scholarly journals Stability analysis and optimal control of mathematical model for the spread of hepatitis E

2020 ◽  
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Stability Analysis ◽  
Hepatitis E

Stability Analysis of a Mathematical Model for Glioma-Immune Interaction under Optimal Therapy

2019 ◽  
Vol 20 (3-4) ◽  
pp. 269-285 ◽  
Author(s):  
Subhas Khajanchi
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Stability Analysis ◽  
Model Simulation ◽  
Equilibrium Points ◽  
Glioma Cells ◽  
Adjoint System ◽  
Cellular Immunotherapy ◽  
Theory Of Optimal Control ◽  
Malignant Glioma Cells

AbstractWe investigate a mathematical model using a system of coupled ordinary differential equations, which describes the interplay of malignant glioma cells, macrophages, glioma specific CD8+T cells and the immunotherapeutic drug Adoptive Cellular Immunotherapy (ACI). To better understand under what circumstances the glioma cells can be eliminated, we employ the theory of optimal control. We investigate the dynamics of the system by observing biologically feasible equilibrium points and their stability analysis before administration of the external therapy ACI. We solve an optimal control problem with an objective functional which minimizes the glioma cell burden as well as the side effects of the treatment. We characterize our optimal control in terms of the solutions to the optimality system, in which the state system coupled with the adjoint system. Our model simulation demonstrates that the strength of treatment $u_{1}(t)$ plays an important role to eliminate the glioma cells. Finally, we derive an optimal treatment strategy and then solve it numerically.

Stability Analysis and Optimization of By-Pass Controlled Heat Exchanger With Boiling

1976 ◽  
Vol 98 (2) ◽  
pp. 161-166 ◽  
Author(s):  
J. S. Ansari
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Stability Analysis ◽  
Heat Exchanger ◽  
Flow Rate ◽  
Distributed Parameter ◽  
Final Temperature ◽  
Razumikhin Theorem ◽  
Sustained Oscillations ◽  
Intermediate Variables

A heat exchanger with boiling is considered. The final temperature of steam is controlled with the help of a controller which regulates the flow rate of by-pass water mixing with the outcoming steam. The simplest known mathematical model retaining the nonlinear and distributed parameter nature of the process is adopted. A known method of analysis, namely, Liapunov-Razumikhin theorem, is used to derive results on stability. An interesting feature of the system is that a positive feedback is required for stability. If the control is designed on the basis of minimization of the error in the final temperature alone, then the optimal control, requiring a negative feeedback, leads to sustained oscillations in the intermediate variables, even when the output is steady. The analysis, therefore suggests that meaningful optimization must take into account fluctuations in intermediate variables in addition to the error. A derivative control is shown to improve the transient response.

scholarly journals The co-dynamics of Hepatitis E and HIV

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4723-4745
Author(s):  
Ebraheem Alzahrani ◽  
Muhammad Khan
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Bifurcation Analysis ◽  
Disease Burden ◽  
Control Strategies ◽  
Hepatitis E ◽  
Control Model ◽  
Full Model ◽  
Dynamics Model ◽  
Infection Dynamics

This work investigates the co-dynamics of Hepatitis E and HIV. Initially, we formulate a co-infection dynamics model of Hepatitis E and HIV. Then, we analyze each model and discuss their mathematical results. After that, we investigate the full model and present their basic mathematical results. A bifurcation analysis for full model is investigated. Further, we formulate a mathematical model with five controls. Optimal control model is formulated and the necessary results of the optimal control characterization are presented. Moreover, numerical results with different control strategies are presented. It is shown that each strategy has its own importance but for the disease elimination the combination of all the five controls at the same time can best decrease the disease burden from the community.

Optimal control strategy for cancer remission using combinatorial therapy: A mathematical model-based approach

2021 ◽  
Vol 145 ◽  
pp. 110789
Author(s):  
Parthasakha Das ◽  
Samhita Das ◽  
Pritha Das ◽  
Fathalla A. Rihan ◽  
Muhammet Uzuntarla ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Strategy ◽  
Optimal Control Strategy ◽  
Combinatorial Therapy ◽  
Model Based ◽  
Cancer Remission

scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

Study on the Calculation Method of Soil-Nailing for High Soil Slope Based on the Logarithmic Spiral Slippery Fracture

2011 ◽  
Vol 261-263 ◽  
pp. 1709-1713
Author(s):  
Meng Yang ◽  
Xiao Min Liu
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Engineering Design ◽  
Calculation Method ◽  
Logarithmic Spiral ◽  
Soil Nailing ◽  
Soil Slope ◽  
Mode Pattern ◽  
Shear Function

This paper introduces a new failure mode pattern of soil slope – the logarithmic spiral slippery fracture. A mathematical model for the logarithmic spiral slippery fracture is established, taking the anti-shear function of the soil-nailing into consideration. The shear of soil-nailing, axial force, and the safety coefficients based on the limiting equilibrium method are derived, leading to an accurate stability analysis of the strengthening of soil slope. A case study shows that the anti-shear function of the soil-nailing can be significant and should not be ignored in engineering design.

scholarly journals Stability of Membrane Elastodynamics with Applications to Cylindrical Aneurysms

2011 ◽  
Vol 2011 ◽  
pp. 1-24 ◽  
Author(s):  
A. Samuelson ◽  
P. Seshaiyer
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Arterial Wall ◽  
Abdominal Aortic Aneurysms ◽  
Medical Problem ◽  
Aortic Aneurysms ◽  
Numerical Techniques ◽  
Abdominal Aortic ◽  
Complex Fluid ◽  
Fluid Solid Interaction

The enlargement and rupture of intracranial and abdominal aortic aneurysms constitutes a major medical problem. It has been suggested that enlargement and rupture are due to mechanical instabilities of the associated complex fluid-solid interaction in the lesions. In this paper, we examine a coupled fluid-structure mathematical model for a cylindrical geometry representing an idealized aneurysm using both analytical and numerical techniques. A stability analysis for this subclass of aneurysms is presented. It is shown that this subclass of aneurysms is dynamically stable both with and without a viscoelastic contribution to the arterial wall.

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