Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 13, Issue 5, Pages 2240-2258Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2012.01.018
Keywords
Globally asymptotically stable; Turing instability; Pattern formation
Categories
Funding
- National Science Foundation of China [31070322]
- State Key Laboratory of Vegetation and Environmental Change
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In this paper, we investigate the complex dynamics of a reaction-diffusion S - I model incorporating demographic and epidemiological processes with zero-flux boundary conditions. By the method of Lyapunov function, the global stability of the disease free equilibrium and the epidemic equilibrium was established. In addition, the conditions of Turing instability were obtained and the Turing space in the parameters space were given. Based on these results, we present the evolutionary processes that involves organism distribution and their interaction of spatially distributed population with local diffusion, and find that the model dynamics exhibits a diffusion-controlled formation growth to holes, holes-stripes, stripes, spots-stripes and spots pattern replication. Furthermore, we indicate that the diseases' spread is getting smaller with R-0 increasing, and the increasing the diffusion of infectious will increase the speed of diseases spreading. Our results indicate that the diffusion has a great influence on the spread of the epidemic and extend well the finding of spatiotemporal dynamics in the epidemic model. (C) 2012 Elsevier Ltd. All rights reserved.
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