数理医学的視点に依る腫瘍免疫応答の確率モデル : がん細胞に対する免疫作用と超過程の消滅性<数学・自然科学>

概要

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The purpose of this paper is to construct a mathematical model to describe immunomechanism against cancer cells. Usually, the process of tumorigenesis proceeds after ordinary cells are transformed into irregular ones by some reasons. As for this, a group of immune cells starts immune response, which is called the host-defense mechanism against cancer. Our main concern is the immunomechanism during the transformation period and disorder proliferation period, and our principal characters are natural killer cells, cytotoxic T lymphocytes and macrophages. In this paper we are going to propose a stochastic model to describe the cytotoxicity of those effectors against cancer, analyze the model mathematically, and provide expository information for qualitative property of life scientific phenomena related to the immune response. We have succeeded in grasping immune capability as reflection of the extinction property of its limit process, based upon a mathematical model of branching particles. A peculiar feature of our model consists in its potential capability in describing effects of immune cells against cancer, which are distinct depending on the location.