Ordinary Differential Equations

Parvinen, K. ORCID: https://orcid.org/0000-0001-9125-6041 (2022). Ordinary Differential Equations. In: Systems Biology Modelling and Analysis: Formal Bioinformatics Methods and Tools. Eds. De Maria, E., pp. 339-361 Hoboken, NJ: John Wiley & Sons, Inc.. ISBN 978-1-119716-5-3 10.1002/9781119716600.ch9.

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Abstract

Ordinary differential equations (ODEs) are widely used in the modelling of biological systems. They are especially useful in modelling large collections of individuals or molecules so that their amounts can be described by densities and when the essential reactions and events take place in continuous time. In this chapter, we consider solving ODEs and also describe methods for finding equilibria and determining their stability, which is especially useful when no analytical solution to the ODE can be found. We also consider the mechanistic derivation of ODEs using elementary reactions. We illustrate the usefulness of ODEs in biological modelling with two examples. The classical Lotka–Volterra predator–prey model is viewed by some as the starting point of mathematical biology. It was used to explain some unexpected effects of fishing to the fish population and catch. As another more recent example, we investigate a model describing the dynamics of cancer cells and killer T-cells, which can be used to increase our understanding of the effect of various treatments to different cancer patients.

Item Type:	Book Section
Research Programs:	Advancing Systems Analysis (ASA) Advancing Systems Analysis (ASA) > Cooperation and Transformative Governance (CAT) Advancing Systems Analysis (ASA) > Exploratory Modeling of Human-natural Systems (EM)
Depositing User:	Michaela Rossini
Date Deposited:	21 Feb 2023 13:24
Last Modified:	21 Feb 2023 13:24
URI:	https://pure.iiasa.ac.at/18638

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