Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
Volume 16, Issue 3, Pages 867-881Publisher
AMER INST MATHEMATICAL SCIENCES
DOI: 10.3934/dcdsb.2011.16.867
Keywords
Long time behavior; epidemic models
Categories
Funding
- NSF from the Division of Mathematical Sciences
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1009102] Funding Source: National Science Foundation
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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.
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