<p> In this work, we study the long time behavior of reaction-diffusion models arising from mathematical biology. First, we study a reaction-diffusion population model with time delay. We establish a comparison principle for coupled upper/lower solutions, prove the existence/uniqueness result for the model, and show the global asymptotic behavior of the model by constructing successive improved upper/lower solutions. Next, we consider a reaction-diffusion equation with continuous delay and spatial variable coefficients. We prove the global attractivity of the positive steady state by showing that the omega limit set is a singleton. Finally, we study an SIS reaction-diffusion model with spatial heterogeneous disease transmission and recovery rates. We define a basic reproduction number and obtain some existence and non-existence results of the endemic equilibrium of the model. We then study the global attractivity of the steady state for two special cases.</p>
| Identifer | oai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:10002390 |
| Date | 24 February 2016 |
| Creators | Wu, Yixiang |
| Publisher | University of Louisiana at Lafayette |
| Source Sets | ProQuest.com |
| Language | English |
| Detected Language | English |
| Type | thesis |
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