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Modelling and finite-time stability analysis of psoriasis pathogenesis |
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| Authors: | Harshal B Oza Rakesh Pandey Daniel Roper Yusur Al-Nuaimi Marc Goodfellow |
| Affiliation: | 1. School of Engineering and Applied Science, Ahmedabad University, Ahmedabad, India;2. College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK;3. National Oceanography Centre, Southampton, UK;4. Department of Dermatology, Royal Devon and Exeter Hospital, Exeter, UK;5. Centre for Biomedical Modelling and Analysis, University of Exeter, Exeter, UK;6. EPSRC Centre for Predictive Modelling in Healthcare, University of Exeter, Exeter, UK |
| Abstract: | 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. |
| Keywords: | Biological modelling psoriasis finite-time stability singular perturbation analysis |