Analysis of functional equations describing dynamics of infectious disease

• Project/Area Number: 17K05365
• 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: Okayama University
• Principal Investigator: Sasaki Toru 岡山大学, 環境生命科学学域, 教授 (20260664)
• Project Period (FY): 2017-04-01 – 2023-03-31
• Project Status: Completed (Fiscal Year 2022)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2021: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 関数方程式 / 数理モデル / 疫学 / 感染症 / ウイルスダイナミクス / ウイルス・ダイナミクス / 応用数学 / 解析学 / 数理生物学 / 関数方程式論

Outline of Final Research Achievements

We demonstrated the stability results for the models that consider the following properties: (1) spatial diffusion, (2) age structure, (3) age structure and multi-strain of virus, (4) age structure, two routes, and two compartments. We obtained results on the asymptotic behavior of the solution for (1). We proved the global asymptotical stability of the equilibria for (2), (3) and (4). We use Lyapunov functions/functionals for the proofs. Detailed discussions on well-definedness of the Lyapunov functions/functionals are different among the models.

Academic Significance and Societal Importance of the Research Achievements

空間拡散を考慮したモデルにおける，解の漸近挙動に対する結果は，空間拡散を考慮しないモデルに対する結果に準じたものになっていて，この結果は空間拡散を考慮しないモデルを用いた応用研究の信頼性を裏づけるものとなっている．また，齢構造を取り入れたモデルにおける，平衡点の大域安定性の関する結果は，議論される事が少なく，しかし数学的には欠かせない点を丁寧に議論した点に学術的意義がある．また，2 つの感染経路と 2 つのコンパートメントを考慮したモデルは，近年生物学的に注目されている点を踏まえたもので，その応用研究の基礎となりうるものである．

Research Products

• [Journal Article] Global stability of an age-structured infection model in vivo with two compartments and two routes (2022)
  • Author(s): Kajiwara Tsuyoshi、Sasaki Toru、Otani Yoji
  • Journal Title: Mathematical Biosciences and Engineering Volume: 19 Issue: 11 Pages: 11047-11070
  • DOI: 10.3934/mbe.2022515
  • Peer Reviewed / Open Access
• [Journal Article] Global stability for an age-structured multistrain virus dynamics model with humoral immunity (2020)
  • Author(s): Kajiwara Tsuyoshi、Sasaki Toru、Otani Yoji
  • Journal Title: Journal of Applied Mathematics and Computing Volume: 62 Issue: 1-2 Pages: 239-279
  • DOI: 10.1007/s12190-019-01283-w
  • Peer Reviewed
• [Journal Article] Global stability of an age-structured model for pathogen-immune interaction (2019)
  • Author(s): Kajiwara Tsuyoshi, Toru Sasaki, Yoji Otani
  • Journal Title: J. Appl. Math. Comput. Volume: 59(1-2) Pages: 631-660
  • Peer Reviewed
• [Journal Article] Asymptotic behaviour of the solutions to a virus dynamics model with diffusion (2018)
  • Author(s): Toru Sasaki and Takashi Suzuki
  • Journal Title: Discrete and Continuous Dynamical Systems, Series B Volume: 23-2 Issue: 2 Pages: 525-541
  • DOI: 10.3934/dcdsb.2017206
  • Peer Reviewed
• [Presentation] Stability of equilibria of pathogen-immune models (2019)
  • Author(s): Toru Sasaki, Tsuyoshi Kajiwara,Yoji Otani, and Yuki Ishimaru
  • Organizer: The 7th China-India-Japan-Korea International Confernce on Mathematical Biology
  • Int'l Joint Research
• [Presentation] ウイルスダイナミクス基本モデルの安定性に関する考察 (2019)
  • Author(s): 佐々木 徹, 梶原 毅, 應谷洋二, 石丸優希
  • Organizer: 日本数理生物学会年会
• [Presentation] 拡散効果を取り入れた病原体・免疫モデルの漸近挙動 (2018)
  • Author(s): 佐々木徹，鈴木貴
  • Organizer: 応用数理学会年会