scholarly journals Global Dynamics of an Avian Influenza A(H7N9) Epidemic Model with Latent Period and Nonlinear Recovery Rate

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Rui Mu ◽  
Youping Yang
Keyword(s):  
Influenza A ◽  
Psychological Effect ◽  
Global Dynamics ◽  
H7n9 Virus ◽  
Compound Matrix ◽  
The Stability ◽  
And Control ◽  
Additive Compound ◽  
Practical Implications ◽  
Available Resources

An SEIR type of compartmental model with nonlinear incidence and recovery rates was formulated to study the combined impacts of psychological effect and available resources of public health system especially the number of hospital beds on the transmission and control of A(H7N9) virus. Global stability of the disease-free and endemic equilibria is determined by the basic reproduction number as a threshold parameter and is obtained by constructing Lyapunov function and second additive compound matrix. The results obtained reveal that psychological effect and available resources do not change the stability of the steady states but can indeed diminish the peak and the final sizes of the infected. Our studies have practical implications for the transmission and control of A(H7N9) virus.

scholarly journals A Mathematical Study of a Generalized SEIR Model of COVID-19

2020 ◽  
Vol 2 ◽  
pp. 30-67
Author(s):  
Abdelkader Intissar
Keyword(s):  
Control Strategies ◽  
Nonlinear Dynamical System ◽  
Globally Asymptotically Stable ◽  
Seir Model ◽  
Nonlinear Dynamical ◽  
Compound Matrices ◽  
Compound Matrix ◽  
The Stability ◽  
Additive Compound ◽  
Disease Free

In this work (Part I), we reinvestigate the study of the stability of the Covid-19 mathematical model constructed by Shah et al. (2020) [1]. In their paper, the transmission of the virus under different control strategies is modeled thanks to a generalized SEIR model. This model is characterized by a five dimensional nonlinear dynamical system, where the basic reproduction number can be established by using the next generation matrix method. In this work (Part I), it is established that the disease free equilibrium point is locally as well as globally asymptotically stable when . When , the local and global asymptotic stability of the equilibrium are determined employing the second additive compound matrix approach and the Li-Wang’s (1998) stability criterion  for real matrices [2]. In the second paper (Part II), some control parameters with uncertainties will be added to stabilize the five-dimensional Covid-19 system studied here, in order to force the trajectories to go to the equilibria. The stability of the Covid-19 system with these new parameters will also be assessed in Intissar (2020) [3] applying the Li-Wang criterion and compound matrices theory. All sophisticated technical calculations including those in part I will be provided in appendices of the part II.

scholarly journals Global dynamics for a Filippov system with media effects

2022 ◽  
Vol 19 (3) ◽  
pp. 2835-2852
Author(s):  
Cunjuan Dong ◽  
◽  
Changcheng Xiang ◽  
Wenjin Qin ◽  
Yi Yang ◽  
...  
Keyword(s):  
Disease Transmission ◽  
Media Coverage ◽  
Equilibrium Points ◽  
Disease Outbreaks ◽  
Global Dynamics ◽  
Threshold Strategy ◽  
Infectious Disease Outbreaks ◽  
Boundary Equilibrium ◽  
The Stability ◽  
And Control

<abstract><p>In the process of spreading infectious diseases, the media accelerates the dissemination of information, and people have a deeper understanding of the disease, which will significantly change their behavior and reduce the disease transmission; it is very beneficial for people to prevent and control diseases effectively. We propose a Filippov epidemic model with nonlinear incidence to describe media's influence in the epidemic transmission process. Our proposed model extends existing models by introducing a threshold strategy to describe the effects of media coverage once the number of infected individuals exceeds a threshold. Meanwhile, we perform the stability of the equilibriua, boundary equilibrium bifurcation, and global dynamics. The system shows complex dynamical behaviors and eventually stabilizes at the equilibrium points of the subsystem or pseudo equilibrium. In addition, numerical simulation results show that choosing appropriate thresholds and control intensity can stop infectious disease outbreaks, and media coverage can reduce the burden of disease outbreaks and shorten the duration of disease eruptions.</p></abstract>

scholarly journals Global Dynamics of Avian Influenza Epidemic Models with Psychological Effect

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Sanhong Liu ◽  
Liuyong Pang ◽  
Shigui Ruan ◽  
Xinan Zhang
Keyword(s):  
Avian Influenza ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Influenza A ◽  
Reproduction Number ◽  
Psychological Effect ◽  
Saturation Effect ◽  
Effective Control ◽  
Global Dynamics ◽  
The Basic Reproduction Number

Cross-sectional surveys conducted in Thailand and China after the outbreaks of the avian influenza A H5N1 and H7N9 viruses show a high degree of awareness of human avian influenza in both urban and rural populations, a higher level of proper hygienic practice among urban residents, and in particular a dramatically reduced number of visits to live markets in urban population after the influenza A H7N9 outbreak in China in 2013. In this paper, taking into account the psychological effect toward avian influenza in the human population, a bird-to-human transmission model in which the avian population exhibits saturation effect is constructed. The dynamical behavior of the model is studied by using the basic reproduction number. The results demonstrate that the saturation effect within avian population and the psychological effect in human population cannot change the stability of equilibria but can affect the number of infected humans if the disease is prevalent. Numerical simulations are given to support the theoretical results and sensitivity analyses of the basic reproduction number in terms of model parameters that are performed to seek for effective control measures for avian influenza.

scholarly journals Data-Driven Stability Assessment of Multilayer Long Short-Term Memory Networks

