The dynamics of medical resource demand during public health crises pose significant challenges to emergency supply chain management, particularly within an evolving and complex social environment. To explore this, the interactive effects of information diffusion and virus spreading on medical resource demand are investigated using a novel three-layer coevolution “information–epidemic–resource” model through Markov process simulations. The study firstly identifies eight factors influencing demand fluctuations in terms of some city characteristics, such as media exposure, consistency of public opinion, self-protection level, and restrictive protection level, while categorizing resources into individual holdings and centralized storage. Then, extensive simulations are examined to elucidate the impact of these factors. The results reveal that various city characteristics can affect fluctuation in demand for both individual holdings and centralized storage. Inaccurate media information tends to inflate fluctuations, while higher public opinion consistency can reduce it. Reinforcing self-protection decreases the demand fluctuations of individuals, and effective restrictive protections can reduce fluctuations in centralized resource storage. Moreover, an analytical simulation of various city scenarios, underpinned by statistical data from selected Chinese and German cities, demonstrates that distinct city characteristics significantly influence medical resource demand changes during epidemics. This underscores the importance of tailoring emergency medical supply strategies to the specific developmental traits of different countries and cities. This study provides valuable insights to researchers, governments, and enterprises, enhancing their preparedness and response for emergency supply chain disruptions.