# Modelling Silicosis: The Structure of Equilibria

## TL;DR

This paper analyzes the equilibrium structures of a complex coagulation-fragmentation-death model for silicosis, providing exact results, existence conditions, and asymptotic analysis for different coefficient cases.

## Contribution

It offers new mathematical insights into the equilibrium multiplicity, existence, and asymptotics of the silicosis model with various coefficient configurations.

## Key findings

- Exact multiplicity results for piecewise-constant coefficients
- Conditions for existence and non-existence of equilibria
- Asymptotic behavior for power law coefficient cases

## Abstract

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, results on existence and non-existence of equilibria in the general case, as well as precise asymptotics for the infinite series that arise in the case of power law coefficients.