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 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 A Mathematical Model for the Eradication of Anopheles Mosquito and Elimination of Malaria

2020 ◽  
pp. 1-14
Author(s):  
Atanyi Yusuf Emmanuel ◽  
Abam Ayeni Omini
Keyword(s):  
Mathematical Model ◽  
Life Cycle ◽  
Steady State ◽  
Stability Analysis ◽  
Equilibrium State ◽  
Numerical Solutions ◽  
Equilibrium Points ◽  
Anopheles Mosquito ◽  
Model Parameters ◽  
The Stability

A mathematical model to eliminate malaria by breaking the life cycle of anopheles mosquito using copepods at larva stage and tadpoles at pupa stage was derived aimed at eradicating anopheles pupa mosquito by introduction of natural enemies “copepods and tadpoles” (an organism that eats up mosquito at larva and pupa stage respectively). The model equations were derived using the model parameters and variables. The stability analysis of the free equilibrium states was analyzed using equilibrium points of Beltrami and Diekmann’s conditions for stability analysis of steady state. We observed that the model free equilibrium state is stable which implies that the equilibrium point or steady state is stable and the stability of the model means, there will not be anopheles adult mosquito in our society for malaria transmission. The ideas of Beltrami’s and Diekmann conditions revealed that the determinant and trace of the Jacobian matrix were greater than zero and less than zero respectively implying that the model disease free equilibrium state is stable. Hence, the number of larva that transforms to pupa is almost zero while the pupa that develop to adult is zero meaning the life-cycle is broken at the larva and pupa stages with the introduction of natural enemy. Maple was used for the symbolic and numerical solutions.

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.

Modeling and Stability Analysis of Hydraulic System for Wave Simulation

2013 ◽  
Vol 291-294 ◽  
pp. 1934-1939
Author(s):  
Jian Jun Peng ◽  
Yan Jun Liu ◽  
Yu Li ◽  
Ji Bin Liu
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Mathematical Models ◽  
Hydraulic System ◽  
Simulation System ◽  
Displacement Sensor ◽  
Schematic Diagram ◽  
Wave Simulation ◽  
The Stability ◽  
The Mathematical Model

This thesis put forward a hydraulic wave simulation system based on valve-controlled cylinder hydraulic system, which simulated wave movement on the land. The mathematical model of valve-controlled symmetric cylinder was deduced and the mathematical models of servo valve, displacement sensor and servo amplifier were established according to the schematic diagram of the hydraulic system designed, on the basis of which the mathematical model of hydraulic wave simulation system was obtained. Then the stability of the system was analyzed. The results indicated that the system was reliable.

scholarly journals Mathematical Modelling of the Addiction of Drug Substances among Students in Tertiary Institutions in Nigeria

2021 ◽  
Vol 2 (9) ◽  
pp. 851-856
Author(s):  
Adeyemi O Binuyo ◽  
Oludare Temitope Osuntokun
Keyword(s):  
Mathematical Model ◽  
Drug Addiction ◽  
Drug Users ◽  
Recruitment Rate ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Tertiary Institutions ◽  
Drug Substances ◽  
The Mathematical Model ◽  
Drug Free

In this paper, we formulated a mathematical model for the addiction of drug substances among students in the tertiary institutions in Nigeria. The model explains the dynamics of the use and the addiction of certain substances that are perceived as mood changing by the students in the tertiary institutions in Nigeria. The drug model will be analysed qualitatively. The basic reproductive number which is the drug addiction number of the mathematical model was determined using the next generation procedure. It was found that the drug free equilibrium point was found to be locally asymptotically stable whenever the drug addiction number is less than one and unstable otherwise. The analysis revealed that an increase in the recruitment rate of students and the rate at which the students return to the use and addiction of drugs would cause an increase in the drug addiction number. There are impacts on interaction among non-drug users and drug users in the system with time. An increase in the contact or limitation rate increases the population of drug users. It is hereby recommended that; government should intensify efforts to reduce or stop the spread of selling and purchasing of the drug substances through government policies among the students in the tertiary institutions in Nigeria.

scholarly journals Practical Computational Approach for the Stability Analysis of Fuzzy Model-Based Predictive Control of Substrate and Biomass in Activated Sludge Processes

Processes ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 531
Author(s):  
Pedro M. Vallejo LLamas ◽  
Pastora Vega
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Activated Sludge ◽  
Predictive Control ◽  
Closed Loop ◽  
Complex Dynamics ◽  
Linear Time ◽  
Fuzzy Model ◽  
The Stability ◽  
The Mathematical Model

