0:30 感染症数理
2:12 SIR model（格子モデル）
5:26 SIR model（駆動粒子モデル）
6:53 目的
7:38 駆動粒子のダイナミクス
9:46 Single file diffusion
11:16 感染伝播
12:56 感染者数の時間発展（数値計算の結果）
14:33 感染緩和時間（数値計算の結果）
17:02 隣接粒子間距離の拡散性
17:58 低い拡散領域での感染ダイナミクス
19:07 感染緩和時間と系の種々の緩和時間との関係
21:40 感染半径と最適拡散係数
22:02 結論
Understanding the spread of infectious diseases requires integrating movement and interaction dynamics into epidemiological models. In this study, we investigate the role of particle diffusivity and physical constraints in shaping infection dynamics within a system of Brownian particles. Through numerical simulations and theoretical analyses, we uncover a nontrivial relationship between diffusivity and infection speed: an optimal diffusion coefficient exists that minimizes the infection spreading speed. This counterintuitive result arises from a balance between particle mixing and interaction frequency. The optimal diffusivity is observed in both interacting and non-interacting systems when the infection radius exceeds the mean lattice spacing and the initial configuration is out of equilibrium. Our findings provide a theoretical framework for understanding and controlling the spread of infections in confined and diffusive environments, with potential implications for designing movement-based strategies for infection control.
参考文献
K. Takahashi, M. Sasada, and T. Akimoto, "Unveiling Optimal Diffusion for Infection Control in Brownian Particle Systems," arXiv.2502.06230.