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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.
T-wave alternans (TWA) has become a clinical index of non-invasive diagnosis
for heart sudden death prediction, and detecting T-wave alternate accurately
is particularly important. This paper introduces an algorithm for detecting
TWA using Poincare mapping method which is a technique for nonlinear dynamic
systems to display periodic behavior. Sample series of beat to beat cycles were
selected to prepare Poincare mapping method.
Vector Angle Index (VAI), which is the mean of the difference between θi (the angle between the line connecting the i point to the origin and the X axis)
and 45 degrees was used to present the presence or absence of TWA. The value of
0.9 rad ≤ VAI ≤ 1.03 rad is accepted as a level determinative for presence of
TWA. VAI via Poincare mapping method (PM) is used for correlation analysis with
T-wave alternans voltage (Vtwa)
by way of the spectral method (SM). The cross-correlation coefficient between Vtwa and VAI is γ = 0.8601. The algorithm can identify
the absence and presence of TWA accurately and provide idea for further study