حل یک مدل اپیدمی SEIRS-α‎ با استفاده از توابع کلاهی درجه سوم

نوع مقاله : اصیل

نویسنده

گروه ریاضی کاربردی، دانشکده علوم ریاضی، دانشگاه مازندران، بابلسر، ایران

چکیده

در این مقاله، به حل عددی دستگاهی از معادلات دیفرانسیل کسری، که مدل ریاضی مربوط به یک بیماری اپیدمی است، پرداخته می‌شود. برای این منظور، ابتدا توابع کلاهی درجه سوم و خواص آنها معرفی می‌شوند. ‏پس از آن، با استفاده از بسط توابع موجود در دستگاه بر اساس توابع پایه‌ای، مسأله مورد نظر به دستگاهی از معادلات جبری تبدیل می‌شود که می‌توان آن را با روش‌های تکراری حل کرد. سپس، با حل مسأله با توجه به داده‌های اولیه مشخص و مقایسه نتایج حاصل با داده‌های واقعی گزارش شده، کارآیی روش نشان داده می‌شود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Solving an SEIRS-α‎ epidemic model using the third degree hat functions

نویسنده [English]

  • Somayeh Nemati
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
چکیده [English]

‎In this paper, ‎numerical solution of a system of fractional differential equations which is the model of an epidemic disease is considered‎. ‎To this aim‎, ‎first‎, ‎third degree hat functions and their properties are introduced‎. After that‎, ‎using the expansion of the existing functions in the system in terms of the basis functions‎, ‎the system under consideration is transformed to a system of algebraic equations that can be solved using iterative methods‎. Then‎, ‎by solving the problem with a given initial data and comparing the results with the reported real data‎, ‎efficiency of the method is shown‎.

کلیدواژه‌ها [English]

  • Human respiratory syncytial virus&lrm
  • Third degree hat functions&lrm
  • &lrm
  • System of fractional differential equations
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