Modelling and finite-time stability analysis of psoriasis pathogenesis

Oza, Harshal B.; Pandey, Rakesh; Roper, Daniel; Al-Nuaimi, Yusur; Spurgeon, Sarah K.; Goodfellow, Marc. 2017 Modelling and finite-time stability analysis of psoriasis pathogenesis. International Journal of Control, 90 (8). 1664-1677. https://doi.org/10.1080/00207179.2016.1217566

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Official URL: https://doi.org/10.1080/00207179.2016.1217566

Abstract/Summary

A new systems model of psoriasis is presented and analysed from the perspective of control theory. Cytokines are treated as actuators to the plant model that govern the cell population under the reasonable assumption that cytokine dynamics are faster than the cell population dynamics. The analysis of various equilibria is undertaken based on singular perturbation theory. Finite-time stability and stabilisation have been studied in various engineering applications where the principal paradigm uses non-Lipschitz functions of the states. A comprehensive study of the finite-time stability properties of the proposed psoriasis dynamics is carried out. It is demonstrated that the dynamics are finite-time convergent to certain equilibrium points rather than asymptotically or exponentially convergent. This feature of finite-time convergence motivates the development of a modified version of the Michaelis–Menten function, frequently used in biology. This framework is used to model cytokines as fast finite-time actuators.

Item Type:	Publication - Article
Digital Object Identifier (DOI):	https://doi.org/10.1080/00207179.2016.1217566
ISSN:	0020-7179
Date made live:	17 Aug 2017 16:08 +0 (UTC)
URI:	https://nora.nerc.ac.uk/id/eprint/517637

Item Type:

Publication - Article

Digital Object Identifier (DOI):

https://doi.org/10.1080/00207179.2016.1217566

ISSN:

0020-7179

Date made live:

17 Aug 2017 16:08 +0 (UTC)

URI:

https://nora.nerc.ac.uk/id/eprint/517637