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

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 Rt 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 Rt. We find the supervised learning of Ct-Transformer outperforms the traditional incidence-based statistic and Ct-based Rt estimating methods, and more importantly Ct-Transformer is robust to the detection resources. Further, we apply the proposed model to self-supervised pre-training tasks and obtain excellent fine-tuned 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 Rt, enabling more easily adapted to the track of the newly emerged epidemic.Author summary: The time-varying effective reproduction number Rt is an important indicator in tracking the epidemic spread. The well-known method to estimate Rt is the incidence-based statistical method, which is constrained with the assumptions and available data. The recent studies show that the time-varying distribution of cycle threshold (Ct) values of the sampled infected population provides a possibility to infer the epidemic trajectory. Here, we propose the Cycle Threshold-based Transformer (Ct-Transformer), a deep neural network based method to estimate Rt. The results on both the synthetic and real-world datasets demonstrate that the Ct-Transformer surpass the traditional incidence-based and the existing Ct-based estimating methods. More importantly, the proposed self-supervised learning of Ct-Transformer estimates the Rt accurately for the newly emerged infectious disease. Our study suggests that Ct-based deep learning method can be employed to improve the tracking of the spread of infectious disease, and especially for the newly emerged epidemic.