Lie algebra solution of population models based on time-inhomogeneous Markov chains

TL;DR

This paper introduces a Lie algebraic method for solving time-inhomogeneous population models based on Markov chains, demonstrating its computational efficiency through three biological examples.

Contribution

It adapts Lie algebra techniques to ecological and social population models, providing a new, efficient solution approach not previously applied in these fields.

Findings

The method yields computationally efficient solutions.

Applied to three biological case studies.

Enhances analysis of time-inhomogeneous stochastic processes.

Abstract

Many natural populations are well modelled through time-inhomogeneous stochastic processes. Such processes have been analysed in the physical sciences using a method based on Lie algebras, but this methodology is not widely used for models with ecological, medical and social applications. This paper presents the Lie algebraic method, and applies it to three biologically well motivated examples. The result of this is a solution form that is often highly computationally advantageous.