Stability analysis for a delayed SIR model with a nonlinear incidence rate
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Authors
Luju Liu
- School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, China.
Yan Wang
- College of Science, China University of Petroleum, Qingdao, 266580, China.
Abstract
We develop an SIR vector-bone epidemic model incorporating
incubation time delay and the nonlinear incidence rate, where the
growth of susceptibles is governed by the logistic equation. The
threshold parameter \(R_0\) is used to determine whether the disease
persists in the population. The model always has the trivial
equilibrium and the disease-free equilibrium whereas admits the
endemic equilibrium if \(R_0\) exceeds one. The disease-free
equilibrium is globally asymptotically stable if \(R_0\) is less than
one, while the system is persistent if \(R_0\) is greater than one.
Furthermore, by applying the time delay as a bifurcation parameter,
the local stability of the endemic equilibrium is discussed and it
loses stability and Hopf bifurcation occurs as the length of the
time delay increases past \(\tau_0\) under certain conditions. An
example is carried out to illustrate the main results.
Share and Cite
ISRP Style
Luju Liu, Yan Wang, Stability analysis for a delayed SIR model with a nonlinear incidence rate, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 11, 5834--5845
AMA Style
Liu Luju, Wang Yan, Stability analysis for a delayed SIR model with a nonlinear incidence rate. J. Nonlinear Sci. Appl. (2017); 10(11):5834--5845
Chicago/Turabian Style
Liu, Luju, Wang, Yan. "Stability analysis for a delayed SIR model with a nonlinear incidence rate." Journal of Nonlinear Sciences and Applications, 10, no. 11 (2017): 5834--5845
Keywords
- Stability analysis
- delayed SIR model
- nonlinear incidence rate
- Lyapunov function
- Hopf bifurcation
MSC
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