New development of applications of branching process and stochastic equation to mathematica;l medicine.

2016 Fiscal Year Final Research Report

• Project/Area Number: 24540114
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Saitama University
• Principal Investigator: DOKU Isamu 埼玉大学, 教育学部, 教授 (60207686)
• Project Period (FY): 2012-04-01 – 2017-03-31
• Keywords: 分枝過程 / 測度値マルコフ過程 / 数理医学 / 局所消滅性 / 腫瘍免疫 / 数理モデル / 環境依存型モデル / 超過程

Outline of Final Research Achievements

We propose an environment-dependent model that is able to describe immune responses of effector group against canceer cells. This model is capable of expressing state transition according to the competition between cancer cells and neighboring immune effects. Scaling limit procedure produces a superprocess, and we investigate the limiting process precisely, with the result that (1) survival of normal cells depends greatly on the parameter of the system; (2) tendency toward cancer depends on the dimension of the system, for instance, it proves to be always cancerous in one dimension, and it heavily depends on the probabilistic property of the system in higher dimensions, and either it has tendency toward cancer or it becomes definitely cancerous according to the Markov property of the system.

Free Research Field

確率過程論