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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.
一般而言，社会行为和人类流动性的模型通常被构建为反应-扩散过程<font color="#ff8000"> Reaction-Diffusion Processes</font> ,在这个模型框架中，每个节点<math>$i$</math>可以容纳任何非负整数个粒子<math>$\mathcal{N}(i)$</math>
一般而言，社会行为和人类流动性的模型通常被构建为反应-扩散过程<font color="#ff8000"> Reaction-Diffusion Processes</font> ,在这个模型框架中，每个节点<math>i</math>可以容纳任何非负整数个粒子<math>\mathcal{N}(i)</math>，因此系统的总粒子数为<math>\mathcal{N}=\sum_i\mathcal{N}(i)</math>。该粒子-网络框架中节点内的每个粒子只能沿着连接节点的连边扩散，且扩散系数取决于节点的度<font color="#ff8000"> Node degree</font>或者节点的其他属性。对于不同的系统，节点内的粒子的反应规则也不同。这样的粒子-网络框架模型的简单示意如图所示。
[[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.]]