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.
|Commitee:||Ackleh, Azmy, Ng, Ping Wong|
|School:||University of Louisiana at Lafayette|
|School Location:||United States -- Louisiana|
|Source:||DAI-B 77/06(E), Dissertation Abstracts International|
|Keywords:||Asymptotic behavior, Population models, Reaction-diffusion equations|
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