Dynamical Behavior of a Stochastic SIRC Model for Influenza A

Zhang, Tongqian; Ding, Tingting; Gao, Ning; Song, Yi

doi:10.3390/sym12050745

Cited by 6 publications

(4 citation statements)

References 48 publications

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“…In work by Casagrandiet et al [3] a SIRC model is presented for describing the dynamic behavior of influenza A by introducing a new component, namely, cross-immunity (C) part of population for people who have recovered from infection with different strains of the same virus subtype at previous time intervals. In [4][5][6] this idea was developed and it was shown in [7] that this model can be used to take into account the infected but asymptomatic part of the population.…”

Section: The Sirc Modelmentioning

confidence: 99%

Mean field game for modeling of COVID-19 spread

Petrakova¹,

Krivorotko²

2021

Preprint

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The paper presents the one of possible approach to model the epidemic propagation. The proposed model is based on the mean-field control inside separate groups of population, namely, suspectable (S), infected (I), removed (R) and cross-immune (C). In the paper the numerical algorithm to solve such a problem is presented, which ensures the conservation the total mass of population during timeline. Numerical experiments demonstrate the result of modelling the propagation of COVID-19 virus during two 100 day periods in Novosibirsk (Russia).

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Section: The Sirc Modelmentioning

confidence: 99%

Mean field game for modeling of COVID-19 spread

Petrakova¹,

Krivorotko²

2021

Preprint

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“…The analysis of symmetry features of ODEs and PDEs is a popular and well-established topic (see [16,17]) and provides a valuable tool for better comprehension of the solution's qualitative behavior. In contrast, a similar theory of SDE symmetries was just recently constructed; the readers are suggested to see [18][19][20]. In this work, we studied a stochastic COVID-19 model by using a very general and elegant approach for solving a SDE via symmetries in a dynamical perspective.…”

Section: Introductionmentioning

confidence: 99%

Extinction and Ergodic Stationary Distribution of COVID-19 Epidemic Model with Vaccination Effects

Batool

Sun

2023

Symmetry

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Human society always wants a safe environment from pollution and infectious diseases, such as COVID-19, etc. To control COVID-19, we have started the big effort for the discovery of a vaccination of COVID-19. Several biological problems have the aspects of symmetry, and this theory has many applications in explaining the dynamics of biological models. In this research article, we developed the stochastic COVID-19 mathematical model, along with the inclusion of a vaccination term, and studied the dynamics of the disease through the theory of symmetric dynamics and ergodic stationary distribution. The basic reproduction number is evaluated using the equilibrium points of the proposed model. For well-posedness, we also test the given problem for the existence and uniqueness of a non-negative solution. The necessary conditions for eradicating the disease are also analyzed along with the stationary distribution of the proposed model. For the verification of the obtained result, simulations of the model are performed.

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“…In the past few decades, mathematical models based on diffusion processes were fruitfully applied to describe stochasticity phenomena belonging to even extremely different disciplinary fields that range in scale from human population in biology [2] to cryptocurrency in finance [3] and from infectious disease in medicine [4] to networks in neuroscience [5]. Mixed-effect parameters diffusion processes provide a convenient tool to account for differences between several experiments or several subjects [6].…”

Section: Introductionmentioning

confidence: 99%

Symmetric and Asymmetric Diffusions through Age-Varying Mixed-Species Stand Parameters

Rupšys

Petrauskas

2021

Symmetry

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(1) Background: This paper deals with unevenly aged, whole-stand models from mixed-effect parameters diffusion processes and Voronoi diagram points of view and concentrates on the mixed-species stands in Lithuania. We focus on the Voronoi diagram of potentially available areas to tree positions as the measure of the competition effect of individual trees and the tree diameter at breast height to relate their evolution through time. (2) Methods: We consider a bivariate hybrid mixed-effect parameters stochastic differential equation for the parameterization of the diameter and available polygon area at age to ensure a proper description of the link between them during the age (time) span of a forest stand. In this study, the Voronoi diagram was used as a mathematical tool for the quantitative characterization of inter-tree competition. (3) Results: The newly derived model considers bivariate correlated observations, tree diameter, and polygon area arising from a particular stand and enables defining equations for calculating diameter, polygon-area, and stand-density predictions and forecasts. (4) Conclusions: From a statistical point of view, the newly developed models produced acceptable statistical measures of predictions and forecasts. All the results were implemented in the Maple computer algebra system.

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Dynamical Behavior of a Stochastic SIRC Model for Influenza A

Cited by 6 publications

References 48 publications

Mean field game for modeling of COVID-19 spread

Mean field game for modeling of COVID-19 spread

Extinction and Ergodic Stationary Distribution of COVID-19 Epidemic Model with Vaccination Effects

Symmetric and Asymmetric Diffusions through Age-Varying Mixed-Species Stand Parameters

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