Stability Analysis of an SEIS Epidemic ModelWith a Nonlinear Incidence Rate

XING Wei; YAN Qi-sheng; YANG Zhi-hui; GAO Jin-fang

doi:10.21656/1000-0887.370166

Volume 37 Issue 11

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XING Wei, YAN Qi-sheng, YANG Zhi-hui, GAO Jin-fang. Stability Analysis of an SEIS Epidemic ModelWith a Nonlinear Incidence Rate[J]. Applied Mathematics and Mechanics, 2016, 37(11): 1247-1254. doi: 10.21656/1000-0887.370166

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Stability Analysis of an SEIS Epidemic ModelWith a Nonlinear Incidence Rate

doi: 10.21656/1000-0887.370166

¹School of Science, East China University of Technology, Nanchang 330013, P.R.China;²Institute of Technology, East China Jiaotong University,Nanchang 330013, P.R.China

Received Date: 2016-05-26
Rev Recd Date: 2016-10-09
Publish Date: 2016-11-15

Abstract

Abstract

An SEIS epidemic model with a nonlinear incidence rate and involving a constant input rate, a natural mortality rate and a mortality rate due to disease, was investigated. Firstly, the basic reproduction number for the model was defined. Then the disease-free equilibrium point was proved to be globally asymptotically stable when R₀<1. Finally, the conditions for the theorem that the unique endemic equilibrium point was globally asymptotically stable, were obtained when R₀>1.
- nonlinear incidence rate,
- SEIS model,
- basic reproduction number,
- global asymptotic stability

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References(12)

References

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