• Corpus ID: 237416529

Modelling silicosis: dynamics of a model with piecewise constant rate coefficients

@inproceedings{Antunes2021ModellingSD,
  title={Modelling silicosis: dynamics of a model with piecewise constant rate coefficients},
  author={Pedro R. S. Antunes and Fernando P. da Costa and Joao T. Pinto and Rafael Sasportes},
  year={2021}
}
We study the dynamics about equilibria of an infinite dimension coagulation-fragmentation-death model for the silicosis disease mechanism introduced recently by da Costa, Drmota, and Grinfeld (2020) [3] in the case where the rate coefficients are piecewise constant. 

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References

SHOWING 1-10 OF 17 REFERENCES
Modelling silicosis: The structure of equilibria
We analyse the structure of equilibria of a coagulation–fragmentation–death model of silicosis. We present exact multiplicity results in the particular case of piecewise constant coefficients,
Long-time behaviour and self-similarity in a coagulation equation with input of monomers
For a coagulation equation with Becker { Doring type interactions and time-independent monomer input we study the detailed long-time behaviour of nonnegative solutions and prove the convergence to a
On the self-similar behaviour of coagulation systems with injection
In this paper we prove the existence of a family of self-similar solutions for a class of coagulation equations with a constant flux of particles from the origin. These solutions are expected to
The Becker-Döring cluster equations: Basic properties and asymptotic behaviour of solutions
Existence and uniqueness results are established for solutions to the Becker-Döring cluster equations. The density ϱ is shown to be a conserved quantity. Under hypotheses applying to a model of a
Mathematical model of phagocytosis and inflammation after the inhalation of quartz at different concentrations.
TLDR
A mathematical model was developed with several distinctive features to represent the various processes leading to silicosis and assures the phagocytosis of quartz by the resident alveolar macrophages, and describes the pathological and other biological reactions to quartz particles in the interstitium.
The phagocytosis of crystalline silica particles by macrophages.
TLDR
It is demonstrated that macrophages internalize silica and that nonopsonized phagocytosis occurs by a temporally, and possibly mechanistically, distinct pathway from Fc receptor-mediated phagcytosis.
Silica binding and toxicity in alveolar macrophages.
TLDR
Current research ideas on silica toxicity and binding in the alveolar macrophage are reviewed and discussed.
Artificial Stone Associated Silicosis: A Systematic Review
TLDR
The characteristics of AS-associated silicosis were comparable to those that were reported for the disease in traditional silica exposure settings, but some critical issues emerged concerning the general lack of suitable strategies for assessing/managing silica risks in these innovative occupational fields.
structure of equilibria, Euro
  • J. Appl. Math., 31 (6),
  • 2020
Velázquez, On the self-similar behaviour of coagulation systems with injection, preprint (June
  • 2021
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