Abstract
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.
Highlights
Many people have been paying attention to the study of some epidemics, and have accumulated a lot of experience
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
In [10], Enatsu et al studied stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates, at the same time, they proved disease-free equilibrium was globally asymptotically stable and endemic equilibrium was permanent under certain conditions
Summary
Many people have been paying attention to the study of some epidemics, and have accumulated a lot of experience. In [10], Enatsu et al studied stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates, at the same time, they proved disease-free equilibrium was globally asymptotically stable and endemic equilibrium was permanent under certain conditions. On the basis of [13], Xu and Ma introduced the saturated incidence rate They showed disease-free equilibrium and endemic equilibrium were globally asymptotically stable under certain condition in [14]. An SIRS epidemic model with pulse vaccination and non-monotonic incidence rate was discussed by Zhang et al [15], and they proved the disease-free equilibrium and endemic equilibrium were asymptotically stable under certain conditions.
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