Master equations for epidemic dynamics in networks

2019 Fiscal Year Final Research Report

• Project/Area Number: 16K05507
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Biological physics/Chemical physics/Soft matter physics
• Research Institution: Hokkaido University
• Principal Investigator: Nemoto Koji 北海道大学, 理学研究院, 教授 (60202248)
• Co-Investigator(Kenkyū-buntansha): 長谷川 雄央 茨城大学, 理工学研究科(理学野), 准教授 (10528425)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Keywords: 相転移 / 感染症ダイナミクス / ネットワーク科学

Outline of Final Research Achievements

The behavior of the SWIR infection model with finite seed ratio (initially infected person) was analyzed on a regular random graph by numerical analysis of AME (approximate master equation), and the existence of two critical infection rates was clarified. In addition, a model that introduced quarantine measures to the SIR infection model on regular random and scale-free networks is proposed, and the superiority to random vaccine measures is clarified. Furthermore, both SWIS and SWSIS models, which are extensions of the SIS model, are examined in a unified manner, and the mechanism of continuous phase transition and discontinuous phase transition that appear in the finite seed ratio variation is clarified.

Free Research Field

統計物理学

Academic Significance and Societal Importance of the Research Achievements

ネットワーク上の感染症ダイナミクス解析手法であるAMEの拡張と様々なモデル計算においてその相転移メカニズムの解明に資する手法の有効性が明らかになり，より正確な感染症ダイナミクスの把握や効果的な隔離対策の有用性を示す解析・研究につながることが期待され，昨今の新型コロナウィルス対策のための数理モデルに対する知見となりうる成果である。合わせて非平衡統計物理学へのフィードバックとして手法の応用を考えることも可能となる。