Induced spreading aims to maximize the infection probabilities of some target nodes by adjusting the nodal infection rates, which can be applied in biochemical and information spreading. We assume that the adjustment of the nodal infection rates has an associated cost and formulate the induced spreading for susceptible-infected-susceptible (SIS) epidemics in networks as an optimization problem under a constraint on total cost. We address and solve both a static model and a dynamic model for the optimization of the induced SIS spreading. By numerical results in some artificial and real networks, we investigate the effect of the network topology on the optimal induced strategy with a quadratic cost function. In the static method, the infection rate increment on each node is coupled to both the degree and the average hops to the targets. In the dynamic method, we show that the effective resistance could be a good metric to indicate the minimum total cost for targeting a single node. We also illustrate that the minimum total cost increases much more slowly with the increasing fraction of targets in the SIS model than in linear control systems.

中文翻译：

---

网络中SIS流行病的最优诱导传播

诱导传播旨在通过调整节点感染率来最大化某些目标结点的感染概率，可将其应用于生化和信息传播。我们假设节点感染率的调整具有相关的成本，并在总成本的约束下将网络中易感性感染易感性（SIS）流行病的诱导传播公式化为优化问题。我们解决并解决了静态模型和动态模型，以优化诱发的SIS扩散。通过在一些人工和真实网络中的数值结果，我们研究了网络拓扑对具有二次成本函数的最优诱导策略的影响。在静态方法中，每个节点上的感染率增量与目标的跳数和平均跳数都相关。在动态方法中，我们表明有效抵抗力可能是指示针对单个节点的最小总成本的良好度量。我们还表明，与线性控制系统相比，SIS模型中随着目标比例的增加，最低总成本的增长要慢得多。