# American Institute of Mathematical Sciences

2013, 10(5&6): 1399-1417. doi: 10.3934/mbe.2013.10.1399

## Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection

 1 Department of Mathematics, Shaanxi University of Science & Technology, Xi'an, 710021, China 2 Department of Mathematics, Xi'an Jiaotong University, Xi'an, 710049 3 Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049

Received  August 2012 Revised  March 2013 Published  August 2013

A discrete SIS epidemic model with the bilinear incidence depending on the new infection is formulated and studied. The condition for the global stability of the disease free equilibrium is obtained. The existence of the endemic equilibrium and its stability are investigated. More attention is paid to the existence of the saddle-node bifurcation, the flip bifurcation, and the Hopf bifurcation. Sufficient conditions for those bifurcations have been obtained. Numerical simulations are conducted to demonstrate our theoretical results and the complexity of the model.
Citation: Hui Cao, Yicang Zhou, Zhien Ma. Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1399-1417. doi: 10.3934/mbe.2013.10.1399
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