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The governments have generally adopted the incidence-based statistical method to estimate the time-varying effective reproduction number <jats:italic>R<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub> 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 <jats:italic>R<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub>. We find the supervised learning of Ct-Transformer outperforms the traditional incidence-based statistic and Ct-based <jats:italic>R<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub> 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 <jats:italic>R<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub>, enabling more easily adapted to the track of the newly emerged epidemic.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1012694","type":"journal-article","created":{"date-parts":[[2024,12,23]],"date-time":"2024-12-23T18:47:16Z","timestamp":1734979636000},"page":"e1012694","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":4,"title":["Estimating the time-varying effective reproduction number via Cycle Threshold-based 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