标题： 带有外源性感染的接触过程和缩放的SIS过程 显示英文标题

标题： Contact Process with Exogenous Infection and the Scaled SIS Process

摘要： 传染在网路中的传播取决于图的拓扑结构。 本文研究静态、无向、有限大小网路上的扩展接触过程的时间渐进行为。 这是一种具有非零外生感染率的接触过程（也称为{\epsilon }-SIS，{\epsilon }易感-感染-易感模型 [1]）。 对此过程的平衡分布的唯一已知解析表征是对于完全网络的情况。 对于具有任意拓扑结构的大规模网络，由于需要求解一个与网络大小 N 成指数关系的矩阵的特征值-特征向量问题，因此数值求解平衡分布是不可行的。 我们证明，在网络过程参数的一定范围内，任意有限大小网络上的扩展接触过程的平衡分布可以很好地由我们之前工作中以闭式形式推导出的缩放 SIS 过程的平衡分布来近似。 我们通过数值模拟验证了这一结果，比较了扩展接触过程与缩放 SIS 过程的平衡分布。 我们利用这一近似，在多项式时间内判断哪些代理和网络子结构更容易受到扩展接触过程的感染。 显示英文摘要

摘要： Propagation of contagion in networks depends on the graph topology. This paper is concerned with studying the time-asymptotic behavior of the extended contact processes on static, undirected, finite-size networks. This is a contact process with nonzero exogenous infection rate (also known as the {\epsilon}-SIS, {\epsilon} susceptible-infected-susceptible, model [1]). The only known analytical characterization of the equilibrium distribution of this process is for complete networks. For large networks with arbitrary topology, it is infeasible to numerically solve for the equilibrium distribution since it requires solving the eigenvalue-eigenvector problem of a matrix that is exponential in N , the size of the network. We show that, for a certain range of the network process parameters, the equilibrium distribution of the extended contact process on arbitrary, finite-size networks is well approximated by the equilibrium distribution of the scaled SIS process, which we derived in closed-form in prior work. We confirm this result with numerical simulations comparing the equilibrium distribution of the extended contact process with that of a scaled SIS process. We use this approximation to decide, in polynomial-time, which agents and network substructures are more susceptible to infection by the extended contact process.