An uncertain SEIR rumor model

2021 ◽  
pp. 1-14
Author(s):  
Qianqian Liu ◽  
Gang Shi ◽  
Yuhong Sheng
Keyword(s):  
Deterministic Model ◽  
Existence And Uniqueness Theorem ◽  
Uncertain Process ◽  
Propagation Process ◽  
Model Driven ◽  
Rumor Propagation ◽  
Proposed Model ◽  
Simulation Results ◽  
The Stability ◽  
Theoretical Results

In this paper, an uncertain SEIR rumor model driven by one uncertain process is formulated to investigate the influence of perturbation in the transmission of rumor. Firstly, the deduced process of the uncertain SEIR rumor model is presented. Then, we proposed the existence and uniqueness theorem for the solution of the model. Moreover, the study of the stability of the uncertain SEIR rumor model was carried out, and then we came to the conclusion that the model stable in mean. In addition, computer algorithm and numerical simulation is used to verify the accuracy of the theoretical results. The simulation results show that the proposed model can explain the trend of rumor propagation correctly and describe the rumor propagation accurately. Finally, we have compared the propagation process of the uncertain rumor model and the deterministic model according to the numerical algorithm, and drew the conclusion that the model with uncertain perturbation fluctuates around the deterministic model.

An extended optimal velocity difference model in a cooperative driving system

2015 ◽  
Vol 26 (05) ◽  
pp. 1550054
Author(s):  
Jinliang Cao ◽  
Zhongke Shi ◽  
Jie Zhou
Keyword(s):  
Traffic Flow ◽  
Linear Stability Theory ◽  
Difference Model ◽  
Optimal Velocity ◽  
Driving System ◽  
Cooperative Driving ◽  
Proposed Model ◽  
De Vries ◽  
The Stability ◽  
Theoretical Results

An extended optimal velocity (OV) difference model is proposed in a cooperative driving system by considering multiple OV differences. The stability condition of the proposed model is obtained by applying the linear stability theory. The results show that the increase in number of cars that precede and their OV differences lead to the more stable traffic flow. The Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations are derived to describe the density waves in the stable, metastable and unstable regions, respectively. To verify these theoretical results, the numerical simulation is carried out. The theoretical and numerical results show that the stabilization of traffic flow is enhanced by considering multiple OV differences. The traffic jams can be suppressed by taking more information of cars ahead.

scholarly journals On the Stochastic Dynamics of a Social Epidemics Model

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Xun-Yang Wang ◽  
Peng-Zhan Zhang ◽  
Qing-Shan Yang
Keyword(s):  
Stochastic System ◽  
Stochastic Dynamics ◽  
Deterministic Model ◽  
Random Disturbance ◽  
Disturbance Intensity ◽  
The Stability ◽  
The Individual ◽  
Theoretical Results ◽  
Two Equilibria

Alcohol abuse is a major social problem, which has caused a lot of damages or hidden dangers to the individual and the society. In this paper, with random factors of alcoholism considered in mortality rate of compartment populations, we formulate a stochastic alcoholism model according to compartment theory of infectious disease. Based on this model, we investigate the long-term stochastic dynamics behaviors of two equilibria of the corresponding deterministic model and point out the effect of random disturbance on the stability of the system. We find that when R0≤1, we get the estimation between the trajectory of stochastic system and E0=(Π/μs,0,0,0) in the average in time with respect to the disturbance intensity, while when R0>1, stochastic system is ergodic and has the unique stationary distribution. Finally, we carry out numerical simulations to support the corresponding theoretical results.

scholarly journals Stability Analysis of Train Movement with Uncertain Factors

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
JingJing Ye ◽  
KePing Li ◽  
XueDong Jiang
Keyword(s):  
Relaxation Time ◽  
Stability Analysis ◽  
Fuzzy Theory ◽  
Traffic Model ◽  
Optimal Velocity ◽  
Car Following ◽  
Proposed Model ◽  
Car Following Model ◽  
Simulation Results ◽  
The Stability

We propose a new traffic model which is based on the traditional OV (optimal velocity) car-following model. Here, some realistic factors are regarded as uncertain quantity, such as the headway distance. Our aim is to analyze and discuss the stability of car-following model under the constraint of uncertain factors. Then, according to the principle of expected value in fuzzy theory, an improved OV traffic model is constructed. Simulation results show that our proposed model can avoid collisions effectively under uncertain environment, and its stability can also be improved. Moreover, we discuss its stability as some parameters change, such as the relaxation time.

