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Multinomial approximation to the Kolmogorov Forward Equation for jump (population) processes

Natiello, Mario LU ; Barriga, Raúl H.; Otero, Marcelo and Solari, Hernán G (2018) In Cogent mathematics and Statistics
Abstract
We develop a simulation method for Markov Jump processes with finite time steps based in a quasilinear approximation of the process and in multinomial random deviates. The second order approximation to the generating function, Error$=O(dt^{2})$, is developed in detail
and an algorithm is presented. The algorithm is implemented for a Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic model and compared to both the deterministic approximation and the exact simulation. Special attention is given to the problem of extinction of the infected population which is the most critical condition for the approximation.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Jump Processes, Continuous-time Markov Chains, Approximating Methods, Multinomial Processes, Feller-Kendall Algorithm, SIRS Epidemic Model
in
Cogent mathematics and Statistics
publisher
Taylor & Francis
ISSN
2574-2558
DOI
10.1080/25742558.2018.1556192
language
English
LU publication?
yes
id
ab542993-b3c4-4429-8f72-c809dd426250
date added to LUP
2018-12-22 23:02:48
date last changed
2019-05-24 19:25:38
@article{ab542993-b3c4-4429-8f72-c809dd426250,
  abstract     = {We develop a simulation method for Markov Jump processes with finite time steps based in a quasilinear approximation of the process and in multinomial random deviates. The second order approximation to the generating function, Error$=O(dt^{2})$, is developed in detail<br/>and an algorithm is presented. The algorithm is implemented for a Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic model and compared to both the deterministic approximation and the exact simulation. Special attention is given to the problem of extinction of the infected population which is the most critical condition for the approximation.},
  author       = {Natiello, Mario and Barriga, Raúl H. and Otero, Marcelo and Solari, Hernán G},
  issn         = {2574-2558},
  keyword      = {Jump Processes, Continuous-time Markov Chains, Approximating Methods, Multinomial Processes, Feller-Kendall Algorithm, SIRS Epidemic Model},
  language     = {eng},
  month        = {12},
  publisher    = {Taylor & Francis},
  series       = {Cogent mathematics and Statistics},
  title        = {Multinomial approximation to the Kolmogorov Forward Equation for jump (population) processes},
  url          = {http://dx.doi.org/10.1080/25742558.2018.1556192},
  year         = {2018},
}