The importance of epidemiology in our life has stimulated researchers to extend the classic Susceptibles-Infectives-Removed (SIR) model to sophisticated models by including more factors in order to give detailed trans...The importance of epidemiology in our life has stimulated researchers to extend the classic Susceptibles-Infectives-Removed (SIR) model to sophisticated models by including more factors in order to give detailed transmission dynamics of epidemic diseases. However, the integration of the quarantine policy and age-structure is less addressed. In this work we propose an age-structured MSIQR (temporarily immune-susceptibles-infectives-quarantined-removed) model to study the impact of quarantine policies on the spread of epidemic diseases. Specifically, we investigate the existence of steady state solutions and stability property of the proposed model. The derived explicit expression of the basic reproductive number shows that the disease-free equilibrium is globally asymptotically stable if, and that the unique endemic equilibrium exists if. In addition, the stability conditions of the endemic equilibrium are derived.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
This article focuses on the study of an age structured SEIRS epidemic model with a vaccination program when the total population size is not kept at constant. We first give the explicit expression of the reproduction ...This article focuses on the study of an age structured SEIRS epidemic model with a vaccination program when the total population size is not kept at constant. We first give the explicit expression of the reproduction number in the presence of vaccine ( is the exponent of growth of total population), and show that the infection-free steady state is linearly stable if and unstable if , then we apply the theoretical results to vaccination policies to determine the optimal age or ages at which an individual should be vaccinated. It is shown that the optimal strategy can be either one- or two-age strategies.展开更多
文摘The importance of epidemiology in our life has stimulated researchers to extend the classic Susceptibles-Infectives-Removed (SIR) model to sophisticated models by including more factors in order to give detailed transmission dynamics of epidemic diseases. However, the integration of the quarantine policy and age-structure is less addressed. In this work we propose an age-structured MSIQR (temporarily immune-susceptibles-infectives-quarantined-removed) model to study the impact of quarantine policies on the spread of epidemic diseases. Specifically, we investigate the existence of steady state solutions and stability property of the proposed model. The derived explicit expression of the basic reproductive number shows that the disease-free equilibrium is globally asymptotically stable if, and that the unique endemic equilibrium exists if. In addition, the stability conditions of the endemic equilibrium are derived.
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.
基金Supported by the NSFC (No.10371105) and the NSF of Henan Province (No.0312002000No.0211044800)
文摘This article focuses on the study of an age structured SEIRS epidemic model with a vaccination program when the total population size is not kept at constant. We first give the explicit expression of the reproduction number in the presence of vaccine ( is the exponent of growth of total population), and show that the infection-free steady state is linearly stable if and unstable if , then we apply the theoretical results to vaccination policies to determine the optimal age or ages at which an individual should be vaccinated. It is shown that the optimal strategy can be either one- or two-age strategies.
