دینامیک سراسری یک مدل ریاضی برای انتشار بیماری های عفونی با نرخ انتشار غیرخطی اشباع

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه ریاضی، دانشکده شهید مهاجر، دانشگاه فنی و حرفه‌ای استان اصفهان، ایران

2 گروه ریاضی، دانشکده علوم پایه، دانشگاه زابل، زابل، ایران

چکیده

یک مدل اپیدمی‌که شامل یک برنامه واکسیناسیون نیز می‌باشد، توصیف و ارائه می‌گردد. این مدل علاوه بر مرگ طبیعی، مرگ در اثر بیماری را نیز در‌بر می‌گیرد و جمعیت کل متغیر است. نقاط تعادل مدل، نقطه تعادل بدون بیماری و نقطه تعادل اندمیک، به‌دست می‌آیند و دینامیک سراسری مدل با به‌کارگیری توابع لیاپانوف مناسب توسط عدد مولد عمومی ‌بیان می‌گردد. وقتی این کمیت کم‌تر یا مساوی واحد است، نقطه تعادل بدون بیماری پایدار مجانبی سراسری است و زمانی که این کمیت بیشتر از واحد است، نقطه تعادل اندمیک پایدار مجانبی سراسری است. بحث و مثال‌های عددی برای تایید یافته‌های تئوری آورده می‌شوند.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Global dynamics of a mathematical model for propagation of infection diseases with saturated incidence rate

نویسندگان [English]

  • Mahmood Parsamanesh 1
  • Majid Erfanian 2
1 Department of Mathematics, Faculty of Mohajer, Isfahan Branch, Technical and Vocational University, Isfahan, Iran
2 Department of Mathematics, Faculty of Science, University of Zabol,, Zabol, Iran
چکیده [English]

An epidemic model is described and introduced in which a vaccination program has been included. The model considers disease-caused death in addition to natural death, and the total population size is variable. The equilibria of the model, the disease-free equilibrium and the endemic equilibrium, are obtained and the global dynamics of the model are stated via the basic reproduction number using proper Lyapunov functions. The disease-free equilibrium is asymptotically globally stable when this quantity is less than or equal to unity and when it is greater than unity, the endemic equilibrium is asymptotically globally stable.

کلیدواژه‌ها [English]

  • epidemic model
  • immunity
  • vaccination
  • global stability
  • Lyapunov function
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