A Research on Nonendangered Population Protection Facing Biological Invasion

In nature, a biological invasion is a common phenomenon that often threatens the existence of local species. Getting rid of the invasive species is hard to achieve after its survival and reproduction. At present, killing some invasive ones and putting artificial local species are usual methods to prevent local species from extinction. An ODE model is constructed to simulate the invasive procedure, and the protection policy is depicted as a series of impulses depending on the state of the variables. Both the ODEs and the impulses form a state feedback impulsive model which describes the invasion and protection together. The existence of homoclinic cycle and bifurcation of order-1 periodic solution of the impulsive model are discussed, and the orbitally asymptotical stability of the order-1 periodic solution is certificated with a novel method. Finally, the numerical simulation result is listed to confirm the theoretical work.

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Dynamical Behaviors for a Predator-Prey System with State-Dependent Impulsive Effects

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.130-134.385 ◽

2011 ◽

Vol 130-134 ◽

pp. 385-390

Author(s):

Ling Zhen Dong ◽

Lan Sun Chen

Keyword(s):

Dynamical System ◽

Periodic Solution ◽

Asymptotic Stability ◽

Impulsive System ◽

Impulsive Effects ◽

Predator Prey ◽

Dynamical Behaviors ◽

Prey System ◽

State Dependent ◽

Impulsive Model

With some theory about continuous and impulsive dynamical system, an impulsive model based on a special predator-prey system is considered. We assume that the impulsive effects occur when the density of the prey reaches a given value. For such a state-dependent impulsive system, the existence, uniqueness and orbital asymptotic stability of an order-1 periodic solution are discussed. Further, the existence of an order-2 periodic solution is also obtained, and persistence of the system is investigated.

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Predicting COVID-19 (Coronavirus Disease) Outbreak Dynamics Using SIR-based Models: Comparative Analysis of SIRD and Weibull-SIRD

10.1101/2020.11.29.20240564 ◽

2020 ◽

Author(s):

Ahmad Sedaghat ◽

Amir Mosavi

Keyword(s):

Dynamic Systems ◽

Optimization Methods ◽

Initial Guess ◽

Biological Data ◽

Data Sets ◽

Mathematical Methods ◽

Ode Model ◽

Initial Value ◽

Novel Method ◽

Insight Into

AbstractThe SIR type models are built by a set of ordinary differential equations (ODE), which are strongly initial value dependant. To fit multiple biological data with SIR type equations requires fitting coefficients of these equations by an initial guess and applying optimization methods. These coefficients are also extremely initial value-dependent. In the vast publication of these types, we hardly see, among simple to highly complicated SIR type methods, that these methods presented more than a maximum of two biological data sets. We propose a novel method that integrates an analytical solution of the infectious population using Weibull distribution function into any SIR type models. The Weibull-SIRD method has easily fitted 4 set of COVID-19 biological data simultaneously. It is demonstrated that the Weibull-SIRD method predictions for susceptible, infected, recovered, and deceased populations from COVID-19 in Kuwait and UAE are superior compared with SIRD original ODE model. The proposed method here opens doors for new deeper studying of biological dynamic systems with realistic biological data trends than providing some complicated, cumbersome mathematical methods with little insight into biological data’s real physics.

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A Study into the Use of Pseudo Random Binary Sequence Pressure Disturbances to Measure Sonic Velocity in a Two-Phase Flow System

Proceedings of the Institution of Mechanical Engineers ◽

10.1243/pime_proc_1972_186_050_02 ◽

1972 ◽

Vol 186 (1) ◽

pp. 449-455 ◽

Cited By ~ 4

Author(s):

K. F. Gill ◽

E. W. Reed

Keyword(s):

Two Phase Flow ◽

Flow System ◽

Binary Sequence ◽

Theoretical Work ◽

Time Shift ◽

Phase Flow ◽

Sonic Velocity ◽

Two Phase ◽

On Line ◽

Novel Method

A literature survey into gas-solids flow has revealed that most of the existing work is of a theoretical nature. Of fundamental importance to this theoretical work is the concept of sonic velocity. Presented here is a novel method that enables this parameter to be measured experimentally. The technique used is to inject small amplitude pseudo random binary sequence pressure disturbances into a two-phase flow system and compute a cross-correlation function between two measuring locations within the flow system. The time shift of the peak value of this function gives a direct measure of the sonic velocity existing between these two locations. The experimental results demonstrate that by using a pseudo random pressure disturbance on-line evaluation of sonic velocity becomes feasible.

