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Abstract The Eden Model in$${\mathbb {R}}^n$$ $R^n$constructs a blob as follows: initially a single unit hypercube is infected, and each second a hypercube adjacent to the infected ones is selected randomly and infected. Manin, Roldán, and Schweinhart investigated the topology of the Eden model in$${\mathbb {R}}^{n}$$ $R^n$by considering the possible shapes which can appear on the boundary. In particular, they give probabilistic lower bounds on the Betti numbers of the Eden model. In this paper, we prove analogous results for the Eden model on any infinite, vertex-transitive, locally finite graph: with high probability as time goes to infinity, every “possible” subgraph (with mild conditions on what “possible” means) occurs on the boundary of the Eden model at least a number of times proportional to an isoperimetric profile of the graph. Using this, we can extend the results about the topology of the Eden model to non-Euclidean spaces, such as hyperbolicn-space and universal covers of certain Riemannian manifolds. 

The COVID-19 pandemic has resulted in more than 440 million confirmed cases globally and almost 6 million reported deaths as of March 2022. Consequently, the world experienced grave repercussions to citizens’ lives, health, wellness, and the economy. In responding to such a disastrous global event, countermeasures are often implemented to slow down and limit the virus’s rapid spread. Meanwhile, disaster recovery, mitigation, and preparation measures have been taken to manage the impacts and losses of the ongoing and future pandemics. Data-driven techniques have been successfully applied to many domains and critical applications in recent years. Due to the highly interdisciplinary nature of pandemic management, researchers have proposed and developed data-driven techniques across various domains. However, a systematic and comprehensive survey of data-driven techniques for pandemic management is still missing. In this article, we review existing data analysis and visualization techniques and their applications for COVID-19 and future pandemic management with respect to four phases (namely, Response, Recovery, Mitigation, and Preparation) in disaster management. Data sources utilized in these studies and specific data acquisition and integration techniques for COVID-19 are also summarized. Furthermore, open issues and future directions for data-driven pandemic management are discussed.