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Mô hình đạo hàm phân thứ cho sự lan truyền COVID-19 với biện pháp cách ly

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Abstract

Bài báo nghiên cứu sự lan truyền của COVID-19 bằng đạo hàm phân thứ. Sự lan truyền được quyết định bởi số sinh sản cơ bản R0 và tính ổn định của các điểm cân bằng. Tính ổn định địa phương được xác định bằng phương pháp giá trị riêng. Tính ổn định tiệm cận đều được chứng minh bằng phương pháp hàm Lyapunov và nguyên lý bất biến Lasalle. Chúng tôi chỉ ra rằng khi R0 < 1 thì điểm cân bằng tự do ổn định địa phương và tiệm cận đều và khi R0 > 1 thì điểm cân bằng bệnh ổn định địa phương và tiệm cận đều. Phân nhánh Transcitical được dùng để giải thích cơ chế của sự lan truyền. Mô phỏng số được thực hiện để kiểm chứng các kết quả lý thuyết.

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