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Global stability of a SIQS epidemic model with #br# nonlinear incidence rate and time delay

YANG Jun-xian, XU li*   

  1. School of Science, Anhui Agricultural University, Hefei 230036, Anhui, China
  • Received:2013-12-25 Online:2014-05-20 Published:2014-06-04

Abstract: In this paper, a SIQS epidemic model with nonlinear incidence rate and time delay is proposed and analyzed. We have defined the basic reproductive number R0. By using eigenvalue, function analysis, comparison principle and iterative methods, the dynamic characteristics of model is analyzed. It is proved that the disease free equilibrium point P0 is globally stable if R0<1, it is unstable if R0>1, and the endemic equilibrium point P* is globally stable if R0>1.

Key words: nonlinear incidence rate, reproductive number, equilibrium point, time delay, global stability

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[2] SHI Xue-wei, JIA Jian-wen. Study on an SIR epidemic model with information variable and graded cure rate [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(3): 51-59.
[3] LIN Qing-teng, WEI Feng-ying. The stability of stochastic SIQS epidemic model with saturated incidences [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(1): 128-134.
[4] FAN Jin-jun, LU Xiao-dong. Existence of nonoscillatory solutions to second order forced neutral dynamic equations with time delay on time scales [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(05): 45-50.
[5] JU Pei-jun. Sufficient and necessary conditions for global stability of generalized Lorenz system and its applications to chaos control [J]. J4, 2012, 47(10): 97-101.
[6] DONG Chun-yan, FU Sheng-mao. The existence of non-constant positive steady state of an epidemic model for pest control [J]. J4, 2011, 46(3): 80-88.
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[9] YAN Peng, SHEN Yanjun, WANG Jianfeng. Stability analysis of a class of neutral type singular systems [J]. J4, 2009, 44(4): 66-71 .
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