scholarly journals Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-type Epidemiological Models

2021 ◽  
Author(s):  
Teddy Lazebnik ◽  
Svetlana Bunimovich-Mendrazitsky ◽  
Leonid Shaikhet
Keyword(s):  
Large Scale ◽  
Initial Conditions ◽  
Scale Model ◽  
Epidemiological Models ◽  
Stochastic Representation ◽  
Asymptotic Stable ◽  
Large Scale Model ◽  
Stable Equilibria ◽  
Novel Method

We present a new analytical method to find the asymptotic stable equilibria states based on the Markov chain technique. We reveal this method on the SIR-type epidemiological model that we developed for viral diseases with long-term immunity memory pandemic. This is a large-scale model containing 15 nonlinear ODE equations, and classical methods have failed to analytically obtain its equilibria. The proposed method is used to conduct a comprehensive analysis by a stochastic representation of the dynamics of the model, followed by finding all asymptotic stable equilibrium states of the model for any values of parameters and initial conditions.

scholarly journals Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological Models

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1120
Author(s):  
Teddy Lazebnik ◽  
Svetlana Bunimovich-Mendrazitsky ◽  
Leonid Shaikhet
Keyword(s):  
Large Scale ◽  
Initial Conditions ◽  
Scale Model ◽  
Epidemiological Models ◽  
Stochastic Representation ◽  
Asymptotic Stable ◽  
Large Scale Model ◽  
Stable Equilibria ◽  
Novel Method

We present a new analytical method to find the asymptotic stable equilibria states based on the Markov chain technique. We reveal this method on the Susceptible-Infectious-Recovered (SIR)-type epidemiological model that we developed for viral diseases with long-term immunity memory. This is a large-scale model containing 15 nonlinear ordinary differential equations (ODEs), and classical methods have failed to analytically obtain its equilibria. The proposed method is used to conduct a comprehensive analysis by a stochastic representation of the dynamics of the model, followed by finding all asymptotic stable equilibrium states of the model for any values of parameters and initial conditions thanks to the symmetry of the population size over time.

Creep Characteristics of Organic Soft Clay Soil Using Large–Scale Model

2021 ◽  
Author(s):  
Raid Al-Omari ◽  
◽  
Mohammed Fattah ◽  
Mudhafar Hameedi ◽  
◽  
...  
Keyword(s):  
Large Scale ◽  
Large Fraction ◽  
Soft Clay ◽  
Laboratory Data ◽  
Soil Surface ◽  
Organic Content ◽  
Scale Model ◽  
Secondary Compression ◽  
Large Scale Model

The long-term settlements in organic clay can create a kind of an engineering challenge that appear in most facilities design and construction in areas with deep deposits of soft clay. Peat ground is widely distributed throughout the southern part of Iraq. Peat contains a large amount of organic matter and has a very high natural water content. Three soil samples were collected from depths of 1.5 m, 2.5 m, and 3.5 m, below the soil surface in Halfaya oilfield, which lies east of Missan governorate southern Iraq. A series of tests were conducted in a large-scale model using a plate footing and considering three different percent of organic content. The percent of secondary settlement found is dependent on the stress level applied. A large fraction of the total settlement may be due to secondary compression. The assumption of a constant coefficient of secondary compression, Cα, may not be valid for a long-term settlement of peats. Laboratory data indicate that Cα generally increases with time. Thus, settlement predictions using constant Cα may underestimate field settlement.

Dynamic Response of Pile-Board Subgrade Based on Large Scale Model Test

2011 ◽  
Vol 71-78 ◽  
pp. 383-387 ◽  
Author(s):  
Qian Su ◽  
Xing Li ◽  
Hao Bai
Keyword(s):  
Dynamic Response ◽  
Dynamic Load ◽  
Large Scale ◽  
Test Group ◽  
Structural Type ◽  
Scale Model ◽  
Load Frequency ◽  
Large Scale Model ◽  
Supporting Effect

A series of tests based on large scale model are designed to study dynamic response of pile-broad subgrade, aiming at structure’s response towards different load frequency and structure’s performance under long-term dynamic load. The test results indicate that dynamic stress of reinforcement and soil decrease slightly with load frequency, while accelerations trend to increase. Soil under loading plate has certain supporting effect because stress of reinforcement is smaller in test group with soil remains. Performance of pile-board subgrade under long-term dynamic load is steady and reliable since none of stress and displacement varies obviously when loading times increase to 106. Ultimate bearing capacity of pile-board subgrade is much bigger than actual demand, so the structural type of pile-broad plate remains to be optimized.

RANCANG BANGUN PERANGKAT EKSPERIMENTASI PROSES PIROLISIS BIOMASA GELOMBANG MIKRO

2013 ◽  
Vol 14 (2) ◽  
Author(s):  
Noor Fachrizal
Keyword(s):  
Large Scale ◽  
Continuous Model ◽  
Biomass Energy ◽  
Scale Model ◽  
Small Scale ◽  
Laboratory Apparatus ◽  
Liquid Form ◽  
Large Scale Model ◽  
Bio Oil ◽  
Pyrolysis Of Biomass

Biomass such as agriculture waste and urban waste are enormous potency as energy resources instead of enviromental problem. organic waste can be converted into energy in the form of liquid fuel, solid, and syngas by using of pyrolysis technique. Pyrolysis process can yield higher liquid form when the process can be drifted into fast and flash response. It can be solved by using microwave heating method. This research is started from developing an experimentation laboratory apparatus of microwave-assisted pyrolysis of biomass energy conversion system, and conducting preliminary experiments for gaining the proof that this method can be established for driving the process properly and safely. Modifying commercial oven into laboratory apparatus has been done, it works safely, and initial experiments have been carried out, process yields bio-oil and charcoal shortly, several parameters are achieved. Some further experiments are still needed for more detail parameters. Theresults may be used to design small-scale continuous model of productionsystem, which then can be developed into large-scale model that applicable for comercial use.

Effect of an Oscillating Flow Direction on Leading Edge Heat Transfer

1984 ◽  
Vol 106 (1) ◽  
pp. 222-228 ◽  
Author(s):  
M. L. Marziale ◽  
R. E. Mayle
Keyword(s):  
Heat Transfer ◽  
Strouhal Number ◽  
Large Scale ◽  
Flow Direction ◽  
Leading Edge ◽  
Periodic Variation ◽  
Scale Model ◽  
Transfer Rates ◽  
Large Scale Model ◽  
Turbulence Length

An experimental investigation was conducted to examine the effect of a periodic variation in the angle of attack on heat transfer at the leading edge of a gas turbine blade. A circular cylinder was used as a large-scale model of the leading edge region. The cylinder was placed in a wind tunnel and was oscillated rotationally about its axis. The incident flow Reynolds number and the Strouhal number of oscillation were chosen to model an actual turbine condition. Incident turbulence levels up to 4.9 percent were produced by grids placed upstream of the cylinder. The transfer rate was measured using a mass transfer technique and heat transfer rates inferred from the results. A direct comparison of the unsteady and steady results indicate that the effect is dependent on the Strouhal number, turbulence level, and the turbulence length scale, but that the largest observed effect was only a 10 percent augmentation at the nominal stagnation position.

Large scale model tests on Royal Schelde SES

1989 ◽  
Author(s):  
R. DE GAAIJ ◽  
E. VAN RIETBERGEN ◽  
M. SLEGERS
Keyword(s):  
Large Scale ◽  
Model Tests ◽  
Scale Model ◽  
Large Scale Model
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