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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>，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。

一般而言，社会行为和人类流动性的网络模型通常被构建为反应-扩散过程<font color="#ff8000"> Reaction-Diffusion Processes</font> ,在这个网络模型框架中，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网络中连接节点的连边进行扩散，并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.]]  

[[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.]]