GLOBAL ASYMPTOTIC STABILITY OF A GENERALIZED SIRS EPIDEMIC MODEL WITH TRANSFER FROM INFECTIOUS TO SUSCEPTIBLE

Yuzhen Bai; Xiaoqing Mu

doi:10.11948/2018.402

2018 Volume 8 Issue 2

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Yuzhen Bai, Xiaoqing Mu. GLOBAL ASYMPTOTIC STABILITY OF A GENERALIZED SIRS EPIDEMIC MODEL WITH TRANSFER FROM INFECTIOUS TO SUSCEPTIBLE[J]. Journal of Applied Analysis & Computation, 2018, 8(2): 402-412. doi: 10.11948/2018.402

Citation:

Yuzhen Bai, Xiaoqing Mu. GLOBAL ASYMPTOTIC STABILITY OF A GENERALIZED SIRS EPIDEMIC MODEL WITH TRANSFER FROM INFECTIOUS TO SUSCEPTIBLE[J]. Journal of Applied Analysis & Computation, 2018, 8(2): 402-412. doi: 10.11948/2018.402

GLOBAL ASYMPTOTIC STABILITY OF A GENERALIZED SIRS EPIDEMIC MODEL WITH TRANSFER FROM INFECTIOUS TO SUSCEPTIBLE

School of Mathematical Sciences, Qufu Normal University, 273165, Qufu, China

Fund Project:

Abstract

Abstract

In this paper, we propose a generalized SIRS epidemic model with varying total population size caused by the death rate due to the disease and transfer from infectious to susceptible, where the incidence rate employed includs a wide range of monotonic and concave incidence rates. Applying the geometric approach developed by Smith, Li and Muldowey, we prove that the endemic equilibrium is globally asymptotically stable provided that the rate of loss of immuity δ is in a critical interval[η,δ) when the basic reproduction number R₀ is greater than unity.
- Generalized SIRS epidemic model /
- varying total population size /
- transfer from infectious to susceptible /
- global asymptotic stability /
- geometric approach
MSC: 34D23;34A26

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References

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