scholarly journals Peer Review #1 of "Θ-SEIHRD mathematical model of Covid19-stability analysis using fast-slow decomposition (v0.1)"

2020 ◽  
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Peer Review ◽  
Slow Decomposition

scholarly journals Θ-SEIHRD mathematical model of Covid19-stability analysis using fast-slow decomposition

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e10019
Author(s):  
OPhir Nave ◽  
Israel Hartuv ◽  
Uziel Shemesh
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Nonlinear Differential Equations ◽  
Equilibrium Points ◽  
Asymptotic Methods ◽  
Fast Subsystem ◽  
The Stability ◽  
System Variables ◽  
The Mathematical Model ◽  
Slow Decomposition

In general, a mathematical model that contains many linear/nonlinear differential equations, describing a phenomenon, does not have an explicit hierarchy of system variables. That is, the identification of the fast variables and the slow variables of the system is not explicitly clear. The decomposition of a system into fast and slow subsystems is usually based on intuitive ideas and knowledge of the mathematical model being investigated. In this study, we apply the singular perturbed vector field (SPVF) method to the COVID-19 mathematical model of to expose the hierarchy of the model. This decomposition enables us to rewrite the model in new coordinates in the form of fast and slow subsystems and, hence, to investigate only the fast subsystem with different asymptotic methods. In addition, this decomposition enables us to investigate the stability analysis of the model, which is important in case of COVID-19. We found the stable equilibrium points of the mathematical model and compared the results of the model with those reported by the Chinese authorities and found a fit of approximately 96 percent.

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.

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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