scholarly journals An uncertain SIR rumor spreading model

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hang Sun ◽  
Yuhong Sheng ◽  
Qing Cui
Keyword(s):  
Differential Equation ◽  
Existence And Uniqueness ◽  
Transmission Mechanism ◽  
Existence And Uniqueness Theorem ◽  
Rumor Spreading ◽  
Model Driven ◽  
Spreading Model ◽  
Liu Process ◽  
Stochastic Sir ◽  
The Stability

AbstractIn this paper, an uncertain SIR (spreader, ignorant, stifler) rumor spreading model driven by one Liu process is formulated to investigate the influence of perturbation in the transmission mechanism of rumor spreading. The deduced process of the uncertain SIR rumor spreading model is presented. Then an existence and uniqueness theorem concerning the solution is proved. Moreover, the stability of uncertain SIR rumor spreading differential equation is proved. In addition, the influence of different parameters on rumor spreading is analyzed through numerical simulation. This paper also presents a paradox of stochastic SIR rumor spreading model.

scholarly journals Fractional SEIRP model for COVID-19 dynamics incorporatingsocial distancing and environment

2021 ◽  
Author(s):  
Saheed Ojo Akindeinde ◽  
E. Okyere ◽  
A. O. Adewumi ◽  
R. S. Lebelo ◽  
O. O. Fabelurin ◽  
...  
Keyword(s):  
Compartmental Model ◽  
Reproduction Number ◽  
Banach Fixed Point Theorem ◽  
The Novel ◽  
Disease Dynamics ◽  
Stability Criteria ◽  
Proposed Model ◽  
Uniqueness Of The Solution ◽  
The Stability ◽  
Theoretical Results

Abstract We propose a Caputo-based fractional compartmental model for the dynamics of the novel COVID-19 epidemic taking into consideration social distancing and the influence of the environment. Using basic concepts such as continuity and Banach fixed-point theorem, the existence and uniqueness of the solution to the proposed model were shown. Furthermore, we analyze the stability of the model in the context of Ulam-Hyers and generalized Ulam-Hyers stability criteria. The concept of next-generation matrices was used to compute the basic reproduction number $R_0,$ a number that determines the spread or otherwise of the disease into the general population. Numerical simulation of the disease dynamics was carried out using the fractional Adam-Bashforth-Moulton method to validate the obtained theoretical results.

THE RESEARCH ON STABILITY OF DIFFUSION AND COMPETITION BETWEEN ONLINE TOPICS

2010 ◽  
Vol 21 (12) ◽  
pp. 1517-1529 ◽  
Author(s):  
YAN-CHAO ZHANG ◽  
YUN LIU ◽  
FEI DING ◽  
XIA-MENG SI
Keyword(s):  
Stability Theory ◽  
Phase Trajectory ◽  
Information Communication ◽  
Consensus Formation ◽  
Network Information ◽  
Proposed Model ◽  
Simulation Results ◽  
The Stability ◽  
Development Tendency ◽  
Important Form

Online topics are becoming an important form of network information communication, and are playing a significant role in consensus formation. When several online topics are published at the same time, the spread of these topics will affect each other. We propose a model to study the development tendency of relationship between two different online topics. We make use of stability theory of differential equations to analyze the model, utilize the phase trajectory to analyze the stability of the equilibrium point, and finally simulate the model with actual data and varied parameters. Simulation results indicate that the proposed model is useful in understanding and explaining the phenomena presented in the diffusion of online topics, especially the interaction and competition among different topics.

scholarly journals Stability of the Discrete Stage–Structure Prey–Predator Model

2020 ◽  
Vol 55 (1) ◽  
Author(s):  
Rehab Noori Shalan ◽  
Shireen R. Jawad ◽  
Alaa Hussien Lafta
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Three Dimensional ◽  
Stage Structure ◽  
Prey Population ◽  
Topological Properties ◽  
Proposed Model ◽  
Predator Model ◽  
The Stability ◽  
Theoretical Results

