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.

Stochastic dynamics for the solutions of a modified Holling–Tanner model with random perturbation

2014 ◽  
Vol 25 (11) ◽  
pp. 1450105 ◽  
Author(s):  
Zhenjie Liu
Keyword(s):  
Stochastic System ◽  
Stochastic Dynamics ◽  
Deterministic Model ◽  
Random Perturbation ◽  
Sufficient Conditions ◽  
Unique Positive Solution ◽  
Initial Value ◽  
Environmental Forcing ◽  
Predator Prey ◽  
Predator Prey Model

In this paper, we consider a stochastic nonautonomous predator–prey model with modified Leslie–Gower and Holling II schemes in the presence of environmental forcing. The deterministic model is the modified Holling–Tanner model which is an extension of the classical Leslie–Gower model. We show that there is a unique positive solution to the stochastic system for any positive initial value. Sufficient conditions for strong persistence in mean and extinction to the stochastic system are established.

Community Ecology of Stream Fishes: Concepts, Approaches, and Techniques

2010 ◽  
Keyword(s):  
Fish Assemblage ◽  
Fish Assemblages ◽  
Stochastic Dynamics ◽  
Low Flow ◽  
Community Stability ◽  
Discharge Data ◽  
Hydrologic Variability ◽  
The Stability ◽  
Stream Fish Assemblages

<em>Abstract.—</em>Stochastic dynamics are central to theory, data analysis, and understanding in the fields of hydrology and population ecology. More importantly, hydrologic variability has been identified as a key process affecting biodiversity and coexistence in stream fish assemblages. Until recently, however, we have lacked tools by which hydrologic variability can be directly linked to measures of community stability. Herein, we show how a modification of Fourier analysis of daily average discharge data can be used to quantify aspects of hydrologic variability for three reference streams and then linked to measures of fish assemblage stability in Coweeta Creek, North Carolina; Sagehen Creek, California; and Otter Creek, Indiana) via multivariate autoregressive (MAR) models. Specifically, we define the magnitude of catastrophic variability as the standard deviation of <em>residual </em>flows referenced to a long-term annual trend, and individual catastrophic events as flows greater than (floods) or less than (droughts) two times this magnitude (i.e., 2 𝛔). We then directly link the magnitude of annual <em>residual </em>flows with MAR models that quantify the relationship between flows and the stability of fish assemblages from the same or nearby streams. Our results confirm that these streams represent a gradient in the stability properties of fish assemblages; Sagehen Creek is the most stable, whereas Otter Creek is the least stable. The timing of catastrophic high and low flows is most predictable in Sagehen Creek and least predictable in Big Raccon Creek (reference stream for Otter Creek), whereas the magnitude and frequency of <em>catastrophic </em>events varied in a manner less consistent with the gradient in fish community stability. Nevertheless, the stability of fish communities covaried significantly with both residual flow magnitudes (high- and low-flow events). Although this technique is not without limitations (e.g., it is most relevant to resident species), it appears to be a promising new tool for linking hydrologic variability directly to fish assemblage stability and, more broadly, for quantifying links between flow regulation and the viability of native aquatic faunas.

The ILRS Contribution to ITRF2020

2021 ◽  
Author(s):  
Vincenza Luceri ◽  
Erricos C. Pavlis ◽  
Antonio Basoni ◽  
David Sarrocco ◽  
Magdalena Kuzmicz-Cieslak ◽  
...  
Keyword(s):  
Time Series ◽  
Tracking System ◽  
A Priori ◽  
Systematic Errors ◽  
Novel Approach ◽  
Priori Information ◽  
The Stability ◽  
The Individual ◽  
Stability And Consistency