2021 ◽  
Vol 11 (4) ◽  
pp. 1829
Author(s):  
Davide Grande ◽  
Catherine A. Harris ◽  
Giles Thomas ◽  
Enrico Anderlini
Keyword(s):  
Neural Network ◽  
Network Architecture ◽  
Short Term Memory ◽  
Moving Average ◽  
Machine Learning Algorithms ◽  
Physical Models ◽  
Data Driven ◽  
The Stability ◽  
And Control ◽  
Nonlinear Autoregressive

Recurrent Neural Networks (RNNs) are increasingly being used for model identification, forecasting and control. When identifying physical models with unknown mathematical knowledge of the system, Nonlinear AutoRegressive models with eXogenous inputs (NARX) or Nonlinear AutoRegressive Moving-Average models with eXogenous inputs (NARMAX) methods are typically used. In the context of data-driven control, machine learning algorithms are proven to have comparable performances to advanced control techniques, but lack the properties of the traditional stability theory. This paper illustrates a method to prove a posteriori the stability of a generic neural network, showing its application to the state-of-the-art RNN architecture. The presented method relies on identifying the poles associated with the network designed starting from the input/output data. Providing a framework to guarantee the stability of any neural network architecture combined with the generalisability properties and applicability to different fields can significantly broaden their use in dynamic systems modelling and control.

scholarly journals Order and Chaos in a Prey-Predator Model Incorporating Refuge, Disease, and Harvesting

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Dahlia Khaled Bahlool ◽  
Huda Abdul Satar ◽  
Hiba Abdullah Ibrahim
Keyword(s):  
Equilibrium Points ◽  
Global Dynamics ◽  
Persistence Conditions ◽  
Local Bifurcation Analysis ◽  
Uniqueness Of The Solution ◽  
Harvesting Process ◽  
Predator Model ◽  
The Stability ◽  
Predator System ◽  
Type Ii Functional Response

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics.

scholarly journals Subgraphs of Interest Social Networks for Diffusion Dynamics Prediction

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 492
Author(s):  
Valentina Y. Guleva ◽  
Polina O. Andreeva ◽  
Danila A. Vaganov
Keyword(s):  
Social Networks ◽  
Sampling Method ◽  
Building Blocks ◽  
Global Dynamics ◽  
Diffusion Dynamics ◽  
Different Types ◽  
Prediction And Control ◽  
Path Lengths ◽  
And Control ◽  
Diffusion Prediction

Finding the building blocks of real-world networks contributes to the understanding of their formation process and related dynamical processes, which is related to prediction and control tasks. We explore different types of social networks, demonstrating high structural variability, and aim to extract and see their minimal building blocks, which are able to reproduce supergraph structural and dynamical properties, so as to be appropriate for diffusion prediction for the whole graph on the base of its small subgraph. For this purpose, we determine topological and functional formal criteria and explore sampling techniques. Using the method that provides the best correspondence to both criteria, we explore the building blocks of interest networks. The best sampling method allows one to extract subgraphs of optimal 30 nodes, which reproduce path lengths, clustering, and degree particularities of an initial graph. The extracted subgraphs are different for the considered interest networks, and provide interesting material for the global dynamics exploration on the mesoscale base.

scholarly journals The Influence of Exploration Mode, Orientation, and Configuration on the Haptic Müller-Lyer Illusion

Perception ◽  
10.1068/p5269 ◽  
2005 ◽  
Vol 34 (12) ◽  
pp. 1475-1500 ◽  
Author(s):  
Morton A Heller ◽  
Melissa McCarthy ◽  
Jennifer Schultz ◽  
Jayme Greene ◽  
Melissa Shanley ◽  
...  
Keyword(s):  
Index Finger ◽  
Spatial Position ◽  
Lyer Illusion ◽  
Free Exploration ◽  
And Control ◽  
The Impact ◽  
Practical Implications

We studied the impact of manner of exploration, orientation, spatial position, and configuration on the haptic Müller-Lyer illusion. Blindfolded sighted subjects felt raised-line Müller-Lyer and control stimuli. The stimuli were felt by tracing with the index finger, free exploration, grasping with the index finger and thumb, or by measuring with the use of any two or more fingers. For haptic judgments of extent a sliding tangible ruler was used. The illusion was present in all exploration conditions, with overestimation of the wings-out compared to wings-in stimuli. Tracing with the index finger reduced the magnitude of the illusion. However, tracing and grasping induced an overall underestimation of size. The illusion was greatly attenuated when stimuli were felt with the index fingers of both hands. Illusory misperception was not altered by the position in space of the Müller-Lyer stimuli. No effects of changes in the thickness of the line shaft were found, but there were effects of the length of the wing endings for the smaller, 5.1 cm stimuli. The theoretical and practical implications of the results are discussed.

scholarly journals Optimal Control of an SIR Model with Delay in State and Control Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Mohamed Elhia ◽  
Mostafa Rachik ◽  
Elhabib Benlahmar
Keyword(s):  
Optimal Control ◽  
Influenza A ◽  
Optimization Strategy ◽  
Sir Epidemic Model ◽  
Optimal Control Strategy ◽  
Control Variables ◽  
Sir Epidemic ◽  
Influenza A H1n1 ◽  
Using Data ◽  
And Control

We will investigate the optimal control strategy of an SIR epidemic model with time delay in state and control variables. We use a vaccination program to minimize the number of susceptible and infected individuals and to maximize the number of recovered individuals. Existence for the optimal control is established; Pontryagin’s maximum principle is used to characterize this optimal control, and the optimality system is solved by a discretization method based on the forward and backward difference approximations. The numerical simulation is carried out using data regarding the course of influenza A (H1N1) in Morocco. The obtained results confirm the performance of the optimization strategy.

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