading through sensitivity analysis of basic reproduction number and model parameters. Meanwhile, the optimal control model of quarantined rate and analysis method are proposed, which can optimize the government control strategies and reduce the number of infected individual. Finally, numerical simulations are given to verify the correctness of theoretical results and a practice application is proposed to predict and control the spreading of COVID-19.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
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
COVID-19 is a constantly challenging global health issue due to its strong intensity,rapid mutation and high infectiousness.The new Delta and Omicron variants have triggered massive outbreaks worldwide.Even China,whic...COVID-19 is a constantly challenging global health issue due to its strong intensity,rapid mutation and high infectiousness.The new Delta and Omicron variants have triggered massive outbreaks worldwide.Even China,which has done a good job in outbreak prevention,is still heavily affected by the virus.The long-term fight against multiple COVID-19 outbreaks is ongoing.In this study,we propose an SEIQR model that considers the incubation period and quarantine measurement.We verified our model using actual outbreak data from four Chinese cities.Numerical simulations show that a five-day delay results in a double resurgence scale.Our model can be used as a tool to understand the spread of the virus quantitatively and provide a reference for policymaking accordingly.展开更多
基金Project supported the Natural Science Foundation of Zhejiang Province, China (Grant No. LQN25F030011)the Fundamental Research Project of Hangzhou Dianzi University (Grant No. KYS065624391)+1 种基金the National Natural Science Foundation of China (Grant No. 61573148)the Science and Technology Planning Project of Guangdong Province, China (Grant No. 2019A050520001)。
文摘This paper investigates a new SEIQR(susceptible–exposed–infected–quarantined–recovered) epidemic model with quarantine mechanism on heterogeneous complex networks. Firstly, the nonlinear SEIQR epidemic spreading dynamic differential coupling model is proposed. Then, by using mean-field theory and the next-generation matrix method, the equilibriums and basic reproduction number are derived. Theoretical results indicate that the basic reproduction number significantly relies on model parameters and topology of the underlying networks. In addition, the globally asymptotic stability of equilibrium and the permanence of the disease are proved in detail by the Routh–Hurwitz criterion, Lyapunov method and La Salle's invariance principle. Furthermore, we find that the quarantine mechanism, that is the quarantine rate(γ1, γ2), has a significant effect on epidemic spreading through sensitivity analysis of basic reproduction number and model parameters. Meanwhile, the optimal control model of quarantined rate and analysis method are proposed, which can optimize the government control strategies and reduce the number of infected individual. Finally, numerical simulations are given to verify the correctness of theoretical results and a practice application is proposed to predict and control the spreading of COVID-19.
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supported by the National Natural Science Foundation of China(Grant No.11971074).
文摘COVID-19 is a constantly challenging global health issue due to its strong intensity,rapid mutation and high infectiousness.The new Delta and Omicron variants have triggered massive outbreaks worldwide.Even China,which has done a good job in outbreak prevention,is still heavily affected by the virus.The long-term fight against multiple COVID-19 outbreaks is ongoing.In this study,we propose an SEIQR model that considers the incubation period and quarantine measurement.We verified our model using actual outbreak data from four Chinese cities.Numerical simulations show that a five-day delay results in a double resurgence scale.Our model can be used as a tool to understand the spread of the virus quantitatively and provide a reference for policymaking accordingly.
