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

Antunes, Pedro R. S.; Costa, Fernando Pestana da; Pinto, João Teixeira; Sasportes, Rafael

http://hdl.handle.net/10400.2/12368

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Authors

Antunes, Pedro R. S.

Costa, Fernando Pestana da

Pinto, João Teixeira

Sasportes, Rafael

Abstract(s)

We study the dynamics about equilibria of an infinite dimensional system of ordinary differential equations of coagulation–fragmentation–death type that was introduced recently by da Costa et al. (Eur J Appl Math 31(6):950–967, 2020) as a model for the silicosis disease mechanism. For a class of piecewise constant rate coefficients an appropriate change of variables allows for the appearance of a closed finite dimensional subsystem of the infinite-dimensional system and the analysis of the eigenvalues of the linearizations of this finite dimensional subsystem about the equilibria is then used to obtain the results on the stability of the equilibria in the original infinite dimensional model.

Keywords

Coagulation-fragmentation-death equations Model of silicosis Local stability of equilibria

URI

http://hdl.handle.net/10400.2/12368

Citation

Antunes, P.R.S., Costa, F.P.d., Pinto, J.T. et al. Modelling Silicosis: Dynamics of a Model with Piecewise Constant Rate Coefficients. J Dyn. Diff. Equat., 36, 1285–1310 (2024). https://doi.org/10.1007/s10884-022-10213-7