scholarly journals Stability Analysis of a Dynamical Model for Malware Propagation with Generic Nonlinear Countermeasure and Infection Probabilities

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xulong Zhang ◽  
Xiaoxia Song
Keyword(s):  
Stability Analysis ◽  
Theoretical Analysis ◽  
Dynamical Model ◽  
Practical Significance ◽  
Asymptotically Stable ◽  
Unique Equilibrium ◽  
Globally Asymptotically Stable ◽  
Effective Strategies ◽  
Malware Propagation ◽  
Theoretical Results

The dissemination of countermeasures is widely recognized as one of the most effective strategies of inhibiting malware propagation, and the study of general countermeasure and infection has an important and practical significance. On this point, a dynamical model incorporating generic nonlinear countermeasure and infection probabilities is proposed. Theoretical analysis shows that the model has a unique equilibrium which is globally asymptotically stable. Accordingly, a real network based on the model assumptions is constructed, and some numerical simulations are conducted on it. Simulations not only illustrate theoretical results but also demonstrate the reasonability of general countermeasure and infection.

scholarly journals Modelling and Analysis of Propagation Behavior of Computer Viruses with Nonlinear Countermeasure Probability and Infected Removable Storage Media

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xulong Zhang ◽  
Yong Li
Keyword(s):  
Theoretical Analysis ◽  
Numerical Experiments ◽  
Computer Virus ◽  
Dynamical Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Computer Viruses ◽  
Viral Spread ◽  
Propagation Behavior ◽  
Storage Media

The dissemination of countermeasures is diffusely recognized as one of the most valid strategies of containing computer virus diffusion. In order to better understand the impacts of countermeasure and removable storage media on viral spread, this paper addresses a dynamical model, which incorporates nonlinear countermeasure probability and infected removable storage media. Theoretical analysis reveals that the unique (viral) equilibrium of the model is globally asymptotically stable. This main result is also illustrated by some numerical experiments. Additionally, the numerical experiments of different countermeasure probabilities are conducted.

NUMERICAL AND STABILITY ANALYSIS OF THE TRANSMISSION DYNAMICS OF SVIR EPIDEMIC MODEL WITH STANDARD INCIDENCE RATE

2019 ◽  
Vol 4 (2) ◽  
pp. 349 ◽  
Author(s):  
Oluwatayo Michael Ogunmiloro ◽  
Fatima Ohunene Abedo ◽  
Hammed Kareem
Keyword(s):  
Reproduction Number ◽  
Disease Spread ◽  
Asymptotically Stable ◽  
Equilibrium Solutions ◽  
Transform Method ◽  
Globally Asymptotically Stable ◽  
Differential Transform ◽  
Mathematical Techniques ◽  
Fourth Order Method ◽  
Theoretical Results

In this article, a Susceptible – Vaccinated – Infected – Recovered (SVIR) model is formulated and analysed using comprehensive mathematical techniques. The vaccination class is primarily considered as means of controlling the disease spread. The basic reproduction number (Ro) of the model is obtained, where it was shown that if Ro<1, at the model equilibrium solutions when infection is present and absent, the infection- free equilibrium is both locally and globally asymptotically stable. Also, if Ro>1, the endemic equilibrium solution is locally asymptotically stable. Furthermore, the analytical solution of the model was carried out using the Differential Transform Method (DTM) and Runge - Kutta fourth-order method. Numerical simulations were carried out to validate the theoretical results. 

Global Dynamics of a Holling-II Amensalism System with Nonlinear Growth Rate and Allee Effect on the First Species

2021 ◽  
Vol 31 (03) ◽  
pp. 2150050
Author(s):  
Demou Luo ◽  
Qiru Wang
Keyword(s):  
Growth Rate ◽  
Allee Effect ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Nonlinear Growth ◽  
Trivial Equilibrium ◽  
Existence And Stability ◽  
Stable Equilibria ◽  
Theoretical Results