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Predicting COVID-19 (Coronavirus Disease) Outbreak Dynamics Using SIR-based Models: Comparative Analysis of SIRD and Weibull-SIRD

10.31219/osf.io/b9nj7 ◽

2020 ◽

Author(s):

Ahmad Sedaghat ◽

Amir Mosavi

Keyword(s):

Dynamic Systems ◽

Optimization Methods ◽

Initial Guess ◽

Biological Data ◽

Data Sets ◽

Mathematical Methods ◽

Ode Model ◽

Initial Value ◽

Novel Method ◽

Insight Into

The SIR type models are built by a set of ordinary differential equations (ODE), which are strongly initial value dependant. To fit multiple biological data with SIR type equations requires fitting coefficients of these equations by an initial guess and applying optimization methods. These coefficients are also extremely initial value-dependent. In the vast publication of these types, we hardly see, among simple to highly complicated SIR type methods, that these methods presented more than a maximum of two biological data sets. We propose a novel method that integrates an analytical solution of the infectious population using Weibull distribution function into any SIR type models. The Weibull-SIRD method has easily fitted 4 set of COVID-19 biological data simultaneously. It is demonstrated that the Weibull-SIRD method predictions for susceptible, infected, recovered, and deceased populations from COVID-19 in Kuwait and UAE are superior compared with SIRD original ODE model. The proposed method here opens doors for new deeper studying of biological dynamic systems with realistic biological data trends than providing some complicated, cumbersome mathematical methods with little insight into biological data's real physics.

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Dynamical Behavior and Bifurcation Analysis of the SIR Model with Continuous Treatment and State-Dependent Impulsive Control

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127419501311 ◽

2019 ◽

Vol 29 (10) ◽

pp. 1950131 ◽

Cited By ~ 2

Author(s):

Qian Li ◽

Yanni Xiao

Keyword(s):

Periodic Solution ◽

Periodic Solutions ◽

Reproduction Number ◽

Continuous Treatment ◽

Positive Order ◽

Susceptible Population ◽

State Dependent ◽

Existence And Stability ◽

Impulsive Model ◽

Disease Free

In this study, we propose a state-dependent impulsive model describing the susceptible individuals-triggered interventions. We find that the model with susceptible individuals-guided impulsive interventions can exhibit very complex dynamical behaviors with rich biological meanings. We note that this formulated impulsive model has disease-free periodic solution, and we can investigate the threshold dynamics by defining the control reproduction number. We study the existence and stability of the disease-free periodic solution (DFPS) for [Formula: see text]. Our results show that, even if the basic reproduction number [Formula: see text], the DFPS can still be stable when the threshold level of susceptible population [Formula: see text], indicating that with a proper chosen [Formula: see text], the state-dependent impulsive strategy can effectively control the development of the infectious disease and eradicate the disease eventually. By employing the bifurcation theory, we investigate the bifurcation phenomenon near the DFPS with respect to some key parameters, and observe that a positive order-1 periodic solution can bifurcate from the DFPS via a transcritical bifurcation. By utilizing numerical simulation, we further explore the existence and stability of the positive order-[Formula: see text] periodic solutions, and found the feasibility of stable positive order-1, order-2 and order-3 periodic solutions, that imply the existence of chaos. In particular, we find that there can be three positive order-1 periodic solutions simultaneously, in which one is stable and the other two are unstable. Our finding indicates that the comprehensive strategy combining continuous treatment with state-dependent impulsive vaccination and isolation plays a crucial role in controlling the prevalence and further spread of the infectious diseases.

