• Corpus ID: 237416529

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

  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},
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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  • J. Appl. Math., 31 (6),
  • 2020
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