Linear Autonomous Pool Models (LAPM)

LAPM is a simple Python package to deal with linear autonomous pool models of the form

\[\frac{d}{dt}\,x(t) = B\,x(t) + u.\]

It provides symbolic and numerical computation of

  • steady state content

  • steady state release

  • transit time, system age, pool age

    • density

    • (cumulative distribution function)

    • mean

    • standard deviation

    • variance

    • higher order moments

    • (Laplace transforms)

Table of Contents

phase_type

Module for phase-type distribution.

linear_autonomous_pool_model

Module for linear autonomous pool models.

dtmc

Module for discrete-time Markov chains (DTMCs).

example_models

Example linear autonomous pool models.

emanuel

Example: Emanuel’s model

Important Note

\(\bf{B}=(b_{ij})\) has always to be an invertible compartmental matrix:

  • \(b_{ii}<0\) for all \(i\)

  • \(b_{ij}\geq 0\) for \(i\neq j\)

  • \(\sum\limits_{i=1}^d b_{ij}\leq 0\) for all \(j\)

Indices and tables