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第130行： − We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. − For all other <math>y</math>, <math>P(x,y)=0</math>.<br/> + − 我们对上面介绍的过程，在离散时间的网络上建模，也就是说，我们可以将它建模为一个离散时间马尔可夫链（DTMC）。假设我们有一个N个节点的网络，那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻，某个节点i和节点j相互作用，然后其中一个节点将改变其状态。 + − 这样，我们定义一个函数<math>f</math> ，使得对于<math>S</math>中的<math>x</math> ，<math>f(x,i,j)</math> 是，当网络状态为<math>x</math>时，节点i和节点j相互作用，其中一个将改变其状态。 − 转移矩阵依赖于节点i和节点j的联系数，以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>，我们设法求<math>P(x,y)</math>。如果节点i处于状态I，节点j处于状态S，则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I，节点j处于状态S，则 p (x，y) = beta a _ { ji }/k _ i; 如果节点i处于状态I，节点j处于状态R，则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>，<math>P(x,y)=0</math>。+ + + + + + + + + + + +
→社会网络中的传染病模型Epidemic models in social network
===社会网络中的传染病模型Epidemic models in social network===
===社会网络中的传染病模型Epidemic models in social network===
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state.
我们对上面介绍的过程，在离散时间的网络上建模，也就是说，我们可以将它建模为一个离散时间马尔可夫链（DTMC）。假设我们有一个N个节点的网络，那么我们可以定义<math> X_i(t)</math>为t时刻的节点 i 的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻，某个节点 i 和节点 j 相互作用，然后其中一个节点将改变其状态。
Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state.
这样，我们定义一个函数<math>f</math> ，使得对于<math>S</math>中的<math>x</math> ，<math>f(x,i,j)</math> 是，当网络状态为<math>x</math>时，节点 i 和节点 j 相互作用，其中一个将改变其状态。
The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>.
For all other <math>y</math>, <math>P(x,y)=0</math>.<br/>
转移矩阵依赖于节点 i 和节点 j 的联系数，以及节点 i 和节点 j 的状态。对于任意<math>y=f(x,i,j)</math>，我们设法求<math>P(x,y)</math>。如果节点 i 处于状态I，节点 j 处于状态S，则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I，节点 j 处于状态S，则 p (x，y) = beta a _ { ji }/k _ i; 如果节点 i 处于状态I，节点 j 处于状态R，则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>，<math>P(x,y)=0</math>。