This paper presents a procedure for the closed-loop stability analysis of a certain variant of the strategy called Fuzzy Model-Based Predictive Control (FMBPC), with a model of the Takagi-Sugeno type, applied to the wastewater treatment process known as the Activated Sludge Process (ASP), with the aim of simultaneously controlling the substrate concentration in the effluent (one of the main variables that should be limited according to environmental legislations) and the biomass concentration in the reactor. This case study was chosen both for its environmental relevance and for special process characteristics that are of great interest in the field of nonlinear control, such as strong nonlinearity, multivariable nature, and its complex dynamics, a consequence of its biological nature. The stability analysis, both of fuzzy systems (FS) and the very diverse existing strategies of nonlinear predictive control (NLMPC), is in general a mathematically laborious task and difficult to generalize, especially for processes with complex dynamics. To try to minimize these difficulties, in this article, the focus was placed on the mathematical simplification of the problem, both with regard to the mathematical model of the process and the stability analysis procedures. Regarding the mathematical model, a state-space model of discrete linear time-varying (DLTV), equivalent to the starting fuzzy model (previously identified), was chosen as the base model. Furthermore, in a later step, the DLTV model was approximated to a local model of type discrete linear time-invariant (DLTI). As regards the stability analysis itself, a computational method was developed that greatly simplified this difficult task (in a local environment of an operating point), compared to other existing methods in the literature. The use of the proposed method provides useful conclusions for the closed-loop stability analysis of the considered FMBPC strategy, applied to an ASP process; at the same time, the possibility that the method may be useful in a more general way, for similar fuzzy and predictive strategies, and for other complex processes, was observed.

scholarly journals Analisis Kestabilan Model Penyebaran Penyakit Toxoplasmosis pada Populasi Manusia dan Kucing

2019 ◽  
Vol 1 (3) ◽  
pp. 37-46
Author(s):  
Febrina Tedjo Utami ◽  
Retno Wahyu Dewanti ◽  
Subchan Subchan
Keyword(s):  
Stability Analysis ◽  
Epidemic Model ◽  
Human Population ◽  
Compartment Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Final Project ◽  
Spread Model ◽  
The Stability ◽  
Models Of Disease

This final project studies the contruction and analyzes the stability of Toxoplasmosis epidemic model. Using a compartment model, Toxoplasmosis epidemic model classified into human population and cat population. The human population is divided into three subpopulations such as susceptible human, infected human, and recovered human. The cat population is divided into two subpopulations such as susceptible cat and infected cat. Stability analysis performed on two equilibrium models of disease free equilibrium and endemic equilibrium point. Stability analysis result showed that cat infected spread, natural birthd rate of cat population, natural death rate of cat population, and the probability of cat natality in the form of basic reproductive number (R0) is value that affect human population and cat population changed spread. When R0<1 the population will be free of disease and when R0>1 the disease will be spread. Model of the simulation is numerically analyzed by Runge Kutta 4th Order methods.

scholarly journals An SEIRS Epidemic Model with Immigration and Vertical Transmission

2020 ◽  
pp. 48-53
Author(s):  
Ruksana Shaikh ◽  
Pradeep Porwal ◽  
V. K. Gupta
Keyword(s):  
Vertical Transmission ◽  
Epidemic Model ◽  
Equilibrium Points ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Asymptotically Stable ◽  
Seirs Epidemic Model ◽  
Model Equations ◽  
The Stability ◽  
Disease Free

The study indicates that we should improve the model by introducing the immigration rate in the model to control the spread of disease. An SEIRS epidemic model with Immigration and Vertical Transmission and analyzed the steady state and stability of the equilibrium points. The model equations were solved analytically. The stability of the both equilibrium are proved by Routh-Hurwitz criteria. We see that if the basic reproductive number R0<1 then the disease free equilibrium is locally asymptotically stable and if R0<1 the endemic equilibrium will be locally asymptotically stable.

scholarly journals Stability Analysis of Divorce Dynamics Models

2020 ◽  
Vol 17 (2) ◽  
pp. 267-279
Author(s):  
Syamsir Muaraf ◽  
Syamsuddin Toaha ◽  
Kasbawati Kasbawati
Keyword(s):  
Stability Analysis ◽  
Local Stability ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Existence And Stability ◽  
Next Generation Matrix ◽  
The Stability ◽  
Dynamics Models ◽  
The Mathematical Model

This article examines the mathematical model of divorce. This model consists of four population classes, namely the Married class (M), the population class who experiences separation of separated beds (S), the population class who is divorced by Divorce (D), and the population class who experiences depression or stress due to divorce Hardship (H). This study focuses on the stability analysis of divorce-free and endemic equilibrium points. Local stability was analyzed using linearization and eigenvalues ​​methods. In addition, the basic reproduction number  is provided via the next generation matrix method. The existence and stability of the equilibrium point are determined from . The results showed that the rate of interaction between population M and populations other than H is very influential on efforts to minimize divorce. Divorce can be minimized when the transmission rate is reduced to . Reducing the transmission rate and increasing the rate of transfer from split bed class to married class can turn divorce endemic cases into non-endemic cases. A numerical simulation is given to confirm the analysis results.

scholarly journals Stability analysis of fractional order SEIR model for malaria disease in Khyber Pakhtunkhwa

2021 ◽  
Vol 54 (1) ◽  
pp. 326-334
Author(s):  
Noor Badshah ◽  
Haji Akbar
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Next Generation ◽  
Seir Model ◽  
Khyber Pakhtunkhwa

Abstract We discussed stability analysis of susceptible-exposed-infectious-removed (SEIR) model for malaria disease through fractional order and check that malaria is epidemic or endemic in Khyber Pakhtunkhwa (Pakistan). We show that the model has two types of equilibrium points and check their stability through Routh-Hurwitz criterion. We find basic reproductive number using next-generation method. Finally, numerical simulations are also presented.

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