scholarly journals BIFURCATION ANALYSIS OF AN SIRS EPIDEMIC MODEL WITH STANDARD INCIDENCE RATE AND SATURATED TREATMENT FUNCTION

2017 ◽  
Vol 7 (3) ◽  
pp. 1070-1094
Author(s):  
Yixian Gao ◽  
◽  
Weipeng Zhang ◽  
Dan Liu ◽  
Yanju Xiao ◽  
...  
Keyword(s):  
Incidence Rate ◽  
Bifurcation Analysis ◽  
Epidemic Model ◽  
Sirs Epidemic Model ◽  
Treatment Function ◽  
Saturated Treatment

DYNAMICS OF SIS EPIDEMIC MODEL WITH THE STANDARD INCIDENCE RATE AND SATURATED TREATMENT FUNCTION

2012 ◽  
Vol 05 (03) ◽  
pp. 1260003 ◽  
Author(s):  
JINGJING WEI ◽  
JING-AN CUI
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Recruitment Rate ◽  
Globally Asymptotically Stable ◽  
Sis Epidemic Model ◽  
Treatment Function ◽  
Two Factors ◽  
Saturated Treatment ◽  
Disease Free ◽  
Sis Epidemic

An SIS epidemic model with the standard incidence rate and saturated treatment function is proposed. The dynamics of the system are discussed, and the effect of the capacity for treatment and the recruitment of the population are also studied. We find that the effect of the maximum recovery per unit of time and the recruitment rate of the population over some level are two factors which lead to the backward bifurcation, and in some cases, the model may undergo the saddle-node bifurcation or Bogdanov–Takens bifurcation. It is shown that the disease-free equilibrium is globally asymptotically stable under some conditions. Numerical simulations are consistent with our obtained results in theorems, which show that improving the efficiency and capacity of treatment is important for control of disease.

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