نشریه علمی مهندسی پزشکی زیستی
Iranian Journal of Biomedical Engineering (IJBME)

پیشنهاد و تحلیل مدل ریاضی مرتبه‌ی کسری برای توصیف انتقال بیماری کووید-19

نوع مقاله : مقاله کامل پژوهشی

نویسندگان

آرمان مرزبان 1
الهام امینی بروجنی 2

1 دانشجوی کارشناسی ارشد، گروه مهندسی برق و کامپیوتر، دانشکده‌ی فنی و مهندسی، دانشگاه خوارزمی، تهران، ایران

2 استادیار، گروه مهندسی برق و کامپیوتر، دانشکده‌ی فنی و مهندسی، دانشگاه خوارزمی، تهران، ایران

https://doi.org/10.22041/ijbme.2023.1996296.1832
چکیده
با توجه ‌به این که مدل‌سازی ریاضی در توصیف و تحلیل رفتار بیماری­های همه­گیر کمک کننده بوده و از طرفی دقت و درجه‌ی آزادی در مدل‌سازی سیستم‌های مرتبه‌ی کسری به دلیل وجود ویژگی حافظه‌ی بلند مدت بیش‌تر از سیستم‌های مرتبه‌ی صحیح می‌باشد، در این مقاله با استفاده از حسابان مرتبه‌ی کسری، مدل مرتبه‌ی صحیح موجود برای توصیف انتقال بیماری کووید-19 به حوزه‌ی سیستم‌های مرتبه‌ی کسری بسط داده شده است. مثبت و محدود بودن پاسخ­های مدل مرتبه‌ی کسری پیشنهادی با استفاده از قضیه‌ی ناحیه‌ی ثابت اثبات شده و به کمک تئوری نقطه‌ی ثابت در فضای باناخ، وجود و یکتایی جواب مدل مرتبه‌ی کسـری پیشـنهادی نشان داده شده است. هم‌چنین رفتار دو مدل مرتبه‌ی صحیح و مرتبه‌ی کسری با بهره­گیری از اطلاعات واقعی منتشر شده برای بیماری کووید-19 در کشور تایلند شبیه‌سازی شده و مورد ارزیابی قرار گرفته است. کارایی و دقت بیش‌تر مدل پیشنهادی مرتبه‌ی کسری در نتایج شبیه‌سازی تایید شده است.

کلیدواژه‌ها

کووید-19
حسابان مرتبه‌ی کسری
مدل‌سازی ریاضی
وجود و یکتایی جواب

موضوعات

عنوان مقاله English

Proposal and Analysis of Fractional Order Mathematical Model to Describe the Transmission of Covid-19 Disease

نویسندگان English

Arman Marzban 1
Elham Amini Boroujeni 2
1 M.Sc. Student, Department of Electrical and Computer Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran
2 Assistant Professor, Department of Electrical and Computer Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran
چکیده English

Considering that mathematical modeling is helpful in describing and analyzing the behavior of epidemic diseases. On the other hand, the accuracy and degree of freedom in modeling fractional order systems are more than that of integer order systems due to the presence of long-term memory property. This paper extends the existing integer order model of Covid-19 disease to fractional order systems using fractional order calculations. The proposed model’s positivity and bounded answers are proved using the invariant region theorem. Using the fixed point theory in Banach space, the existence and uniqueness of the solution of the proposed fractional order model are proved. The behavior of both integer and fractional order has been simulated and evaluated using real information published for Covid-19 in Thailand. The higher efficiency and accuracy of the proposed model of fractional order are confirmed in the simulation results.

کلیدواژه‌ها English

Covid-19
Fractional Order Calculus
Mathematical Modeling
Existence and Uniqueness of the Answer
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نشریه علمی مهندسی پزشکی زیستی
دوره 16، شماره 4
زمستان 1401
صفحه 321-333

  • تاریخ دریافت 24 اسفند 1401
  • تاریخ بازنگری 14 خرداد 1402
  • تاریخ پذیرش 29 خرداد 1402

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