Synchronization of multi-group coupled systems on networks with reaction-diffusion terms based on the graph-theoretic approach

2017 ◽  
Vol 227 ◽  
pp. 54-63 ◽  
Author(s):  
Tianrui Chen ◽  
Ruisong Wang ◽  
Boying Wu
Keyword(s):  
Reaction Diffusion ◽  
Coupled Systems ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Graph Theoretic Approach

scholarly journals Dynamics of a Diffusive Multigroup SVIR Model with Nonlinear Incidence

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Jinhu Xu ◽  
Yan Geng
Keyword(s):  
Reproduction Number ◽  
Classical Method ◽  
Reaction Diffusion ◽  
Theoretic Approach ◽  
Globally Asymptotically Stable ◽  
Nonlinear Incidence ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Special Case ◽  
Disease Free

In this paper, a multigroup SVIR epidemic model with reaction-diffusion and nonlinear incidence is investigated. We first establish the well-posedness of the model. Then, the basic reproduction number ℜ 0 is established and shown as a threshold: the disease-free steady state is globally asymptotically stable if ℜ 0 < 1 , while the disease will be persistent when ℜ 0 > 1 . Moreover, applying the classical method of Lyapunov and a recently developed graph-theoretic approach, we established the global stability of the endemic equilibria for a special case.

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