&lt;p&gt;The International Laser Ranging Service (ILRS) contribution to ITRF2020 has been prepared after the re-analysis of the data from 1993 to 2020, based on an improved modeling of the data and a novel approach that ensures the results are free of systematic errors in the underlying data. This reanalysis incorporates an improved &amp;#8220;target signature&amp;#8221; model (CoM) that allows better separation of true systematic error of each tracking system from the errors in the model describing the target&amp;#8217;s signature. The new approach was developed after the completion of ITRF2014, the ILRS Analysis Standing Committee (ASC) devoting almost entirely its efforts on this task. The robust estimation of persistent systematic errors at the millimeter level permitted the adoption of a consistent set of long-term mean corrections for data collected in past years, which are now applied a priori (information provided by the stations from their own engineering investigations are still taken into consideration). The reanalysis used these corrections, leading to improved results for the TRF attributes, reflected in the resulting new time series of the TRF origin and especially in the scale. Seven official ILRS Analysis Centers computed time series of weekly solutions, according to the guidelines defined by the ILRS ASC. These series were combined by the ILRS Combination Center to obtain the official ILRS product contribution to ITRF2020.&lt;/p&gt;&lt;p&gt;The presentation will provide an overview of the analysis procedures and models, and it will demonstrate the level of improvement with respect to the previous ILRS product series; the stability and consistency of the solution are discussed for the individual AC contributions and the combined SLR time series.&lt;/p&gt;

scholarly journals The impact of antiretroviral therapy on population-level virulence evolution of HIV-1

2015 ◽  
Vol 12 (113) ◽  
pp. 20150888 ◽  
Author(s):  
Hannah E. Roberts ◽  
Philip J. R. Goulder ◽  
Angela R. McLean
Keyword(s):  
Antiretroviral Therapy ◽  
Deterministic Model ◽  
Population Level ◽  
Threshold Condition ◽  
Virulence Evolution ◽  
Downward Pressure ◽  
The Individual ◽  
The Impact ◽  
Hiv 1

In HIV-infected patients, an individual's set point viral load (SPVL) strongly predicts disease progression. Some think that SPVL is evolving, indicating that the virulence of the virus may be changing, but the data are not consistent. In addition, the widespread use of antiretroviral therapy (ART) has the potential to drive virulence evolution. We develop a simple deterministic model designed to answer the following questions: what are the expected patterns of virulence change in the initial decades of an epidemic? Could administration of ART drive changes in virulence evolution and, what is the potential size and direction of this effect? We find that even without ART we would not expect monotonic changes in average virulence. Transient decreases in virulence following the peak of an epidemic are not necessarily indicative of eventual evolution to avirulence. In the short term, we would expect widespread ART to cause limited downward pressure on virulence. In the long term, the direction of the effect is determined by a threshold condition, which we define. We conclude that, given the surpassing benefits of ART to the individual and in reducing onward transmission, virulence evolution considerations need have little bearing on how we treat.

scholarly journals Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence Rate

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yongli Cai ◽  
Xixi Wang ◽  
Weiming Wang ◽  
Min Zhao
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Stochastic Dynamics ◽  
Complex Dynamics ◽  
Deterministic Model ◽  
Mass Action ◽  
Sirs Epidemic Model ◽  
Stochastic Epidemic ◽  
The Stability ◽  
Disease Free

We investigate the complex dynamics of an epidemic model with nonlinear incidence rate of saturated mass action which depends on the ratio of the number of infectious individuals to that of susceptible individuals. We first deal with the boundedness, dissipation, persistence, and the stability of the disease-free and endemic points of the deterministic model. And then we prove the existence and uniqueness of the global positive solutions, stochastic boundedness, and permanence for the stochastic epidemic model. Furthermore, we perform some numerical examples to validate the analytical findings. Needless to say, both deterministic and stochastic epidemic models have their important roles.

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.

DYNAMICAL BEHAVIORS OF AN INFLUENZA EPIDEMIC MODEL WITH VIRUS MUTATION

2018 ◽  
Vol 26 (03) ◽  
pp. 455-472
Author(s):  
LILI LIU ◽  
XINZHI REN ◽  
XIANNING LIU
Keyword(s):  
Influenza Virus ◽  
Epidemic Model ◽  
Endemic Equilibrium ◽  
Threshold Condition ◽  
Influenza Epidemic ◽  
Globally Asymptotically Stable ◽  
Dynamical Behaviors ◽  
The Stability ◽  
Theoretical Results ◽  
Two Equilibria

