非局所拡張疫病モデルの安定性解析と数値シミュレーション:陽性維持スキームの使用
Muhammad Yousuf1, Narjes Alshakhoury2
1Department of Mathematics, King Fahd University of Petroleum & Minerals, Dhahran, 31261, Saudi Arabia. myousuf@kfupm.edu.sa.
Scientific reports
|January 21, 2026
まとめ
本研究は、分数次疫病モデルをシミュレートするための新しい数値フレームワークを導入し、分数次拡散が病気の蔓延にどのように影響するかを明らかにする。本研究の結果は、公衆衛生政策および疫病制御戦略のための堅牢な計算ツールを提供する。
科学分野:
- 数理生物学
- 計算疫学
- 数値解析
背景:
- 疫病モデリングは、病気の蔓延を理解するために不可欠である。
- 従来のモデルは、しばしば空間時間ダイナミクスを単純化する。
- 分数次微積分学は、複雑な病気伝染パターンを捉えるための強力なツールを提供する。
研究 の 目的:
- 分数次拡散を伴う非局所拡張疫病モデルのための堅牢な数値フレームワークを開発する。
- 分数次拡散が病気伝染ダイナミクスに与える影響を調査する。
- 公衆衛生政策および疫病制御のための計算ツールを提供する。
主な方法:
- 空間離散化のためのフーリエスペクトルアプローチ。
- 時間積分のための陽性維持指数時間差分。
- SIRおよびSEIR分数次疫病モデルの解析。
主要な成果:
- 数値スキームはL安定であり、陽性を維持する。
- 分数次拡散は、病気の空間分布と時間的進化に大きく影響する。
- 開発された方法は、2次精度を達成する。
結論:
- 分数次拡散は疫病モデリングにおいて重要な役割を果たす。
- 提案された数値フレームワークは、複雑な病気ダイナミクスをシミュレートするために効果的である。
- 本研究は、公衆衛生および疫病制御における将来の研究の基礎を提供する。
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