The birth-death exposed-infectious (BDEI) model describes the transmission of pathogens featuring an incubation period (when the host is already infected but not yet infectious), for example Ebola and SARS-CoV-2. In a phylodynamics framework, it serves to infer such epidemiological parameters as the basic reproduction number R 0 , the incubation period and the infectious time from a phylogenetic tree (a genealogy of pathogen sequences). With constantly growing sequencing data, the BDEI model should be extremely useful for unravelling information on pathogen epidemics. However, existing implementations of this model in a phylodynamic framework have not yet caught up with the sequencing speed. While the accuracy of estimations should increase with data set size, existing BDEI implementations are limited to medium data sets of up to 500 samples, for both computing time and numerical instability reasons. We improve accuracy and drastically reduce computing time for the BDEI model by rewriting its differential equations in a highly parallelizable way, and by using a combination of numerical analysis methods for their efficient resolution. Our implementation takes one minute on a phylogenetic tree of 10 000 samples. We compare our parameter estimator to the existing implementations on simulated data. Results show that we are not only much faster (50 000 times), but also more accurate. An application of our method to the 2014 Ebola epidemic in Sierra-Leone is also convincing, with very fast calculation and precise estimates. Our BDEI estimator should become an important tool for routine epidemiological surveillance. It is available at github.com/evolbioinfo/BDEI . Significance Statement Phylodynamics uses pathogen genomes as a source of information for epidemiological parameter inference. With constantly growing genome sequence availability, phylodynamics has a high potential for shedding light on epidemics, especially in the beginning, when classical epidemiological data (e.g. incidence curves) are yet limited. However due to the high complexity of differential equations used in phylodynamic models, current implementations suffer from numerical instability and are only applicable to datasets of limited size (<500 sequences). We solve this computational bottleneck for the birth-death exposed-infectious model, which describes the transmission of pathogens with an incubation period (e.g. Ebola, SARS-CoV-2). Our fast and accurate estimator is applicable to very large datasets (10 000 samples) permitting phylodynamics to catch up with constantly growing pathogen sequencing efforts.