Deciphering population-level response under spatial drug heterogeneity on microhabitat structures

Bacteria and cancer cells inhabit spatially heterogeneous environments, where migration shapes microhabitat structures critical for colonization and metastasis. The interplay between growth, migration, and spatial structure complicates the prediction of population responses to drug treatment--such as clearance or persistence--even under the same spatially averaged growth rate. Accurately predicting these responses is essential for designing effective treatment strategies. Here, we propose a minimal growth-migration model to study population dynamics on discrete microhabitat structures under spatial drug heterogeneity. By applying a kernel transformation, we map the original structure to an effective fully connected graph and derive a new exact criterion for population response based on a regularized Laplacian kernel reweighted by local growth rates. This criterion connects to forest closeness centrality and yields analytical bounds and sufficient conditions for population growth or decline. We find that higher structural connectivity--like increased migration--generally promotes decline. Our framework also informs optimal spatial drug assignments, which reduce to selecting interconnected subcores in the effective complete graph. For partially controllable microhabitats or unknown drug distributions, we identify strategies that ensure population decline. Overall, our results offer a new theoretical perspective on drug response in spatially structured populations and provide practical guidance for optimizing spatially explicit dosing strategies in heterogeneous environments.