مروری بر راهکارهای کنترل بهینه برای مهار بیماری های عفونی واگیردار

نوع مقاله : مقاله مروری

نویسندگان

1 گروه ریاضی- دانشگاه پیام نور- تهران- ایران

2 گروه ریاضی- دانشگاه صنعتی شیراز- شیراز- ایران

چکیده

استفاده از مدلهای ریاضی برای توصیف بیماری‌های عفونی و سپس نحوه مهار و حذف آنها توسط واکسن و یا دیگر درمان‌ها کمک بسیار بزرگی به سازمان‌های بهداشت عمومی می‌کند. ریشه‌کنی این دسته از بیماری‌ها وقتی امکان‌پذیر است که داروها در زمان مناسب و با میزان و فرایند مناسب تجویز شوند که در این راستا نظریه کنترل بهینه، به عنوان ابزاری موفق عمل نموده است. هدف در این مقاله، مروری بر ادبیات موجود در خصوص چنین راهکارهایی در مقابله با بیماری‌های عفونی در قالب مدل پایه ای  مشهور SRI است. بدین منظور در این مطالعه، نحوه استفاده از تابع کنترل و چگونگی  تبیین راهکارهای ارائه شده در راستای بررسی جمعیت‌های سالم، عفونی و بهبودیافته با در نظر گرفتن اهداف مورد نیاز، در بین فعالیت‌های انجام شده مورد ارزیابی و تحلیل قرار گرفته است. براساس تعداد متغیرهای کنترل به‌کار گرفته شده در درمان که مبین طرق مختلف پیشگیری‌های هم‌زمان اعم از واکسیناسیون، درمان عفونت، قرنطینه و نظایر آن است و یا نوع مدل، این مطالعه دسته‌بندی و نتایج حاصل ارائه گردیده است؛ همچنین در این مرور به نحوه‌های پیاده‌سازی مدل‌ها از نظر محاسبات عددی نیز پرداخته شده است و حالت‌های تأخیر زمانی، تصادفی و گسسته زمانی در مورد  SIR نیز بررسی شده است. این مرور برای پژوهشگران به‌منظور شناخت و اشراف داشتن به موضوع و فعالیت های انجام شده جهت ادامه تحقیقات بسیار مفید خواهد بود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

A review of optimal control strategies to inhibit contagious infectious diseases

نویسندگان [English]

  • Maryam Nikbakht 1
  • Alireza Fakharzadeh Jahromi 2
1 Department of Mathematics, Payame Noor University, Tehran, Iran
2 Department of Mathematics, Faculty of Basic Sciences, Shiraz University of Technology, Shiraz, Iran
چکیده [English]

Using mathematical models to describe infectious diseases and then how to control and eliminate them by vaccines or other treatments, is a great help to public health organizations. Eradication of this category of diseases is possible when treatments are prescribed at the right time and with the right amount and process; In this regard, optimal control theory has been applied as a successful tool. The main purpose of this article is to review the existing literature considering such strategies in dealing with infectious diseases in the form of the famous basic model SIR. For this purpose, this study, deals with the way to use the control functions and how to explain the provided solutions, indeed the aims are to investigate susceptible, infected, and recovered populations in terms of the required goals, among the performed activities by evaluation and analyzing. Based on the number of used control variables in the treatment model, which indicate different methods of simultaneous prevention, including vaccination, treatment of infection, quarantine, and like or, the type of model, this study has been categorized and the results are presented. Also, in this review, the methods of implementing models from a numerical computation point of view and reality have also been discussed and time delay, stochastic, and discrete-time models in the case of SIR are also investigated. This review would help the researchers in order to have knowledge about the subject and activities carried out to continue research in this area are very helpful.

کلیدواژه‌ها [English]

  • Optimal Control
  • Mathematical Model SIR
  • differentiail equation
  • infectious disease
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۲۱۲۹ .۴۲۷۸۸ .۲۰۲۳ .JAⅯⅯ/۲۲۰۵۵ .۱۰ ⅾoi: .۲۹۶ −۲۸۴ صص، ۲(۱۳) ،ریاضی پیشرفته سازی مدل مجله
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