Mathematical Analysis on Stability and Unstable Phenomena of Immune Models
| Project/Area Number |
26400211
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Foundations of mathematics/Applied mathematics
|
|---|
| Research Institution | Aoyama Gakuin University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2014-04-01 – 2019-03-31
|
| Project Status |
Completed (Fiscal Year 2018)
|
| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
|---|
| Keywords | 数理モデル / ウィルス免疫系 / 数理生物学 / 時間遅れ / 免疫 / ガン / 安定性 / 分岐現象 / 癌 / カオス |
|---|
| Outline of Final Research Achievements |
The purpose of the research is to make clear the relationship between the structure and function of virus infection versus immune response of human. Particular we focus on the unstable phenomena of the immune dynamics. First, we construct a general mathematical models ofimmune systems describing virus infection process and activating process of our immune systems. Further, we introduce the time delays into the model to express the time duration for the infected cell to produce the virus particles and for the immune systems to be activated. We consider the effects of the these time delays on the dynamics of the mathematical models. Especially we investigate the effect of the time delays on the global stability of the model and unstable dynamics.
|
| Academic Significance and Societal Importance of the Research Achievements |
デング熱感染におけるＴ細胞の適応免疫細胞としての役割を考慮した数理モデルを構築し，デング熱ウイルスとの闘いにおけ るＴ細胞の役割を解析 した．またＴ細胞を活性化させる免疫療法の効果を議論した．また富栄養化のパラドクスとして知られている有名な個体群生態学におけ る数理モデルに対して， 捕食者の成長段階を考慮（捕食者の成長に対する時間遅れ）した数理モデルに拡張し，ダイナミクスを考察した．この時間遅れによっ て，富栄養化のパラドクス が消滅することを証明した.
|
Report
(6 results)
Research Products
(65 results)
-
[Journal Article] Global dynamics of a latent HIV infection model with general incidence function and multiple delays2019
Author(s)
Yang Yu、,School of Science and Technology, Zhejiang International Studies University, Hangzhou 310023, China、Dong Yueping、Takeuchi Yasuhiro、,Faculty of Engineering, Kyushu University, Fukuoka 819-0395, Japan、,College of Science and Engineering, Aoyama Gakuin University, Kanagawa 252-5258, Japan
-
Journal Title
Discrete & Continuous Dynamical Systems - B
Volume: 24
Issue: 2
Pages: 783-800
DOI
Related Report
Peer Reviewed
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
