Multinomial approximation to the Kolmogorov Forward Equation for jump (population) processes
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/ab542993-b3c4-4429-8f72-c809dd426250
- author
- Natiello, Mario LU ; Barriga, Raúl H. ; Otero, Marcelo and Solari, Hernán G
- organization
- publishing date
- 2018-12-07
- 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
- 2020-06-05 15:49:46
@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}}, keywords = {{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}}, doi = {{10.1080/25742558.2018.1556192}}, year = {{2018}}, }