Stochastic tumor-immune interaction model with external treatments and time delays: An optimal control problem
Source of Publication
Mathematical Biosciences and Engineering
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.
American Institute of Mathematical Sciences (AIMS)
Medicine and Health Sciences
tumor-immure interactions, optimal control, stochastic noise, stationary distribution, time-delays
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Alsakaji, H. J.; Rihan, F. A.; Udhayakumar, K.; and El Ktaibi, F., "Stochastic tumor-immune interaction model with external treatments and time delays: An optimal control problem" (2023). All Works. 6172.
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Open Access Type
Gold: This publication is openly available in an open access journal/series