Few studies have examined the transmission dynamics of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in rural areas and clarified rural–urban differences. Moreover, the effectiveness of non-pharmaceutical interventions (NPIs) relative to vaccination in rural areas is uncertain. We addressed this knowledge gap through using an improved statistical stochastic method based on the Galton–Watson branching process, considering both symptomatic and asymptomatic cases. Data included 1136 SARS-2-CoV infections of the rural outbreak in Hebei, China, and 135 infections of the urban outbreak in Tianjin, China. We reconstructed SARS-CoV-2 transmission chains and analyzed the effectiveness of vaccination and NPIs by simulation studies. The transmission of SARS-CoV-2 showed strong heterogeneity in urban and rural areas, with the dispersion parameters k = 0.14 and 0.35, respectively (k < 1 indicating strong heterogeneity). Although age group and contact-type distributions significantly differed between urban and rural areas, the average reproductive number (R) and k did not. Further, simulation results based on pre-control parameters (R = 0.81, k = 0.27) showed that in the vaccination scenario (80% efficacy and 55% coverage), the cumulative secondary infections will be reduced by more than half; however, NPIs are more effective than vaccinating 65% of the population. These findings could inform government policies regarding vaccination and NPIs in rural and urban areas.

Motivation: Dimensionality reduction for single-cell RNA-sequencing (scRNA-seq) data involving multiple biological samples presents a significant analytical challenge. Results: We introduce MUlti-Sample Trajectory-Assisted Reduction of Dimensions (MUSTARD), an innovative trajectory-guided dimensionality reduction method specifically designed for multi-sample, multi-condition scRNA-seq data. By integrating pseudotemporal information, MUSTARD provides a comprehensive unsupervised approach that simultaneously captures major gene expression variation patterns along pseudotime trajectories and across multiple samples, facilitating the discovery of biologically meaningful sample heterogeneity, endotypes, and associated gene markers and modules. In data-driven simulations, MUSTARD outperformed existing methods in distinguishing sample groups, achieving superior out-of-sample prediction accuracy. In two COVID-19 datasets and a tuberculosis dataset, MUSTARD identified components linked to symptom severity, batch effect, and other known biological variations, with notable overlap in immune response genes across the two independent COVID-19 datasets. These results underscore MUSTARD’s flexibility and power in identifying biologically relevant sample heterogeneity across diverse datasets. Availability and implementation: The R package MUSTARD with a detailed user manual is publicly available at https://github.com/haotian-zhuang/MUSTARD and Zenodo (DOI: 10.5281/zenodo.18293392). The source code to reproduce the results in this paper is available at https://github.com/haotian-zhuang/MUSTARD_Paper and Zenodo (DOI: 10.5281/zenodo.18293392).