ﻳﮏ ﻣﺪﻝ جدید همه گیر ﺷﻨﺎسی در زیست بوم با انتشار و تابع پاسخ رادیکالی

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده علوم ریاضی، دانشگاه یزد، یزد، ایران

چکیده

هدف از این پژوهش مطالعه یک مدل همه‌گیرشناسی در یک زیست بوم با نرخ شیوع دوخطی و تابع پاسخ رادیکالی است. ابتدا نقاط تعادل و پایداری سیستم را برای مقادیر مختلف پارامترها بررسی می‌کنیم. چالش اصلی در مدل های جمعیت، یافتن یک روش عددی برای تقریب جواب نامنفی است. برخی از روش های عددی مانند روش اویلر ناکارآمد اند زیرا گاهی اوقات قادر به ایجاد جواب نامنفی نیستند. تقریب‌های نامنفی حاصل از روش‌های تفاضل متناهی غیراستاندارد نیز مشروط اند. در این مقاله، یک روش عددی را پیشنهاد می‌کنیم که پاسخ‌های قابل قبول نامشروط را ارائه می کند. پس از آن سازگاری روش عددی پیشنهادی را مورد بحث قرار می دهیم. سپس با استفاده از شبیه سازی عددی کارایی روش پیشنهادی را با دو روش اویلر و غیر استاندارد مقایسه می‌کنیم. در نهایت اثر رفتار گله‌ایی گونه شکار را بر تراکم جمعیت گونه‌ها مورد بررسی قرار داده و برای برخی از مقادیر عددی از پارامترهای موجود در مسئله، مدل دینامیکی را تجزیه و تحلیل می‌کنیم.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

A new eco-epidemiological model with diffusion and square root functional response

نویسندگان [English]

  • Ghasem Barid Loghmani
  • Mohammad Heydari
  • Mohammad Hossein Akrami
  • safieh Bagheri Hamane
Department of Mathematical sciences, Yazd University, Yazd, Iran
چکیده [English]

The aim of this study is to investigate an eco-epidemiological model with a bilinear incidence rate and a square root functional response. First, we examine the equilibrium and stability points of the system for various parameter values. The main challenge in population models is finding a numerical method for approximating non-negative solutions. Some numerical methods, such as the Euler method, are inefficient as they sometimes fail to produce non-negative solutions. Non-negative approximations obtained from non-standard finite difference methods are also conditional. In this paper, we propose a numerical method that provides unconditional and acceptable solutions. We then discuss the compatibility of the proposed numerical method. Finally, we compare the efficiency of the proposed method with the Euler and non standard methods using numerical simulations. We also investigate the effect of the hunting behavior of the prey species on the population density and analyze the dynamic model for some numerical values of the parameters involved in the problem.

کلیدواژه‌ها [English]

  • Diffusion
  • Square root functional
  • Finite difference method
  • Epidemiology
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