Equilibrium Point Of Model Research Articles

Model Predator-Prey Leslie-Gower dengan Fungsi Respon Sokol-Howell dan Perilaku Anti Predator

This study discusses the Leslie-Gower predator-prey model with the Sokol-Howell response function and anti-predator behavior. It is assumed that prey has anti-predator behavior that aims to reduce the risk of predation and not as an attempt by prey to find food. This study aims to formulate a Leslie-Gower predator-prey model with the Sokol-Howell response function and anti-predator behavior, analyze the model's equilibrium point and model interpretation. Stability analysis was carried out using the linearization method. The type of stability is determined based on the characteristic eigenvalues ​​obtained using Routh-Hurwitz criteria. The results of the analysis of the equilibrium point show that prey populations will exist and predators will become extinct if the anti-predator coefficient is greater than the intrinsic growth coefficient of predators, while prey and predator populations will always exist if the intrinsic growth coefficient of predators is greater than the anti-predator coefficient and fulfills other conditions required. Based on the numerical simulations performed, the interpretation is that an enlarged anti-predator coefficient increases the number of prey populations until they approach the carrying capacity, while predator populations decrease significantly and over time experience extinction.

Leader‐following consensus and qualitative analysis of a new multi‐agent‐based epidemic model

AbstractThis paper addresses an investigation into a leader‐following consensus problem in a novel multi‐agent‐based SIS (Susceptible‐Infected‐Susceptible) epidemic model. As infectious diseases are easily spread through travel, the model considers each agent to represent a city in an infected country, interacting with neighbouring cities towards achieving disease eradication through consensus. To make the model more realistic, the Effect Terms (ETs) arising from the effects of agent states on each other are also considered. The differential equations' positivity and existence of solutions are examined, and the proposed model's equilibrium points are obtained, with stability analysed using new local and global basic reproduction numbers defined in this study. Additionally, a leader‐following consensus control for the multi‐agent‐based system is proposed to drive each agent to follow a virtual leader agent. Finally, numerical simulations are included to validate the theoretical findings corresponding to the proposed scheme.

A fractional order vaccination model for COVID-19 incorporating environmental transmission: a case study using Nigerian data

In this work, a fractional-order vaccination model for the novel Coronavirus 2019 (COVID-19) incorporating environmental transmission is considered and analyzed using tools of fractional calculus. The Laplace transform technique and the fixed point theorem lay out the model solutions' existence and uniqueness. The solutions' positivity and boundedness are also demonstrated. Additionally, the stability of the model's equilibrium points is discussed using the fractional-order system stability theory. The model is fitted using the data sets for the Pfizer vaccination program in Nigeria from April 1, 2021, to June 10, 2021. In conclusion, simulation results for various fractional parameter values are presented. It has been observed that increasing fractional-order values has distinct effects on the various model compartments, for R0 < 1 and R0 > 1, respectively.

The dynamics of a duopoly Stackelberg game with marginal costs among heterogeneous players.

One of the famous economic models in game theory is the duopoly Stackelberg model, in which a leader and a follower firm manufacture a single product in the market. Their goal is to obtain the maximum profit while competing with each other. The desired dynamics for a firm in a market is the convergence to its Nash equilibrium, but the dynamics of real-world markets are not always steady and can result in unpredictable market changes that exhibit chaotic behaviors. On the other hand, to approach reality more, the two firms in the market can be considered heterogeneous. The leader firm is bounded rationale, and the follower firm is adaptable. Modifying the cost function that affects the firms' profit by adding the marginal cost term is another step toward reality. We propose a Stackelberg model with heterogeneous players and marginal costs, which exhibits chaotic behavior. This model's equilibrium points, including the Nash equilibrium, are calculated by the backward induction method, and their stability analyses are obtained. The influence of changing each model parameter on the consequent dynamics is investigated through one-dimensional and two-dimensional bifurcation diagrams, Lyapunov exponents spectra, and Kaplan-Yorke dimension. Eventually, using a combination of state feedback and parameter adjustment methods, the chaotic solutions of the model are successfully tamed, and the model converges to its Nash equilibrium.

Modeling and analysis of monkeypox disease using fractional derivatives

The frequency of monkeypox outbreaks and the extent of the projected outbreaks in human populations have both steadily increased. This paper proposes Atangana-Baleanu fractional-order derivatives define in Caputo sense to investigate the kinetics of Monkeypox transmission in Ghana. We determine the stability of the recommended model's equilibrium points and basic reproduction number. The solution's existence and originality, as well as the model's Hyers-Ullam stability, are proven. The models basic reproduction number was found to be R0 = 0.1940. The numerical simulation showed the fractional operator had an influence on the various compartments of the model. The dynamics of the disease in the community were shown to be influenced by fractional-order derivatives, and infections were eradicated within the first five (5) days when π = 0.2.

ANALISIS KESTABILAN MODEL LESLIE-GOWER DENGAN PENGARUH WAKTU TUNDA DAN PEMANENAN PROPORSIONAL

The main purpose of this research is to study the Leslie-Gower model and the response of the Holling type II with time delay and proportional harvesting. The method used in the completion of the model is qualitative, namely by analyzing the stability of the model's equilibrium point. The Leslie-Gower model and Holling type II response with delay time and proportional harvesting have four equilibrium points. There is one point of unstable equilibrium and one point of equilibrium that is stable. Meanwhile, for the other two equilibrium points, it depends on the value of the parameters taken. The delay time resulted in oscillations in the model. The greater the delay time value used, the greater the inequality in oscillations that occur in the system. This means the model will take longer to stabilize.

