STABILITY ANALYSIS OF AN SEIS EPIDEMIC MODEL WITH NONLINEAR INCIDENCE AND TIME DELAY

Xiaohong Tian; Rui Xu

doi:10.11948/2014023

2014 Volume 4 Issue 4

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Xiaohong Tian, Rui Xu. STABILITY ANALYSIS OF AN SEIS EPIDEMIC MODEL WITH NONLINEAR INCIDENCE AND TIME DELAY[J]. Journal of Applied Analysis & Computation, 2014, 4(4): 405-418. doi: 10.11948/2014023

Citation:

Xiaohong Tian, Rui Xu. STABILITY ANALYSIS OF AN SEIS EPIDEMIC MODEL WITH NONLINEAR INCIDENCE AND TIME DELAY[J]. Journal of Applied Analysis & Computation, 2014, 4(4): 405-418. doi: 10.11948/2014023

STABILITY ANALYSIS OF AN SEIS EPIDEMIC MODEL WITH NONLINEAR INCIDENCE AND TIME DELAY

Institute of Applied Mathematics, Mechanical Engineering College, No. 97 Heping West Road, 050003 Shijiazhuang, China

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Abstract

Abstract

In this paper, an SEIS epidemic model with nonlinear incidence and time delay is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the model is established. By using suitable Lyapunov functional and LaSalle's invariance principle, it is shown that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity. If the basic reproduction number is greater than unity, by means of an iteration technique, sufficient conditions are derived for the global stability of the endemic equilibrium. Numerical simulations are carried out to illustrate the theoretical results.
- SEIS epidemic model /
- nonlinear incidence /
- time delay /
- stability
MSC: 34K20;34K60;92D25

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