| Volume 8, Number 2, 2018, Pages 402-412 DOI：10.11948/2018.402 |
| Global asymptotic stability of a generalized SIRS epidemic model with transfer from infectious to susceptible |
| Yuzhen Bai,Xiaoqing Mu |
| Keywords:Generalized SIRS epidemic model, varying total population size, transfer from infectious to susceptible, global asymptotic stability, geometric approach. |
| 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 $\delta$ is in a critical interval $[\eta,\bar\delta)$ when the basic reproduction number $R_0$ is greater than unity. |
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