分数順序の微分と深層ニューラルネットワークによるポリオの動態
Ashraf Al-Quran1, Ramsha Shafqat2, Ateq Alsaadi3
1Department of Mathematics and Statistics, King Faisal University, 31982, Hofuf, Saudi Arabia.
Scientific reports
|August 31, 2025
まとめ
この研究では,アタンガナ-バレーヌ派生体の分数型モデルを使用して,ポリオ (ポリオ) の拡散を分析しました. 低分数順序と深層ニューラルネットワークは 病気の予測と制御戦略を改善します
科学分野:
- 流行病学について
- 数学生物学
- コンピュータ・ダイナミクス
背景:
- ポリオ感染のダイナミクスは複雑で ワクチン接種や病気の記憶などの要因に 影響されています
- 分数順の微分方程式は,病気の伝播における遺伝的性質をモデル化するための高度なツールを提供します.
研究 の 目的:
- ワクチン接種と麻痺後効果を含む小児麻痺の伝播の分数型モデルを開発し分析する.
- 病気のダイナミクスを予測し,データに基づいたシミュレーションを行うための深層ニューラルネットワーク技術を統合する.
主な方法:
- Atangana-Baleanu 派生式 (ABC) と Mittag-Leffler カーネルによる2つの分数順序モデルを使用した.
- 固定点理論と非線形テクニックを用いて,モデルの存在,ユニークさ,ウラム・ハイアースの安定性を確立した.
- 数値的な近似と分類と予測のための深層ニューラルネットワーク (DNN) を採用した.
主要な成果:
- 分数型モデリングは複雑な病気の行動を効果的に捉え,より低い分数型順序でより速い安定化を示します.
- すべてのモデルコンパートメントは,時間とともに収束とダイナミックな安定性を示した.
- DNNベースの予測は数値シミュレーションと密接に連携し,ハイブリッドアプローチを検証しました.
結論:
- ABC誘導体の分数型モデリングは 脊髓灰質炎を分析するための堅固な枠組みを提供します
- DNNを統合することで,感染症の動態に関する予測の精度が向上します.
- このハイブリッドアプローチは ワクチン接種によるポリオの拡散を理解し管理するための強力なツールです
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