Optimal Control for Mathematical Models of Tumor Immune System Interactions

2015 ◽  
pp. 317-380 ◽  
Author(s):  
Heinz Schättler ◽  
Urszula Ledzewicz
Keyword(s):  
Optimal Control ◽  
Immune System ◽  
Mathematical Models

scholarly journals Optimal control for variable order fractional HIV/AIDS and malaria mathematical models with multi-time delay

2020 ◽  
Vol 59 (5) ◽  
pp. 3149-3162 ◽  
Author(s):  
N.H. Sweilam ◽  
S.M. AL-Mekhlafi ◽  
Z.N. Mohammed ◽  
D. Baleanu
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Mathematical Models ◽  
Variable Order ◽  
Hiv Aids

scholarly journals OPTIMAL CONTROL APPLIED TO HEPATITIS C THERAPY CONSIDERING IMMUNE SYSTEM

2018 ◽  
Vol 19 (1) ◽  
pp. 9-35 ◽  
Author(s):  
Alejandro Peregrino ◽  
◽  
Lourdes Esteva ◽  
Gamaliel Blé ◽  
◽  
...  
Keyword(s):  
Optimal Control ◽  
Immune System ◽  
Hepatitis C ◽  
Hepatitis C Therapy

scholarly journals A Dual-Aggressive Model of Tumor-Immune System Interactions

2019 ◽  
Vol 15 (10) ◽  
pp. 155
Author(s):  
Abdulkareem Ibrahim Afolabi ◽  
Normah Maan
Keyword(s):  
Steady State ◽  
Immune System ◽  
Numerical Analysis ◽  
Mathematical Models ◽  
Malignant Tumor ◽  
Physical Phenomenon ◽  
Biomedical Literature ◽  
The Stability ◽  
Total Elimination ◽  
Insight Into

<p class="0abstract">Biomedical literature suggested that the tumor-immune system physical phenomenon usually climaxes into either tumor elimination or escape. In retort to the phenomenological mechanics of tumor-immune system interaction, researchers had used Mathematical models mostly prey-predator and competitive extensively, to model the dynamics of tumor immune system interaction. However, these models had not accounted for total elimination and, or escape of tumor as hypothesizes by immunoediting hypotheses. In this work, we propose a dual aggressive model based on the biological narration of tumor-immune system interactions. The stability analyses of tumor-negative steady state are stable if the rate at which body cells dies is less than their proliferation rate a confirmation of biological listed causes of the tumor. The tumor-positive steady state is always unstable and saddle with the likelihood of either elimination or escape of tumor. Numerical analysis validates our analytical results and provides insight into the dynamics of the benignant and malignant tumor. The immunosuppression by tumor is not only visible but also validated by both analytical and numerical analysis.</p>

The Testing Filtering and Majorized Algorithm of a Kind of Nonstationary Stochastic Transmission System in Intelligence Control

2014 ◽  
Vol 926-930 ◽  
pp. 3581-3584
Author(s):  
Xiao Nan Xiao
Keyword(s):  
Stochastic Process ◽  
Optimal Control ◽  
Mathematical Models ◽  
Incomplete Data ◽  
Transmission System ◽  
Linear Filtering ◽  
Optimal Coding ◽  
Non Linear ◽  
Intelligence Control ◽  
Nonstationary Stochastic Process

In intelligence control, applying the method of optimal non-linear filtering and majorized algorithm, this paper discusses the optimal control of a kind of incomplete data and continuous nonstationary stochastic process; yields two optimal control mathematical models in these two situations; illustrates how to establish the optimal coding and decoding of the nonstationary stochastic process; and provides an effective and reliable approach for the optimal control of such a process.

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