Harmonic Oscillators of Mathematical Biology: Many Faces of a Predator-Prey Model

TL;DR

This paper reveals that various biological models, including virus dynamics and epidemiology, can be viewed as damped predator-prey systems similar to harmonic oscillators, using Lyapunov functions for analysis.

Contribution

It introduces a unified framework linking biological models to damped harmonic oscillators and employs Lyapunov functions to analyze their dynamics.

Findings

Biological models can be reformulated as damped predator-prey systems.

Lyapunov functions help characterize the stability and behavior of these models.

The analogy provides new insights into the dynamics of biological systems.

Abstract

We show that a number of models in virus dynamics, epidemiology and plant biology can be presented as ``damped" versions of the Lotka-Volterra predator-prey model, by analogy to the damped harmonic oscillator. The analogy deepens with the use of Lyapunov functions, which allow us to characterize their dynamics and even make some estimates.