This study considers SEIVR epidemic model with generalized nonlinear saturated inci- dence rate in the host population horizontally to estimate local and global equilibriums. By using the Rout^Hurwitz criteria, it is ...This study considers SEIVR epidemic model with generalized nonlinear saturated inci- dence rate in the host population horizontally to estimate local and global equilibriums. By using the Rout^Hurwitz criteria, it is shown that if the basic reproduction number R0 〈 1, the disease-free equilibrium is locally asymptotically stable. When the basic reproduction number exceeds the unity, then the endemic equilibrium exists and is stable locally asymptotically. The system is globally asymptotically stable about the disease-free equilibrium if R0 〈 1. The geometric approach is used to present the global stability of the endemic equilibrium. For R0〉 1, the endemic equilibrium is stable globally asymptotically. Finally, the numerical results are presented to justify the mathematical results.展开更多
In this paper, an SEIR epidemic model with vaccination is formulated. The results of our mathematical analysis indicate that the basic reproduction number plays an important role in studying the dynamics of the system...In this paper, an SEIR epidemic model with vaccination is formulated. The results of our mathematical analysis indicate that the basic reproduction number plays an important role in studying the dynamics of the system. If the basic reproduction number is less than unity, it is shown that the disease-free equilibrium is globally asymptotically stable by comparison arguments. If it is greater than unity, the system is permanent and there is a unique endemic equilibrium. In this case, sufficient conditions are established to guarantee the global stability of the endemic equilibrium by the theory of the compound matrices. Numerical simulations are presented to illustrate the main results.展开更多
In this paper, we have developed a compartment of epidemic model with vaccination. We have divided the total population into five classes, namely susceptible, exposed, infective, infective in treatment and recovered c...In this paper, we have developed a compartment of epidemic model with vaccination. We have divided the total population into five classes, namely susceptible, exposed, infective, infective in treatment and recovered class. We have discussed about basic properties of the system and found the basic reproduction number （R0） of the system. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at disease-free equilibrium E0 when R0 〈1. When R0 〉1 endemic equilibrium E1 exists and the system becomes locally asymptotically stable at E1 under some conditions. We have also discussed the epidemic model with two controls, vaccination control and treatment control. An objective functional is considered which is based on a combination of minimizing the number of exposed and infective individuals and the cost of the vaccines and drugs dose. Then an optimal control pair is obtained which minimizes the objective functional. Our numerical findings are illustrated through computer simulations using MATLAB. Epidemiological implications of our analytical findings are addressed critically.展开更多
文摘This study considers SEIVR epidemic model with generalized nonlinear saturated inci- dence rate in the host population horizontally to estimate local and global equilibriums. By using the Rout^Hurwitz criteria, it is shown that if the basic reproduction number R0 〈 1, the disease-free equilibrium is locally asymptotically stable. When the basic reproduction number exceeds the unity, then the endemic equilibrium exists and is stable locally asymptotically. The system is globally asymptotically stable about the disease-free equilibrium if R0 〈 1. The geometric approach is used to present the global stability of the endemic equilibrium. For R0〉 1, the endemic equilibrium is stable globally asymptotically. Finally, the numerical results are presented to justify the mathematical results.
基金This work was supported by the National Natural Science Foundation of China （11371368）, the Nature Science Foundation for Young Scientists of Hebei Province, China （A2013506012） and Basic Courses Department of Mechanical Engineering College Foundation （JCKY1507）.
文摘In this paper, an SEIR epidemic model with vaccination is formulated. The results of our mathematical analysis indicate that the basic reproduction number plays an important role in studying the dynamics of the system. If the basic reproduction number is less than unity, it is shown that the disease-free equilibrium is globally asymptotically stable by comparison arguments. If it is greater than unity, the system is permanent and there is a unique endemic equilibrium. In this case, sufficient conditions are established to guarantee the global stability of the endemic equilibrium by the theory of the compound matrices. Numerical simulations are presented to illustrate the main results.
文摘In this paper, we have developed a compartment of epidemic model with vaccination. We have divided the total population into five classes, namely susceptible, exposed, infective, infective in treatment and recovered class. We have discussed about basic properties of the system and found the basic reproduction number （R0） of the system. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at disease-free equilibrium E0 when R0 〈1. When R0 〉1 endemic equilibrium E1 exists and the system becomes locally asymptotically stable at E1 under some conditions. We have also discussed the epidemic model with two controls, vaccination control and treatment control. An objective functional is considered which is based on a combination of minimizing the number of exposed and infective individuals and the cost of the vaccines and drugs dose. Then an optimal control pair is obtained which minimizes the objective functional. Our numerical findings are illustrated through computer simulations using MATLAB. Epidemiological implications of our analytical findings are addressed critically.
