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October 2011, 16(3): 867-881. doi: 10.3934/dcdsb.2011.16.867
Long time behavior of some epidemic models
Fang Li 1, and Nung Kwan Yip 1,
Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN 47907, United States
Received August 2010 Revised March 2011 Published June 2011
In this paper, we prove two results concerning the long time behavior of two systems of reaction diffusion equations motivated by the S-I-R model in epidemic modeling. The results generalize and simplify previous approaches. In particular, we consider the presence of directed diffusions between the two species. The new system contains an ill-posed region for arbitrary parameters. Our result is established under the assumption of small initial data.
Keywords: epidemic models., Long time behavior.
Mathematics Subject Classification: Primary: 35B40, 35K51; Secondary: 92B05, 92D3.
Citation: Fang Li, Nung Kwan Yip. Long time behavior of some epidemic models. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 867-881. doi: 10.3934/dcdsb.2011.16.867
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Fang Li Nung Kwan Yip