Estimating the time-varying effective reproduction number via Cycle Threshold-based Transformer

by Xin-Yu Zhang, Lan-Lan Yu, Wei-Yi Wang, Gui-Quan Sun, Jian-Cheng Lv, Tao Zhou, Quan-Hui Liu

Monitoring the spread of infectious disease is essential to design and adjust the interventions timely for the prevention of the epidemic outbreak and safeguarding the public health. The governments have generally adopted the incidence-based statistical method to estimate the time-varying effective reproduction number R_t and evaluate the transmission ability of epidemics. However, this method exhibits biases arising from the reported incidence data and assumes the generation interval distribution which is not available at the early stage of epidemic. Recent studies showed that the viral loads characterized by cycle threshold (Ct) of the infected populations evolving throughout the course of epidemic and providing a possibility to infer the epidemic trajectory. In this work, we propose the Cycle Threshold-based Transformer (Ct-Transformer) to estimate R_t. We find the supervised learning of Ct-Transformer outperforms the traditional incidence-based statistic and Ct-based R_t estimating methods, and more importantly Ct-Transformer is robustness to the detection resources. Further, we apply the proposed model to self-supervised pre-training tasks and obtain excellent fine-tuning performance, which attains comparable performance with the supervised Ct-Transformer, verified by both the synthetic and real-world datasets. We demonstrate that the Ct-based deep learning method can improve the real-time estimates of R_t, enabling more easily adapted to the track of the newly emerged epidemic.