非同质病毒在网络中的传播
In-homogeneous Virus Spread in Networks
摘要：
我们的$N$交织模型（现在称为NIMFA）的病毒传播的任何网络与$N$节点扩展到一个完整的异构设置。亚稳态的稳态节点感染概率指定的广义拉普拉斯算子，具有类似的性质作为经典的拉普拉斯在图论。通过一个$N$维向量来表征将全局网络感染与全局网络健康分开的临界阈值，该向量使得修改后的邻接矩阵的最大特征值等于1。最后，节点$i$的稳态感染概率在自身的治愈率$δ_{i}$下是凸的，而在网络中的其他节点$1\leq j\neq i\leq N$的治愈率$δ_{j}$下是凹的。
英文摘要：
Our $N$-intertwined model (now called NIMFA) for virus spread in any network with $N$ nodes is extended to a full heterogeneous setting. The metastable steady-state nodal infection probabilities are specified in terms of a generalized Laplacian, that possesses analogous properties as the classical Laplacian in graph theory. The critical threshold that separates global network infection from global network health is characterized via an $N$ dimensional vector that makes the largest eigenvalue of a modified adjacency matrix equal to unity. Finally, the steady-state infection probability of node $i$ is convex in the own curing rate $δ_{i}$, but concave in the curing rates $δ_{j}$ of the other nodes $1\leq j\neq i\leq N$ in the network.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
