scholarly journals Stability and Asymptotic Behavior of a Regime-Switching SIRS Model with Beddington–DeAngelis Incidence Rate

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Shan Wang ◽  
Youhua Peng ◽  
Feng Wang
Keyword(s):  
Asymptotic Behavior ◽  
Incidence Rate ◽  
Regime Switching ◽  
Invariant Set ◽  
Stochastic Noise ◽  
Threshold Values ◽  
Unique Positive Solution ◽  
Stochastic Asymptotic Stability ◽  
Sirs Model

A regime-switching SIRS model with Beddington–DeAngelis incidence rate is studied in this paper. First of all, the property that the model we discuss has a unique positive solution is proved and the invariant set is presented. Secondly, by constructing appropriate Lyapunov functionals, global stochastic asymptotic stability of the model under certain conditions is proved. Then, we leave for studying the asymptotic behavior of the model by presenting threshold values and some other conditions for determining disease extinction and persistence. The results show that stochastic noise can inhibit the disease and the behavior will have different phenomena owing to the role of regime-switching. Finally, some examples are given and numerical simulations are presented to confirm our conclusions.

scholarly journals Dynamics of a Stochastic SIRS Epidemic Model with Regime Switching and Specific Functional Response

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Amine EL Koufi ◽  
Abdelkrim Bennar ◽  
Noura Yousfi
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Regime Switching ◽  
Unique Positive Solution ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Incident Rate ◽  
Stochastic Sirs Epidemic Model

The purpose of this work is to investigate the dynamic behaviors of the SIRS epidemic model with nonlinear incident rate under regime switching. We establish the existence of a unique positive solution of our system. Furthermore, we obtain the conditions for the extinction of diseases, and we show the existence of the stationary distribution for our stochastic SIRS model under regime switching. Numerical simulations are employed to illustrate our theoretical analysis.

scholarly journals A Stochastic Kinetic Type Reactions Model for COVID-19

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1221
Author(s):  
Giorgio Sonnino ◽  
Fernando Mora ◽  
Pasquale Nardone
Keyword(s):  
Real Data ◽  
Stochastic Noise ◽  
Mathematical Basis ◽  
Sis Model ◽  
Theoretical Predictions ◽  
Coronavirus Infection ◽  
Massive Distribution ◽  
Second Wave ◽  
Stochastic Sis Model

We propose two stochastic models for the Coronavirus pandemic. The statistical properties of the models, in particular the correlation functions and the probability density functions, were duly computed. Our models take into account the adoption of lockdown measures as well as the crucial role of hospitals and health care institutes. To accomplish this work we adopt a kinetic-type reaction approach where the modelling of the lockdown measures is obtained by introducing a new mathematical basis and the intensity of the stochastic noise is derived by statistical mechanics. We analysed two scenarios: the stochastic SIS-model (Susceptible ⇒ Infectious ⇒ Susceptible) and the stochastic SIS-model integrated with the action of the hospitals; both models take into account the lockdown measures. We show that, for the case of the stochastic SIS-model, once the lockdown measures are removed, the Coronavirus infection will start growing again. However, the combined contributions of lockdown measures with the action of hospitals and health institutes is able to contain and even to dampen the spread of the SARS-CoV-2 epidemic. This result may be used during a period of time when the massive distribution of vaccines in a given population is not yet feasible. We analysed data for USA and France. In the case of USA, we analysed the following situations: USA is subjected to the first wave of infection by Coronavirus and USA is in the second wave of SARS-CoV-2 infection. The agreement between theoretical predictions and real data confirms the validity of our approach.

scholarly journals The Invariant Set Postulate: a new geometric framework for the foundations of quantum theory and the role played by gravity

2009 ◽  
Vol 465 (2110) ◽  
pp. 3165-3185 ◽  
Author(s):  
T. N. Palmer
Keyword(s):  
Quantum Theory ◽  
Science Fiction ◽  
State Space ◽  
Fractal Geometry ◽  
Quantum Physics ◽  
Nonlinear Dynamical Systems ◽  
Physical Reality ◽  
Invariant Set ◽  
Geometric Framework

