This paper studies algorithmic strategies to effectively reduce the number of infections in susceptible-infected-recovered (SIR) epidemic models. We consider a Markov chain SIR model and its two instantiations in the deterministic SIR (D-SIR) model and the independent cascade SIR (IC-SIR) model. We investigate the problem of minimizing the number of infections by restricting contacts under realistic constraints. Under moderate assumptions on the reproduction number, we prove that the infection numbers are bounded by supermodular functions in the D-SIR model and the IC-SIR model for large classes of random networks. We propose efficient algorithms with approximation guarantees to minimize infections. The theoretical results are illustrated by numerical simulations.

中文翻译：

---

SIR流行模型中用于最小化传播的边缘删除算法

本文研究了有效减少易感感染恢复（SIR）流行病模型中感染数量的算法策略。我们在确定性SIR（D-SIR）模型和独立级联SIR（IC-SIR）模型中考虑了Markov链SIR模型及其两个实例。我们研究通过在现实的约束下限制接触来最大限度地减少感染数量的问题。在对繁殖数进行适度假设的情况下，我们证明了对于大类随机网络，D-SIR模型和IC-SIR模型中的感染数受超模函数的限制。我们提出了带有近似保证的有效算法，以最大程度地减少感染。理论结果通过数值模拟说明。