Simulation of an epidemic model with nonlinear cross-diffusion

2012 ◽  
pp. 331-338
Author(s):  
Stefan Berres ◽  
Ricardo Ruiz-Baier
Keyword(s):  
Epidemic Model ◽  
Cross Diffusion

scholarly journals Stationary Patterns of a Cross-Diffusion Epidemic Model

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Yongli Cai ◽  
Dongxuan Chi ◽  
Wenbin Liu ◽  
Weiming Wang
Keyword(s):  
Global Stability ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Complex Dynamics ◽  
Reproduction Number ◽  
Steady States ◽  
Nonnegative Constant ◽  
Cross Diffusion ◽  
Existence And Nonexistence ◽  
The Basic Reproduction Number

We investigate the complex dynamics of cross-diffusionSIepidemic model. We first give the conditions of the local and global stability of the nonnegative constant steady states, which indicates that the basic reproduction number determines whether there is an endemic outbreak or not. Furthermore, we prove the existence and nonexistence of the positive nonconstant steady states, which guarantees the existence of the stationary patterns.

Spatial Pattern of an Epidemic Model with Cross-diffusion

2008 ◽  
Vol 25 (9) ◽  
pp. 3500-3503 ◽  
Author(s):  
Li Li ◽  
Jin Zhen ◽  
Sun Gui-Quan
Keyword(s):  
Spatial Pattern ◽  
Epidemic Model ◽  
Cross Diffusion

PATTERN SELECTION IN AN EPIDEMIC MODEL WITH SELF AND CROSS DIFFUSION

2011 ◽  
Vol 19 (01) ◽  
pp. 19-31 ◽  
Author(s):  
WEIMING WANG ◽  
YEZHI LIN ◽  
HAILING WANG ◽  
HOUYE LIU ◽  
YONGJI TAN
Keyword(s):  
Epidemic Model ◽  
Control Parameter ◽  
Pattern Selection ◽  
Turing Pattern ◽  
Amplitude Equations ◽  
General Survey ◽  
Cross Diffusion ◽  
Model Dynamics ◽  
Flux Boundary Conditions ◽  
Spatial Epidemic Model

In this paper, we have presented Turing pattern selection in a spatial epidemic model with zero-flux boundary conditions, for which we have given a general survey of Hopf and Turing bifurcations, and have derived amplitude equations for the excited modes. Furthermore, we present novel numerical evidence of typical Turing patterns, and find that the model dynamics exhibits complex pattern replication: on increasing the control parameter r, the sequence "H0-hexagons → H0-hexagon-stripe mixtures → stripes → Hπ-hexagon-stripe mixtures → Hπ-hexagons" is observed. This may enrich the research of the pattern formation in diffusive epidemic models.

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