Of concern is the global dynamics of a two-species Holling-II amensalism system with nonlinear growth rate. The existence and stability of trivial equilibrium, semi-trivial equilibria, interior equilibria and infinite singularity are studied. Under different parameters, there exist two stable equilibria which means that this model is not always globally asymptotically stable. Together with the existence of all possible equilibria and their stability, saddle connection and close orbits, we derive some conditions for transcritical bifurcation and saddle-node bifurcation. Furthermore, the global dynamics of the model is performed. Next, we incorporate Allee effect on the first species and offer a new analysis of equilibria and bifurcation discussion of the model. Finally, several numerical examples are performed to verify our theoretical results.

scholarly journals Adaptive 3D Distance-Based Formation Control of Multiagent Systems with Unknown Leader Velocity and Coplanar Initial Positions

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Xuejing Lan ◽  
Wenbiao Xu ◽  
Yun-Shan Wei
Keyword(s):  
Theoretical Analysis ◽  
Multiagent Systems ◽  
Relative Position ◽  
Formation Control ◽  
Control Law ◽  
Asymptotically Stable ◽  
Coordinate Systems ◽  
Lyapunov Theorem ◽  
Globally Asymptotically Stable ◽  
3 Dimensional

This paper considers the distributed 3-dimensional (3D) distance-based formation control of multiagent systems, where the agents are connected based on an acyclic minimally structural persistent (AMSP) graph. A parameter is designed according to the desired formation shape and is used to solve the problem that there are two formation shapes satisfying the same distance requirements. The unknown moving velocity of the leader agent is estimated adaptively by the followers requiring only the relative position measurements with respect to their local coordinate systems. In addition, the proposed formation controller provides a new way for the agent to leave the initial coplanar location. The 3D formation control law is globally asymptotically stable and has been demonstrated based on the Lyapunov theorem. Finally, two numerical simulations are presented to support the theoretical analysis.

scholarly journals A Delay Differential Equation Model of HIV Infection, with Therapy and CTL Response

2014 ◽  
Vol 9 ◽  
pp. 53-68 ◽  
Author(s):  
B. El Boukari ◽  
N. Yousfi
Keyword(s):  
Reproduction Number ◽  
Equation Model ◽  
Asymptotically Stable ◽  
Differential Equation Model ◽  
Globally Asymptotically Stable ◽  
Intracellular Delay ◽  
Immunodeficiency Virus ◽  
Delay Differential ◽  
Theoretical Results ◽  
Disease Free

In this work we investigate a new mathematical model that describes the interactions betweenCD4+ T cells, human immunodeficiency virus (HIV), immune response and therapy with two drugs.Also an intracellular delay is incorporated into the model to express the lag between the time thevirus contacts a target cell and the time the cell becomes actively infected. The model dynamicsis completely defined by the basic reproduction number R0. If R0 ≤ 1 the disease-free equilibriumis globally asymptotically stable, and if R0 > 1, two endemic steady states exist, and their localstability depends on value of R0. We show that the intracellular delay affects on value of R0 becausea larger intracellular delay can reduce the value of R0 to below one. Finally, numerical simulationsare presented to illustrate our theoretical results.

Stability analysis and optimal control of an epidemic model with vaccination

2015 ◽  
Vol 08 (03) ◽  
pp. 1550030 ◽  
Author(s):  
Swarnali Sharma ◽  
G. P. Samanta
Keyword(s):  
Optimal Control ◽  
Stability Analysis ◽  
Epidemic Model ◽  
Asymptotically Stable ◽  
Control Pair ◽  
Globally Asymptotically Stable ◽  
The Stability ◽  
The Cost ◽  
Objective Functional ◽  
Disease Free

In this paper, we have developed a compartment of epidemic model with vaccination. We have divided the total population into five classes, namely susceptible, exposed, infective, infective in treatment and recovered class. We have discussed about basic properties of the system and found the basic reproduction number (R0) of the system. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at disease-free equilibrium E0when R0< 1. When R0> 1 endemic equilibrium E1exists and the system becomes locally asymptotically stable at E1under some conditions. We have also discussed the epidemic model with two controls, vaccination control and treatment control. An objective functional is considered which is based on a combination of minimizing the number of exposed and infective individuals and the cost of the vaccines and drugs dose. Then an optimal control pair is obtained which minimizes the objective functional. Our numerical findings are illustrated through computer simulations using MATLAB. Epidemiological implications of our analytical findings are addressed critically.

