Spread of Tuberculosis Among Smokers

2020 ◽  
pp. 49-73
Author(s):  
Purvi M. Pandya ◽  
Ekta N. Jayswal ◽  
Yash Shah
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Psychological Health ◽  
Matrix Method ◽  
Equilibrium Points ◽  
Research Work ◽  
Linear Ordinary Differential Equations ◽  
Smoking Addiction ◽  
The Mathematical Model

Smoking tobacco has some hazardous implications on an individual's physical, physiological, and psychological health; health of the passive smokers near him or her; and on the surrounding environment. From carcinomas to auto-immune disorders, smoking has a role to play. Therefore, there arises a need to frame a systemic pathway to decipher relationship between smoking and a perilous disease such as tuberculosis. This research work focuses on how drugs or medications can affect individuals who are susceptible to tuberculosis because of smoking habits and also on individuals who have already developed symptoms of tuberculosis due to their smoking addiction. The mathematical model is formulated using non-linear ordinary differential equations, and then threshold is calculated for different equilibrium points using next generation matrix method. Stability analysis along with numerical simulations are carried out to validate the data.

scholarly journals A Mathematical Model to Study the Effectiveness of Some of the Strategies Adopted in Curtailing the Spread of COVID-19

2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Isa Abdullahi Baba ◽  
Bashir Abdullahi Baba ◽  
Parvaneh Esmaili
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Government Policy ◽  
Local Stability ◽  
Equilibrium Points ◽  
Compartmental Models ◽  
Effective Strategy ◽  
Local Stability Analysis ◽  
The Government

In this paper, we developed a model that suggests the use of robots in identifying COVID-19-positive patients and which studied the effectiveness of the government policy of prohibiting migration of individuals into their countries especially from those countries that were known to have COVID-19 epidemic. Two compartmental models consisting of two equations each were constructed. The models studied the use of robots for the identification of COVID-19-positive patients. The effect of migration ban strategy was also studied. Four biologically meaningful equilibrium points were found. Their local stability analysis was also carried out. Numerical simulations were carried out, and the most effective strategy to curtail the spread of the disease was shown.

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 Stability Analysis of the Corruption Free Equilibrium of the Mathematical Model of Corruption in Nigeria

2020 ◽  
Vol 8 (2) ◽  
pp. 61-68
Author(s):  
Victor Akinsola ◽  
ADEYEMI BINUYO
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Equilibrium State ◽  
Equilibrium Points ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Operator Technique ◽  
Eigen Values ◽  
The Stability ◽  
The Mathematical Model

In this paper, a mathematical model of the transmission dynamics of corruption among populace is analyzed. The corruption free equilibrium state, characteristic equation and Eigen values of the corruption model were obtained. The basic reproductive number of the corruption model was also determined using the next generation operator technique at the corruption free equilibrium points. The condition for the stability of the corruption free equilibrium state was determined. The local stability analysis of the mathematical model of corruption was done and the results were presented and discussed accordingly. Recommendations were made from the results on measures to reduce the rate of corrupt practices among the populace.   

scholarly journals On the generalized fractional snap boundary problems via G-Caputo operators: existence and stability analysis

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammad Esmael Samei ◽  
Mohammed M. Matar ◽  
Sina Etemad ◽  
Shahram Rezapour
Keyword(s):  
Mathematical Model ◽  
Integral Equation ◽  
Fixed Point ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Boundary Problems ◽  
Existence And Stability ◽  
Existence Criterion ◽  
The Mathematical Model ◽  
Fixed Point Techniques

AbstractThis research is conducted for studying some qualitative specifications of solution to a generalized fractional structure of the standard snap boundary problem. We first rewrite the mathematical model of the extended fractional snap problem by means of the $\mathbb{G}$ G -operators. After finding its equivalent solution as a form of the integral equation, we establish the existence criterion of this reformulated model with respect to some known fixed point techniques. Then we analyze its stability and further investigate the inclusion version of the problem with the help of some special contractions. We present numerical simulations for solutions of several examples regarding the fractional $\mathbb{G}$ G -snap system in different structures including the Caputo, Caputo–Hadamard, and Katugampola operators of different orders.

