Reactive–diffusion epidemic model on human mobility networks: Analysis and applications to COVID-19 in China

The complex dynamics of human mobility, combined with sporadic cases of local outbreaks, make assessing the impact of large-scale social distancing on COVID-19 propagation in China a challenge. In this paper, with the travel big dataset supported by Baidu migration platform, we develop a reactive–diffusion epidemic model on human mobility networks to characterize the spatio-temporal propagation of COVID-19, and a novel time-dependent function is incorporated into the model to describe the effects of human intervention. By applying the system control theory, we discuss both constant and time-varying threshold behavior of proposed model. In the context of population mobility-mediated epidemics in China, we explore the transmission patterns of COVID-19 in city clusters. The results suggest that human intervention significantly inhibits the high correlation between population mobility and infection cases. Furthermore, by simulating different population flow scenarios, we reveal spatial diffusion phenomenon of cases from cities with high infection density to cities with low infection density. Finally, our model exhibits acceptable prediction performance using actual case data. The localized analytical results verify the ability of the PDE model to correctly describe the epidemic propagation and provide new insights for controlling the spread of COVID-19.