The basic reproduction number of a networked epidemic model, denoted $R_0$, can be computed from a network's topology to quantify epidemic spread. However, disclosure of $R_0$ risks revealing sensitive information about the underlying network, such as an individual's relationships within a social network. Therefore, we propose a framework to compute and release $R_0$ in a differentially private way. First, we provide a new result that shows how $R_0$ can be used to bound the level of penetration of an epidemic within a single community as a motivation for the need of privacy, which may also be of independent interest. We next develop a privacy mechanism to formally safeguard the edge weights in the underlying network when computing $R_0$. Then we formalize tradeoffs between the level of privacy and the accuracy of values of the privatized $R_0$. To show the utility of the private $R_0$ in practice, we use it to bound this level of penetration under privacy, and concentration bounds on these analyses show they remain accurate with privacy implemented. We apply our results to real travel data gathered during the spread of COVID-19, and we show that, under real-world conditions, we can compute $R_0$ in a differentially private way while incurring errors as low as $7.6\%$ on average.

翻译：网络化流行病模型的基本再生数（记为$R_0$）可通过网络拓扑结构计算以量化疫情传播强度。然而，披露$R_0$可能泄露底层网络的敏感信息，例如个体在社交网络中的关系。因此，我们提出一个框架，以差分隐私方式计算并公开$R_0$。首先，我们给出一个新结果，表明$R_0$如何用于约束单一社区内疫情渗透程度，这既可作为隐私需求的动机，也可能具有独立研究价值。其次，我们开发了一种隐私机制，在计算$R_0$时正式保护底层网络的边权重。然后，我们形式化了隐私级别与私有化$R_0$数值精度之间的权衡。为展示私有$R_0$的实际效用，我们利用其在隐私保护下约束疫情渗透程度，且这些分析的概率界表明，在实施隐私保护后仍能保持准确性。我们将研究结果应用于COVID-19传播期间收集的真实旅行数据，结果表明，在现实条件下，我们能以差分隐私方式计算$R_0$，平均误差低至7.6%。