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.

Systems Actuated by Shape Memory Alloys: Identification and Modeling

2021 ◽  
Vol 1 (2) ◽  
pp. 12-20
Author(s):  
Najmeh Keshtkar ◽  
Johannes Mersch ◽  
Konrad Katzer ◽  
Felix Lohse ◽  
Lars Natkowski ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Constitutive Model ◽  
Shape Memory Alloys ◽  
Numerical Simulations ◽  
Shape Memory ◽  
Transfer Equation ◽  
Mechanical Parameters ◽  
Heat Transfer Equation ◽  
The Mathematical Model

This paper presents the identification of thermal and mechanical parameters of shape memory alloys by using the heat transfer equation and a constitutive model. The identified parameters are then used to describe the mathematical model of a fiber-elastomer composite embedded with shape memory alloys. To verify the validity of the obtained equations, numerical simulations of the SMA temperature and composite bending are carried out and compared with the experimental results.

scholarly journals Motion Simulation for Triangular-Shaped Autonomous Underwater Vehicle (TAUV) with Controllable Rudder

2021 ◽  
Vol 2107 (1) ◽  
pp. 012046
Author(s):  
I Y Amran ◽  
K Isa
Keyword(s):  
Mathematical Model ◽  
Autonomous Underwater Vehicle ◽  
Research Work ◽  
Underwater Vehicle ◽  
Open Loop ◽  
Vehicle Speed ◽  
Motion Simulation ◽  
Loop Control ◽  
Angular Velocities ◽  
The Mathematical Model

Abstract The dynamic model and motion simulation for a Triangular-Shaped Autonomous Underwater Vehicle (TAUV) with independently controlled rudders are described in this paper. The TAUV is designed for biofouling cleaning in aquaculture cage fishnet. It is buoyant underwater and moves by controlling two thrusters. Hence, in this research work, the authors designed a TAUV that is propelled by two thrusters and maneuvered by using an independently controllable rudder. This paper discussed the development of a mathematical model for the TAUV and its dynamic characteristics. The mathematical model was simulated by using Matlab and Simulink to analyze the TAUV’s motion based on open-loop control of different rudder angles. The position, linear and angular velocities, angle of attack, and underwater vehicle speed are all demonstrated in the findings.

Walking Stability Analysis of Multi-Legged Crablike Robot over Slope

2013 ◽  
Vol 572 ◽  
pp. 636-639
Author(s):  
Xi Chen ◽  
Gang Wang
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Stability Criterion ◽  
Stability Margin ◽  
Static Stability ◽  
Matlab Simulation ◽  
And Performance ◽  
The Stability ◽  
The Mathematical Model ◽  
The Relationship

This paper deals with the walking stability analysis of a multi-legged crablike robot over slope using normalized energy stability margin (NESM) method in order to develop a common stabilization description method and achieve robust locomotion for the robot over rough terrains. The robot is simplified with its static stability being described by NESM. The mathematical model of static stability margin is built so as to carry out the simulation of walking stability over slope for the crablike robot that walks in double tetrapod gait. As a consequence, the relationship between stability margin and the height of the robots centroid, as well as its inclination relative to the ground is calculated by the stability criterion. The success and performance of the stability criterion proposed is verified through MATLAB simulation and real-world experiments using multi-legged crablike robot.

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 of Car Trailer Systems With Special Regard to Trailer Design

1974 ◽  
Vol 96 (2) ◽  
pp. 236-243 ◽  
Author(s):  
R. L. Collins ◽  
J. P. Wong
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Moment Of Inertia ◽  
Tire Pressure ◽  
Special Regard ◽  
Articulated Vehicle ◽  
The Mathematical Model ◽  
Solution Techniques

A linear stability analysis is performed on the articulated vehicle to provide information on the effects that various trailer parameters and variations in tire pressure have on the inherent towing stability of the typical car-trailer combination. Although certain portions of the mathematical model and solution techniques are similar to some previous efforts, the results are generalized to include a much larger class of vehicles than previously presented. The results indicate that hitch loading, trailer length, mass and moment of inertia, and fairly small variations in the car tire pressures can influence trailer towing stability.

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