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Dynamic Analysis of a Plankton-Herbivore State-Dependent Impulsive Model With Action Threshold Depending On The Density and Its Changing Rate

10.21203/rs.3.rs-710111/v1 ◽

2021 ◽

Author(s):

Wei Li ◽

Tonghua Zhang ◽

Yufei Wang ◽

Huidong Cheng

Keyword(s):

Periodic Solution ◽

Poincaré Map ◽

Complex Dynamics ◽

Economic Benefits ◽

Rate Of Change ◽

Poincare Map ◽

The Sustainable Development ◽

State Dependent ◽

Action Threshold ◽

Impulsive Model

Abstract A plankton-herbivore state-dependent impulsive model with nonlinear impulsive functions and action threshold including population density and rate of change is proposed. Since the use of action threshold makes the model have complex phase set and pulse set, we adopt the Poincaré map as a tool to study its complex dynamics. The Poincaré map is defined on the phase set and its properties in different situations are analyzed. Furthermore, the periodic solution of model are discussed, including the existence and stability conditions of the order-1 periodic solution and the existence of the order-k (k ≥ 2) periodic solutions. Compared with the fixed threshold in the existing literature, our results show that the use of action threshold is more practical, which is conducive to the sustainable development of population and makes people obtain more economic benefits. The analysis method used in this paper can study the complex dynamics of the model more comprehensively and deeply.

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Balloon-Occluded Retrograde Transvenous Obliteration (BRTO): A Novel Method of Obliterating Gastric Varices. Report of Six Cases and Review of Literature

Journal of Advances in Internal Medicine ◽

10.3126/jaim.v9i2.31049 ◽

2020 ◽

Vol 9 (2) ◽

pp. 89-93

Author(s):

Ajit Thapa ◽

Dinesh Koirala ◽

Rahul Pathak ◽

Dinesh Chataut ◽

Sashi Sharma ◽

...

Keyword(s):

Balloon Catheter ◽

Invasive Procedure ◽

Gastric Varix ◽

Gastric Varices ◽

Minimal Invasive ◽

Balloon Occlusion ◽

Endoscopic Variceal Ligation ◽

Review Of Literature ◽

Gastroesophageal Varices ◽

Novel Method

Portal hypertension results in various complications, gastroesophageal varices being one of them. Although less common than esophageal varices, gastric varices are difficult to obliterate and carry a higher mortality rate when bleeding occurs. They are less amenable to sclerotherapy, endoscopic variceal ligation. Balloon-Occluded Retrograde Transvenous Obliteration (BRTO) has been developed as a minimal invasive procedure to obliterate gastric varices. BRTO is an endovascular procedure where a balloon catheter is inserted into a draining vein of gastric varix, and the sclerosant can be injected into the varices through the catheter during balloon occlusion. We report six cases where BRTO was done for gastric varices obliteration.

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Periodic Solution of A Delayed Intraguild Predation Impulsive System with Strong Allee Effect

Journal of Physics Conference Series ◽

10.1088/1742-6596/2068/1/012044 ◽

2021 ◽

Vol 2068 (1) ◽

pp. 012044

Author(s):

Jiao Ai ◽

Kaihua Wang

Keyword(s):

Periodic Solution ◽

Intraguild Predation ◽

Sufficient Conditions ◽

Positive Periodic Solution ◽

Impulsive System ◽

Allee Effects ◽

Mawhin’S Continuation Theorem ◽

Strong Allee Effect ◽

Impulsive Model ◽

Theoretical Results

Abstract With periodic coefficients and strong Allee effects, we establish a delayed intraguild predation impulsive model. We obtain a set of sufficient conditions for the existence of positive periodic solution of the model using Mawhin’s continuation theorem and analysis techniques. Finally, we identify the effectiveness of the theoretical results through some numerical simulations.

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