Influenza virus mutates frequently. This poses immense challenges to prevent the spread of influenza. This paper aims to investigate an influenza epidemic model in which influenza virus can mutate into a mutant influenza virus. We find a threshold condition that determines the stability of the disease-free equilibrium. Two equilibria may also exist: mutant-dominant equilibrium and endemic equilibrium. We show that the mutant-dominant equilibrium is globally asymptotically stable under some biological feasible conditions. Furthermore, the influenza is endemic in the sense of permanence if and only if the endemic equilibrium exists. Numerical simulations are also performed to illustrate theoretical results and demonstrate the effects of disease-induced death on the dynamics of the model.

scholarly journals Survival and Stationary Distribution in a Stochastic SIS Model

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yanli Zhou ◽  
Weiguo Zhang ◽  
Sanling Yuan
Keyword(s):  
Stationary Distribution ◽  
Deterministic Model ◽  
Deterministic System ◽  
Initial Value ◽  
Sis Model ◽  
Sis Epidemic Model ◽  
Stochastic Sis Epidemic Model ◽  
Theoretical Results ◽  
Disease Free

The dynamics of a stochastic SIS epidemic model is investigated. First, we show that the system admits a unique positive global solution starting from the positive initial value. Then, the long-term asymptotic behavior of the model is studied: whenR0≤1, we show how the solution spirals around the disease-free equilibrium of deterministic system under some conditions; whenR0>1, we show that the stochastic model has a stationary distribution under certain parametric restrictions. In particular, we show that random effects may lead the disease to extinction in scenarios where the deterministic model predicts persistence. Finally, numerical simulations are carried out to illustrate the theoretical results.

scholarly journals THE COVID-19 PANDEMIC - HOW WELL ARE WE BALANCING HEALTH, FREEDOM, AND THE ECONOMY?

2020 ◽  
Author(s):  
Fedeli Piergiorgio ◽  
◽  
Cingolani Mariano ◽  
Nunzia Cannovo ◽  
Roberto Scendoni ◽  
...  
Keyword(s):  
Careful Analysis ◽  
Right To Health ◽  
Negative Consequences ◽  
Right To Work ◽  
The Stability ◽  
The Individual ◽  
The Right ◽  
Individual Choices ◽  
National Governments

The worsening healthcare emergency with the COVID-19 pandemic has demanded a prompt reaction from authorities to contain the damage related to the spread of the virus. Our aim is to provide a bioethical contribution, with a careful analysis about the balance of individual rights with those of the whole community. The protection of the right to health in the emergency phase, with the restriction of the right to work and other rights, can have long-term negative consequences on the economy, with fallout affecting funding for the healthcare system as well. The right to health in its community dimension can sometimes clash with the protection of the sacrosanct dignity of the individual. Choices to protect health may have social and economic repercussions that could undermine the stability of many national governments.

scholarly journals ON THE BEHAVIOR OF ARMOR UNIT IN THE COVERLAYER

1986 ◽  
Vol 1 (20) ◽  
pp. 157
Author(s):  
Hans Werner Pertenscky ◽  
John Rutte ◽  
Reinold Schmidt
Keyword(s):  
Large Scale ◽  
Standardized Test ◽  
Model Tests ◽  
Scale Model ◽  
Test Procedures ◽  
Long Term Stability ◽  
Number Of Factors ◽  
The Stability ◽  
The Individual

As a result of the large-scale failure of the rubblemound breakwater at SINES, Portugal in 1978 a number of research programs were begun. At present, however, very little information is available from technical publications regarding new design criteria, recommendations, or test procedures for model tests of rubblemound breakwaters. The need still exists, therefore, for economically practical model tests and standardized test procedures so that more tests can be conducted and reproducible results from different institutions can be compared. At the same time, a number of factors related to the stability of rubblemound surface elements, and the interrelationships between those factors, have not been adequately examined or explained. Apparently without extensive model tests, for example, it has been suggested that greater stability can be obtained by using elements with greater unit weights (comparing elements of the same absolute weight) , either by adding scrap metal or denser materials, such as granite, to the concrete. Furthermore, susceptibility to breakage is of major importance to the long-term stability of armour layer units, particularly for dolos and similar less massive element types. This aspect has been generally neglected in laboratory tests, however, and attempts to simulate the lower ultimate strength of elements in reduced-scale model tests appear extremely difficult, as well as costly in terms of time and materials. Several other factors which can significantly affect the stability of an armour layer include the surface roughness of the individual elements, as well as boundary conditions such as the beach slope.

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