گسترش مدل چرخه سلولی سرطان

نوع مقاله : اصیل

نویسندگان

گروه ریاضی کاربردی، دانشگاه گیلان

چکیده

در این مقاله یک مدل ریاضی تاخیری از چرخه سلولی را بررسی میکنیم. با اصلاح و بهبود مدل با افزودن تغییرات سمیت دارو و ارائه یک تابع لیاپانوف به بررسی پایداری مدل جدید میپردازیم. در ادامه با بدست آوردن یک معیار برای کنترل مطلوب، نشان میدهیم که با اعمال دارودهی مطابق این معیار، سیستم به سمت نقطه تعادل سلامت میل خواهد کرد.

کلیدواژه‌ها


عنوان مقاله [English]

Extension of Cell Cycle Model

نویسندگان [English]

  • Mohammad Keyanpour
  • Tahereh Akbarian
Department of Applied Mathematics, University of Guilan, Rasht, Iran
چکیده [English]

In this paper we consider a delayed mathematical model of cell cycle. Adding drug toxicity, the model is modified and developed. A proper Lyapunov function is suggested for stability analysis. Furthermore,  by obtaining a criterion for appropriate control, it is shown that any treatment strategy which satisfies  the criterion, causes  the system converge to tumor free equilibrium point.

کلیدواژه‌ها [English]

  • Delay differential equations
  • Equilibrium point
  • Mathematical modeling of cancer
  • Lyapunov stability criterion
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