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== 反应扩散过程 ==
== 反应扩散过程 ==
[[File:Snipaste_2020-10-23_22-40-33.png|thumb|right|(a) Schematic illustration of the simplified modeling framework based on the particle-network scheme. At the macroscopic level the system is composed of a heterogeneous network of subpopulations. The contagion process in one subpopulation can spread to other subpopulations because of particles diffusing across subpopulations. (b) At the microscopic level, each subpopulation contains a population of individuals. The dynamical process, for instance, a contagion phenomenon, is described by a simple compartmentalization (compartments are indicated by different colored dots in the picture). Within each subpopulation, individuals can mix homogeneously or according to a subnetwork and can diffuse with probability p from one subpopulation to another following the edges of the network. (c) A critical value $p_c$ of the individuals or particles diffusion identifies a phase transition between a regime in which the contagion affects a large fraction of the system and one in which only a small fraction is affected.]]
More in general models of social behavior and human mobility are often framed as reaction-diffusion processes where each node $i$ is allowed to host any nonnegative integer number of particles $\mathcal{N}(i)$, so that the total particle population of the system is $\mathcal{N}=\sum_i\mathcal{N}(i)$. This particle-network framework considers that each particle diffuses along the edges connecting nodes with a diffusion coefficient that depends on the node degree and/or other node attributes. Within each node particles may react according to different schemes characterizing the interaction dynamics of the system. A simple sketch of the particle-network framework is represented in the Figure.
More in general models of social behavior and human mobility are often framed as reaction-diffusion processes where each node $i$ is allowed to host any nonnegative integer number of particles $\mathcal{N}(i)$, so that the total particle population of the system is $\mathcal{N}=\sum_i\mathcal{N}(i)$. This particle-network framework considers that each particle diffuses along the edges connecting nodes with a diffusion coefficient that depends on the node degree and/or other node attributes. Within each node particles may react according to different schemes characterizing the interaction dynamics of the system. A simple sketch of the particle-network framework is represented in the Figure.
其中$\bar{S}(t)=\sum_k P(k)S_k$。
其中$\bar{S}(t)=\sum_k P(k)S_k$。
== 参考文献 References ==
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<small>此页参考来源： Pastor-Satorras R, Castellano C, Van Mieghem P, et al. Epidemic processes in complex networks[J]. Reviews of modern physics, 2015, 87(3): 925.