Understanding how respiratory infections spread between cities with different socioeconomic and functional roles is vital for targeted public health action. Traditional spatial models often use geographic distance as a proxy for connectivity, but modern transport and travel patterns make distance an incomplete measure of pathogen spread. This study integrates empirical mobility data with an agent-based branching process model to assess whether intercity human movement alone can reproduce observed early spatial spread and to quantify how transmission risk varies across urban tiers for pathogens with contrasting transmissibility.
The authors extracted anonymised, aggregated daily migration data from Baidu Maps (Baidu Qianxi) for 366 mainland Chinese cities from 1 January 2021 to 5 April 2022. For each city-day they obtained an outbound migration scale index and the proportion of outflow directed to each destination city. These components were combined and normalised to create city-to-city travel probabilities and assembled into mobility transition matrices. The analysis period was chosen to represent routine travel patterns during China’s “dynamic zero-COVID” response phase, a context of heightened alertness with relatively stable intercity travel compared with lockdown periods.
Three COVID-19 outbreaks were used for model validation: the Omicron outbreak in Shanghai, the Delta outbreak in Nanjing, and a multi-province Delta outbreak in northwestern China. Outbreak definitions used the first detected case as the start and either the last confirmed case or the timing of substantial public health and social measures (PHSM) as the end. The three outbreaks involved 121, 28, and 26 cities respectively. Daily new infection data were obtained from official press releases of the National Health Commission of China and used to derive observed first arrival times at the city level.
The spatial model operates at the city level as an agent-based branching process. Each infected individual generates secondary infections drawn from a negative binomial distribution with mean equal to the reproduction number (R0) to capture transmission heterogeneity. Infection times for secondary cases are sampled from a pathogen-specific serial interval distribution: Gamma for SARS-CoV-2 and Weibull for Influenza A. Travel probability from a given city is modelled as a sigmoid function of the local migration index; when travel occurs the destination is sampled according to empirically observed outbound proportions. The modeled process records infection and travel events to determine when a destination city first receives infection.
The primary outcome of interest is the city-level first arrival time, defined as the elapsed time between outbreak onset in the seed city and the first infection recorded in a destination city. Simulations were run 10,000 times per outbreak-origin scenario to capture stochastic variability. In one validation approach the mobility-driven component was run without pathogen-specific R0 and serial interval to isolate mobility effects; an extended validation incorporated outbreak-specific epidemiological parameters. Predicted first arrival times showed strong agreement with observed data (reported correlations of r = 0.68 and r = 0.76). Mobility-based predictions more accurately identified outbreak origins than models that relied on geographic distance alone.
Cities were classified into hierarchical tiers based on commercial concentration, transport hub centrality, and similar criteria ranging from super-tier metropolises to lower-tier cities. The modelling identified contrasting diffusion patterns for the two representative pathogens. Influenza A showed relatively stable, stratified diffusion: transmission remained concentrated within the same tier or adjacent tiers, and early importation risk remained persistently higher in upper-tier cities. By contrast, SARS-CoV-2 (Omicron) initially concentrated in super-tier and tier-1 cities but rapidly seeded lower-tier cities; this produced a pronounced hierarchical spread that quickly attenuated tier-level differences in transmission risk. Across pathogens, higher-tier cities faced greater early importation risk, but that disparity persisted for Influenza A and was rapidly reduced for Omicron because of its higher transmissibility and faster spatial expansion.
The study reports that mobility-informed transition matrices derived from observed travel flows better reproduced city-level first arrival times and more accurately identified outbreak origins than distance-based proxies. This finding supports using real movement data rather than geographic proximity when forecasting early spatial spread in highly connected systems.
Key limitations noted by the authors include validation against city-level first arrival times rather than full epidemic trajectories, which constrains assessment of downstream epidemic dynamics. The model was parameterised using mobility data from China’s dynamic zero-COVID period; the authors caution that direct quantitative generalisability to other settings or to periods with different intervention regimes may be limited. Details on some model parameters and extended results are provided in the study’s supplementary appendices.
Spatial transmission risk emerges from an interaction between pathogen transmissibility and the hierarchical organisation of urban mobility. The results suggest that surveillance and control strategies effective for less transmissible pathogens may not suffice for highly transmissible variants that rapidly erode tier-based risk gradients. Mobility-informed, tier-specific risk assessment could support earlier, more adaptive public health responses and targeted interventions, using routinely available mobility data and minimal pathogen-specific inputs to scale preparedness for future respiratory threats.
All datasets used, including Baidu Migration data and first confirmed case data, and processed analytical inputs, are publicly archived on Zenodo. Analysis code is publicly available on GitHub and archived in Zenodo as cited in the original article.