<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we analyse the local stability of a gene-regulatory network and immunotherapy for cancer modelled as nonlinear time-delay systems. A numerically generated kernel, using the sum-of-squares decomposition of multivariate polynomials, is used in the construction of an appropriate Lyapunov–Krasovskii functional for stability analysis of the networks around an equilibrium point. This analysis translates to verifying equivalent LMI conditions. A delay-independent asymptotic stability of a second-order model of a gene regulatory network, taking into consideration multiple commensurate delays, is established. In the case of cancer immunotherapy, a predator–prey type model is adopted to describe the dynamics with cancer cells and immune cells contributing to the predator–prey population, respectively. A delay-dependent asymptotic stability of the cancer-free equilibrium point is proved. Apart from the system and control point of view, in the case of gene-regulatory networks such stability analysis of dynamics aids mimicking gene networks synthetically using integrated circuits like neurochips learnt from biological neural networks, and in the case of cancer immunotherapy it helps determine the long-term outcome of therapy and thus aids oncologists in deciding upon the right approach.</p></abstract>

In this paper, we analyse the local stability of a gene-regulatory network and immunotherapy for cancer modelled as nonlinear time-delay systems. A numerically generated kernel, using the sum-of-squares decomposition of multivariate polynomials, is used in the construction of an appropriate Lyapunov–Krasovskii functional for stability analysis of the networks around an equilibrium point. This analysis translates to verifying equivalent LMI conditions. A delay-independent asymptotic stability of a second-order model of a gene regulatory network, taking into consideration multiple commensurate delays, is established. In the case of cancer immunotherapy, a predator–prey type model is adopted to describe the dynamics with cancer cells and immune cells contributing to the predator–prey population, respectively. A delay-dependent asymptotic stability of the cancer-free equilibrium point is proved. Apart from the system and control point of view, in the case of gene-regulatory networks such stability analysis of dynamics aids mimicking gene networks synthetically using integrated circuits like neurochips learnt from biological neural networks, and in the case of cancer immunotherapy it helps determine the long-term outcome of therapy and thus aids oncologists in deciding upon the right approach.

Stability Analysis of Nonlinear Time–Delayed Systems with Application to Biological Models

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In this paper, we analyse the local stability of a gene-regulatory network and immunotherapy for cancer modelled as nonlinear time-delay systems. A numerically...

Stability Analysis of Nonlinear Time–Delayed Systems with Application to Biological Models

Published Online: May 04, 2017

Page range: 91 - 103

Received: Apr 05, 2016

Accepted: Oct 12, 2016

DOI: https://doi.org/10.1515/amcs-2017-0007

Keywords
time-delay, cancer immunotherapy, gene-regulatory network, sum of squares

© by Arun D. Mahindrakar

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Stability Analysis of Nonlinear Time–Delayed Systems with Application to Biological Models

Published Online: May 04, 2017

Page range: 91 - 103

Received: Apr 05, 2016

Accepted: Oct 12, 2016

DOI: https://doi.org/10.1515/amcs-2017-0007

Keywordstime-delay, cancer immunotherapy, gene-regulatory network, sum of squares

© by Arun D. Mahindrakar

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
time-delay, cancer immunotherapy, gene-regulatory network, sum of squares