We study the following model of disease spread in a social network. At first, all individuals are either infected or healthy. Next, in discrete rounds, the disease spreads in the network from infected to healthy individuals such that a healthy individual gets infected if and only if a sufficient number of its direct neighbors are already infected. We represent the social network as a graph. Inspired by the real-world restrictions in the current epidemic, especially by social and physical distancing requirements, we restrict ourselves to networks that can be represented as geometric intersection graphs. We show that finding a minimal vertex set of initially infected individuals to spread the disease in the whole network is computationally hard, already on unit disk graphs. Hence, to provide some algorithmic results, we focus ourselves on simpler geometric graph classes, such as interval graphs and grid graphs.

翻译：我们研究社交网络中疾病传播的以下模型。初始时，所有个体均处于感染或健康状态。随后在离散时间步中，疾病在网络上从感染者向健康者传播，其传播规则为：健康个体当且仅当其足够数量的直接邻居已被感染时才会被感染。我们将社交网络表示为图结构。受当前疫情中现实限制条件（尤其是社交距离与物理距离要求）的启发，我们将研究范围限定为可表示为几何交线图的网络。研究表明：即使在单位圆盘图上，寻找最小初始感染者顶点集以实现全网传播的问题在计算上具有高复杂度。为获得若干算法结果，我们将聚焦于更简单的几何图类，如区间图与网格图。