In this paper,we study a kind of the delayed SEIQR infectious disease model withthe quarantine and latent, and get the threshold value which determines the globaldynamics and the outcome of the disease. The model has a disease-free equilibriumwhich is unstable when the basic reproduction number is greater than unity.At thesame time, it has a unique endemic equilibrium when the basic reproduction numberis greater than unity. According to the mathematical dynamics analysis, we showthat disease-free equilibrium and endemic equilibrium are locallyasymptotically stable byusing Hurwitz criterion and they are globally asymptotically stable by using suitableLyapunov functions for any Besides,the SEIQR model with nonlinear incidence rate is studied, and thethat the basic reproduction number is a unity can be found out. Finally, numerical simulations are performed to illustrate and verify theconclusions that will be useful for us to control the spread of infectious diseases.Meanwhile, thewill effect changing trends ofin system (1),which is obvious in simulations. Here, we takeas an example to explain that.
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