scholarly journals Modeling Transmission of Tuberculosis with MDR and Undetected Cases

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Yongqi Liu ◽  
Zhendong Sun ◽  
Guiquan Sun ◽  
Qiu Zhong ◽  
Li Jiang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Control Strategies ◽  
Multidrug Resistant ◽  
Vital Role ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Tb Control ◽  
Disease Free

This paper presents a novel mathematical model with multidrug-resistant (MDR) and undetected TB cases. The theoretical analysis indicates that the disease-free equilibrium is globally asymptotically stable ifR0<1; otherwise, the system may exist a locally asymptotically stable endemic equilibrium. The model is also used to simulate and predict TB epidemic in Guangdong. The results imply that our model is in agreement with actual data and the undetected rate plays vital role in the TB trend. Our model also implies that TB cannot be eradicated from population if it continues to implement current TB control strategies.

scholarly journals Stability Analysis of a Vector-Borne Disease with Variable Human Population

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Muhammad Ozair ◽  
Abid Ali Lashari ◽  
Il Hyo Jung ◽  
Young Il Seo ◽  
Byul Nim Kim
Keyword(s):  
Mathematical Model ◽  
Human Population ◽  
Feasible Region ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Vector Borne Disease ◽  
Vector Borne ◽  
Theoretical Results ◽  
Disease Free ◽  
Varying Population

A mathematical model of a vector-borne disease involving variable human population is analyzed. The varying population size includes a term for disease-related deaths. Equilibria and stability are determined for the system of ordinary differential equations. IfR0≤1, the disease-“free” equilibrium is globally asymptotically stable and the disease always dies out. IfR0>1, a unique “endemic” equilibrium is globally asymptotically stable in the interior of feasible region and the disease persists at the “endemic” level. Our theoretical results are sustained by numerical simulations.

scholarly journals Dynamics of the Stochastic Belousov-Zhabotinskii Chemical Reaction Model

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 663
Author(s):  
Ying Yang ◽  
Daqing Jiang ◽  
Donal O’Regan ◽  
Ahmed Alsaedi
Keyword(s):  
Chemical Reaction ◽  
Existence And Uniqueness ◽  
Reaction Model ◽  
Equation Model ◽  
Asymptotically Stable ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
Globally Asymptotically Stable ◽  
Chemical Reaction Model ◽  
Theoretical Results

In this paper, we discuss the dynamic behavior of the stochastic Belousov-Zhabotinskii chemical reaction model. First, the existence and uniqueness of the stochastic model’s positive solution is proved. Then we show the stochastic Belousov-Zhabotinskii system has ergodicity and a stationary distribution. Finally, we present some simulations to illustrate our theoretical results. We note that the unique equilibrium of the original ordinary differential equation model is globally asymptotically stable under appropriate conditions of the parameter value f, while the stochastic model is ergodic regardless of the value of f.

scholarly journals Global Dynamics of a Discrete-Time MERS-Cov Model

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 563
Author(s):  
Mahmoud H. DarAssi ◽  
Mohammad A. Safi ◽  
Morad Ahmad
Keyword(s):  
Discrete Time ◽  
Global Attractivity ◽  
Endemic Equilibrium ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Proposed Model ◽  
Threshold Conditions ◽  
Theoretical Results ◽  
Disease Free

In this paper, we have investigated the global dynamics of a discrete-time middle east respiratory syndrome (MERS-Cov) model. The proposed discrete model was analyzed and the threshold conditions for the global attractivity of the disease-free equilibrium (DFE) and the endemic equilibrium are established. We proved that the DFE is globally asymptotically stable when R0≤1. Whenever R˜0>1, the proposed model has a unique endemic equilibrium that is globally asymptotically stable. The theoretical results are illustrated by a numerical simulation.

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