This paper introduces a novel approach for epidemic nowcasting and forecasting over networks using total variation (TV) denoising, a method inspired by classical signal processing techniques. Considering a network that models a population as a set of $n$ nodes characterized by their infection statuses $Y_i$ and that represents contacts as edges, we prove the consistency of graph-TV denoising for estimating the underlying infection probabilities $\{p_i\}_{ i \in \{1,\cdots, n\}}$ in the presence of Bernoulli noise. Our results provide an important extension of existing bounds derived in the Gaussian case to the study of binary variables -- an approach hereafter referred to as one-bit total variation denoising. The methodology is further extended to handle incomplete observations, thereby expanding its relevance to various real-world situations where observations over the full graph may not be accessible. Focusing on the context of epidemics, we establish that one-bit total variation denoising enhances both nowcasting and forecasting accuracy in networks, as further evidenced by comprehensive numerical experiments and two real-world examples. The contributions of this paper lie in its theoretical developments, particularly in addressing the incomplete data case, thereby paving the way for more precise epidemic modelling and enhanced surveillance strategies in practical settings.

翻译：本文提出了一种利用全变分（TV）去噪进行网络流行病即时预测与预报的新方法，该方法受经典信号处理技术的启发。考虑一个将人口建模为$n$个节点（其特征由感染状态$Y_i$刻画）并以边表示接触关系的网络，我们证明了在伯努利噪声下，图TV去噪用于估计潜在感染概率$\{p_i\}_{ i \in \{1,\cdots, n\}}$的一致性。这一结果为现有高斯情形下的界向二元变量研究提供了重要扩展——该方法此后被称为一比特全变分去噪。该方法进一步被推广以处理不完整观测，从而拓展了其在多种实际场景（其中可能无法获取完整图上的观测）中的适用性。聚焦流行病背景，我们证明一比特全变分去噪能提升网络中的即时预测与预报精度，综合数值实验及两个实际案例进一步验证了这一点。本文的贡献在于理论上的突破，尤其是解决了不完整数据情形，从而为更精确的流行病建模及实际条件下的增强监测策略铺平了道路。