Stochastic tumor-immune interaction model with external treatments and time delays: An optimal control problem

H. J. Alsakaji, F. A. Rihan, K. Udhayakumar, F. El Ktaibi

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Herein, we discuss an optimal control problem (OC-P) of a stochastic delay differential model to describe the dynamics of tumor-immune interactions under stochastic white noises and external treatments. The required criteria for the existence of an ergodic stationary distribution and possible extinction of tumors are obtained through Lyapunov functional theory. A stochastic optimality system is developed to reduce tumor cells using some control variables. The study found that combining white noises and time delays greatly affected the dynamics of the tumor-immune interaction model. Based on numerical results, it can be shown which variables are optimal for controlling tumor growth and which controls are effective for reducing tumor growth. With some conditions, white noise reduces tumor cell growth in the optimality problem. Some numerical simulations are conducted to validate the main results.

Original languageEnglish
Pages (from-to)19270-19299
Number of pages30
JournalMathematical Biosciences and Engineering
Volume20
Issue number11
DOIs
Publication statusPublished - 2023

Keywords

  • optimal control
  • stationary distribution
  • stochastic noise
  • time-delays
  • tumor-immure interactions

ASJC Scopus subject areas

  • Modelling and Simulation
  • General Agricultural and Biological Sciences
  • Computational Mathematics
  • Applied Mathematics

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