A new law of physics is proposed, defined on the cosmological scale but with significant implications for the microscale. Motivated by nonlinear dynamical systems theory and black-hole thermodynamics, the Invariant Set Postulate proposes that cosmological states of physical reality belong to a non-computable fractal state-space geometry I , invariant under the action of some subordinate deterministic causal dynamics D I . An exploratory analysis is made of a possible causal realistic framework for quantum physics based on key properties of I . For example, sparseness is used to relate generic counterfactual states to points p ∉ I of unreality, thus providing a geometric basis for the essential contextuality of quantum physics and the role of the abstract Hilbert Space in quantum theory. Also, self-similarity, described in a symbolic setting, provides a possible realistic perspective on the essential role of complex numbers and quaternions in quantum theory. A new interpretation is given to the standard ‘mysteries’ of quantum theory: superposition, measurement, non-locality, emergence of classicality and so on. It is proposed that heterogeneities in the fractal geometry of I are manifestations of the phenomenon of gravity. Since quantum theory is inherently blind to the existence of such state-space geometries, the analysis here suggests that attempts to formulate unified theories of physics within a conventional quantum-theoretic framework are misguided, and that a successful quantum theory of gravity should unify the causal non-Euclidean geometry of space–time with the atemporal fractal geometry of state space. The task is not to make sense of the quantum axioms by heaping more structure, more definitions, more science fiction imagery on top of them, but to throw them away wholesale and start afresh. We should be relentless in asking ourselves: From what deep physical principles might we derive this exquisite structure? These principles should be crisp, they should be compelling. They should stir the soul. Chris Fuchs ( Gilder 2008 , p. 335)

Sociо-economic security as a factor in the development of the state

2021 ◽  
Vol 5 (1) ◽  
pp. 19-25
Author(s):  
E.L. Arhipov ◽  
◽  
E.N. Boguslav ◽  
Klimina K.V. ◽  
◽  
...  
Keyword(s):  
Economic System ◽  
Economic Security ◽  
The State ◽  
Threshold Values ◽  
Criteria And Indicators ◽  
Entire Process ◽  
Methodological Basis ◽  
Development Rates ◽  
Economic Sphere

The article examines one of the most important topics of our state, which affects its development - social and economic security. With the help of the methodological basis, the analysis of assessments of economic security and their threshold values, the entire process of ensuring the socio-economic security of the Rus-sian Federation is being studied. Threats and ways of their solution are identified on the basis of the stud-ied criteria and indicators, as well as the role of the interests of members of society in the socio-economic system of the country. One of the main tools and factors in the development of Russia is the methodological substantiation and analysis, based on indicators, of ensuring socio-economic security, since they help to predict the direction of the state's development rates in the economic sphere, as well as the effectiveness of government bodies’ work.

The Role of Stochastic Noise on the Glass Transition

1995 ◽  
Vol 407 ◽  
Author(s):  
Fernando C. Perez-Cardenas ◽  
Hao Gan
Keyword(s):  
Relaxation Time ◽  
Glass Transition ◽  
Time Spectrum ◽  
Structure Evolution ◽  
Stochastic Noise ◽  
Relaxation Time Spectrum ◽  
Glass Transition Region ◽  
Type Differential Equation ◽  
Glass Relaxation

ABSTRACTGlasses are amorphous solids that exhibit an intricate structural relaxation. A broad relaxation time spectrum always emerges when these systems are perturbed. By using a Langevin-type differential equation to describe the structure dynamicsof these materials, it is depicted how the broad relaxation time spectrum arises due to the stochastic noise and how this affects the system's structure evolution as it is cooled down into the glass transition region. This stochastic model provides a macroscopic as well a microscopic view of the glass relaxation process.

Dynamics Analysis of an SEIQS Model with a Nonlinear Incidence Rate

2012 ◽  
Vol 157-158 ◽  
pp. 1220-1223
Author(s):  
Ning Cui ◽  
Jun Hong Li ◽  
Jiao Qu ◽  
Hong Dan Xue
Keyword(s):  
Lyapunov Function ◽  
Incidence Rate ◽  
Matrix Theory ◽  
Invariant Set ◽  
Dynamics Analysis ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Asymptotical Stable ◽  
Compound Matrix ◽  
Disease Free

This paper considers an SEIQS model with nonlinear incidence rate. By means of Lyapunov function and LaSalle’s invariant set theorem, we proved the global asymptotical stable results of the disease-free equilibrium. It is then obtained the sufficent conditions for the global stability of the endemic equilibrium by the compound matrix theory. In addition, we also study the phenomena of limit cycle of the systems with the numerical simulations.

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