Dynamic hematological disease: a review

DOI10.1007/s00285-008-0165-3zbMath1161.92338OpenAlexW2092663493WikidataQ33378850 ScholiaQ33378850MaRDI QIDQ999321

Publication date: 3 February 2009

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00285-008-0165-3

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Dynamical systems in biology (37N25) Medical applications (general) (92C50)

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Cites Work