{
  "annotation_id": "b692c435-fe29-45b4-8ed8-26232ee0ba5b",
  "date_created": "2026-03-02T18:01:32.337000Z",
  "date_modified": "2026-03-02T18:01:32.337000Z",
  "file_hash": "6a42ec182f6996c13ad956727801554026ea2e1e31402b5d5aac5208b251cd58",
  "private": false,
  "record": {
    "abstract": "We develop some techniques to prove analytically the existence and stability\nof long period oscillations of stem cell populations in the case of periodic\nchronic myelogenous leukemia. Such a periodic oscillation $p_\\infty $ can be\nanalytically constructed when the hill coefficient involved in the nonlinear\nfeedback is infinite, and we show it is possible to obtain a contractive\nreturning map (for the semiflow defined by the modeling functional differential\nequation) in a closed and convex cone containing $p_\\infty $ when the hill\ncoefficient is large, and the fixed point of such a contractive map gives the\nlong period oscillation previously observed both numerically and\nexperimentally.",
    "arxiv_id": "q-bio/0409002",
    "authors": [
      "Michael C. Mackey",
      "Chunhua Ou",
      "Laurent Pujo-Menjouet",
      "Jianhong Wu"
    ],
    "categories": [
      "q-bio.TO"
    ],
    "title": "Periodic Oscillations of Blood Cell Populations in Chronic Myelogenous   Leukemia",
    "url": "https://arxiv.org/abs/q-bio/0409002"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "52ea62ae-f56c-41f4-bf65-a836db480e7e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}