AN EXACT STOCHASTIC SIMULATION METHOD FOR FRACTIONAL ORDER COMPARTMENT MODELS

Zhuang Xu, Christopher N. Angstmann, Daniel Han, Bruce I. Henry, Stuart James M. Burney, Byron A. Jacobs

Research output: Contribution to journalArticlepeer-review

Abstract

Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models obtained by simply replacing integer order derivatives with fractional order derivatives. In these models, inherent stochasticity becomes important, particularly when dealing with the dynamics of small populations far from the continuum limit of large particle numbers. The necessity for stochastic simulations arises from deviations of the mean states from the solutions obtained from the governing equations in these scenarios. To address this, our work presents an exact stochastic simulation algorithm designed for fractional order compartment models, based on a semi-Markov process. We have considered a fractional order resusceptibility SIS model and a fractional order recovery SIR model as illustrative examples, highlighting significant disparities between deterministic and stochastic dynamics when the total population is small. Beyond its modeling applications, the algorithm presented serves as a versatile tool for solving fractional order differential equations via Monte Carlo simulations.

Original languageEnglish
Pages (from-to)2132-2151
Number of pages20
JournalSIAM Journal on Applied Mathematics
Volume84
Issue number5
DOIs
Publication statusPublished - 2024
Externally publishedYes

Keywords

  • compartment models
  • epidemiology
  • fractional calculus
  • pharmacokinetics
  • stochastic simulation method

ASJC Scopus subject areas

  • Applied Mathematics

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