Evaluation of the Number of Visits to Chinese Medical Institutions Using a Logistic Differential Equation Model

In this study, we established a two-dimensional logistic differential equation model to study the number of visits in Chinese PHCIs and hospitals based on the behavior of patients. We determine the model's equilibrium points and analyze their stability and then use China medical services data to fit the unknown parameters of the model. Finally, the sensitivity of model parameters is evaluated to determine the parameters that are susceptible to influence the system. The results indicate that the system corresponds to the zero-equilibrium point, the boundary equilibrium point, and the positive equilibrium point under different parameter conditions. We found that, in order to substantially increase visits to PHCIs, efforts should be made to improve PHCI comprehensive capacity and maximum service capacity.

Stability Analysis of SEIL Tuberculosis Epidemic Model with Logistic Growth in Susceptible Compartment

This article discusses modifications to the SEIL model that involve logistical growth. This model is used to describe the dynamics of the spread of tuberculosis disease in the population. The existence of the model's equilibrium points and its local stability depends on the basic reproduction number. If the basic reproduction number is less than unity, then there is one equilibrium point that is locally asymptotically stable. The equilibrium point is a disease-free equilibrium point. If the basic reproduction number ranges from one to three, then there are two equilibrium points. The two equilibrium points are disease-free equilibrium and endemic equilibrium points. Furthermore, for this case, the endemic equilibrium point is locally asymptotically stable.

Mathematics Model of Diabetes Mellitus Illness without Genetic Factors with Treatment

Diabetes Mellitus is a metabolic disorder characterized by an increase in glucose levels in the blood (hyperglycemia), which causes various chronic complications due to abnormalities in insulin secretion. Diabetes Mellitus is known as the Mother of Disease because it is the mother of various other diseases such as hypertension, heart disease, stroke and blindness. In this paper, what would be studied was a mathematical model of Diabetes Mellitus without genetic factors with treatment, the model used for the approach in this case was in the form of SEIIT. The analysis includes determining the model's equilibrium point, determining the basic reproduction number (R0) and analyzing the stability around the equilibrium point. Furthermore, numerical simulation using MAPLE was given based on the values of the related parameters in the mathematical model that describes the conditions in each subpopulation class.

Stability analysis of the hiv model through incommensurate fractional-order nonlinear system.

In this study, it is employed a new model of HIV infection in the form of incommensurate fractional differential equations systems involving the Caputo fractional derivative. Existence of the model's equilibrium points has been investigated. According to some special cases of the derivative-orders in the proposed model, the asymptotic stability of the infection-free equilibrium and endemic equilibrium has been proved under certain conditions. These stability conditions related to the derivative-orders depend on not only the basic reproduction rate frequently emphasized in the literature but also the newly obtained conditions in this study. Qualitative analysis results were complemented by numerical simulations in Matlab, illustrating the obtained stability result.

Study on the stability of fractional order Ebola virus model

No AccessStudy on the stability of fractional order Ebola virus modelChangcheng Wei and Juanyan FangChangcheng WeiDepartment of Mathematics and Computer Science, Tongling University, Tongling, Anhui, China and Juanyan FangDepartment of Mathematics and Computer Science, Tongling University, Tongling, Anhui, ChinaPublished Online:July 12, 2018pp 298-307https://doi.org/10.1504/IJCSM.2018.093165PDF ToolsAdd to FavouritesDownload CitationsTrack Citations Share this article on social mediaShareShare onFacebookTwitterLinkedInReddit AboutAbstractThis paper attempts to study the dynamical behaviour of the fractional-order model of Ebola virus. Based on the basic reproduction number, the stability of this model's equilibrium points is analysed.Keywordsfractional-order, Ebola virus, stability, basic reproduction number Previous article FiguresReferencesRelatedDetails Volume 9Issue 32018 ISSN: 1752-5055eISSN: 1752-5063 HistoryPublished onlineJuly 12, 2018 Copyright © 2018 Inderscience Enterprises Ltd.Keywordsfractional-orderEbola virusstabilitybasic reproduction numberAuthors and AffiliationsChangcheng Wei1 Juanyan Fang2 1. Department of Mathematics and Computer Science, Tongling University, Tongling, Anhui, China2. Department of Mathematics and Computer Science, Tongling University, Tongling, Anhui, ChinaPDF download

Study on the stability of fractional order Ebola virus model

This paper attempts to study the dynamical behaviour of the fractional-order model of Ebola virus. Based on the basic reproduction number, the stability of this model's equilibrium points is analysed.

Effects of selection and mutation on epidemiology of X-linked genetic diseases

The epidemiology of X-linked recessive diseases, a class of genetic disorders, is modeled with a discrete-time, structured, non linear mathematical system. The model accounts for both de novo mutations (i.e., affected sibling born to unaffected parents) and selection (i.e., distinct fitness rates depending on individual's health conditions). Assuming that the population is constant over generations and relying on Lyapunov theory we found the domain of attraction of model's equilibrium point and studied the convergence properties of the degenerate equilibrium where only affected individuals survive. Examples of applications of the proposed model to two among the most common X-linked recessive diseases (namely the red and green color blindness and the Hemophilia A) are described.

Selection and mutation in X-linked recessive diseases epidemiological model.

To describe the epidemiology of X-linked recessive diseases we developed a discrete time, structured, non linear mathematical model. The model allows for de novo mutations (i.e. affected sibling born to unaffected parents) and selection (i.e., distinct fitness rates depending on individual's health conditions). Applying Lyapunov direct method we found the domain of attraction of model's equilibrium point and studied the convergence properties of the degenerate equilibrium where only affected individuals survive.

Robe's restricted three-body problem with drag

Robe's restricted three-body problem is investigated with regards to the effects of a linear drag force. In particular. the stability of the model's equilibrium points is studied in this respect. Two scenarios are envisaged: the one originally discussed by Robe himself and the one suggested by him and recently analyzed by the present authors, that assumes for the fluid body the structure of a Roche's ellipsoid.