This paper discusses the discrete stage–structure prey-predator model involved in the Beddington–DeAngelis type of functional response described by differential equation systems proposed as three-dimensional systems. Furthermore, the predators are divided into two types of populations, namely, mature and immature, along with the prey population. The stability of all possible fixed points is demonstrated by solving our proposed model analytically using the standard lemma and topological properties, which give all possible properties to each fixed point. In the same manner, we identify three fixed points, which are as follows: the origin fixed point, which means there are no species; the axial fixed point, which means the prey population increases logistically with the absence of a predator one (mature and immature populations); and the positive fixed point, which signifies the coexistence of all species. We show that the numerical simulations part is used not only to plot the time series of fixed values, but also, to find and illustrate the theoretical results.

scholarly journals Analisis Perilaku Model Multi Agen dengan Gangguan

CAUCHY ◽  
2013 ◽  
Vol 2 (4) ◽  
pp. 189
Author(s):  
Sentot Achmadi ◽  
Miswanto Miswanto
Keyword(s):  
Lyapunov Method ◽  
Bounded Function ◽  
Dimensional Space ◽  
Stable Model ◽  
Agent Model ◽  
Proposed Model ◽  
Multi Agent ◽  
Simulation Results ◽  
The Stability ◽  
Disturbance Function

This paper discuss multi-agent model of the N-dimensional space with the function of attraction and repulsion. In this model is given the disturbance function which is a bounded function. In this paper also discuss about stationary of each agency and stability of the models use stability of Lyapunov. From the analytical results obtained center of the multi-agent is stationary. Also test the stability with Lyapunov method is obtained that the proposed model is a stable model. Numerical simulation results show that each agent will converges to a region that has a certain distance to the center of the multi-agent model

Chaos and bifurcations in a discretized fractional model of quasi-periodic plasma perturbations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ahmed Ezzat Matouk
Keyword(s):  
Homoclinic Orbits ◽  
Flip Bifurcation ◽  
Invariant Curves ◽  
Bifurcation Diagrams ◽  
Homoclinic Connections ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Simulation Results ◽  
The Stability ◽  
Theoretical Results

Abstract The nonlinear dynamics of a discretized form of quasi-periodic plasma perturbations model (Q-PPP) with nonlocal fractional differential operator possessing singular kernel are investigated. For example, the conditions for the stability and occurrence of Neimark–Sacker (NS) and flip bifurcations in the proposed discretized equations are provided. Moreover, analysis of nonlinearities such as the existence of chaos in this map is proved numerically via bifurcation diagrams, Lyapunov exponents and analytically via Marotto’s Theorem. Also, some simulation results are utilized to confirm the theoretical results and to show that the obtained map exhibits double routes to chaos: one is via flip bifurcation and the other is via NS bifurcation. Furthermore, more complex dynamical phenomena such as existence of closed invariant curves, homoclinic orbits, homoclinic connections, period 3 and period 4 attractors are shown. This kind of research is useful for physicists who work with tokamak models.

scholarly journals Transmission dynamic and backward bifurcation of Middle Eastern respiratory syndrome coronavirus

2022 ◽  
Vol 27 (1) ◽  
pp. 54-69
Author(s):  
Bibi Fatima ◽  
Gul Zaman ◽  
Fahd Jarad
Keyword(s):  
Deterministic Model ◽  
Middle Eastern ◽  
Primary Source ◽  
Backward Bifurcation ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Source Of Infection ◽  
Proposed Model ◽  
The Stability ◽  
The Impact

Middle East respiratory syndrome coronavirus (MERS-CoV) remains an emerging disease threat with regular human cases on the Arabian Peninsula driven by recurring camels to human transmission events. In this paper, we present a new deterministic model for the transmission dynamics of (MERS-CoV). In order to do this, we develop a model formulation and analyze the stability of the proposed model. The stability conditions are obtained in term of R0, we find those conditions for which the model become stable. We discuss basic reproductive number R0 along with sensitivity analysis to show the impact of every epidemic parameter. We show that the proposed model exhibits the phenomena of backward bifurcation. Finally, we show the numerical simulation of our proposed model for supporting our analytical work. The aim of this work is to show via mathematical model the transmission of MERS-CoV between humans and camels, which are suspected to be the primary source of infection.

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