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

Mario Natiello; Raúl H. Barriga; Marcelo Otero; Hernán G Solari

doi:10.1080/25742558.2018.1556192

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

Mario Natiello, Raúl H. Barriga, Marcelo Otero, Hernán G Solari

University of Buenos Aires

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Journal	Cogent mathematics and Statistics
DOIs	https://doi.org/10.1080/25742558.2018.1556192
Publication status	Published - 2018 Dec 7

Subject classification (UKÄ)

Probability Theory and Statistics
Health Sciences
Other Biological Topics

Free keywords

Jump Processes, Continuous-time Markov Chains, Approximating Methods, Multinomial Processes, Feller-Kendall Algorithm, SIRS Epidemic Model

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1080/25742558.2018.1556192Licence: CC BY

Cite this

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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 detailand 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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T1 - Multinomial approximation to the Kolmogorov Forward Equation for jump (population) processes

AU - Natiello, Mario

AU - Barriga, Raúl H.

AU - Otero, Marcelo

AU - Solari, Hernán G

PY - 2018/12/7

Y1 - 2018/12/7

N2 - 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 detailand 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.

AB - 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 detailand 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.

KW - Jump Processes, Continuous-time Markov Chains, Approximating Methods, Multinomial Processes, Feller-Kendall Algorithm, SIRS Epidemic Model

U2 - 10.1080/25742558.2018.1556192

DO - 10.1080/25742558.2018.1556192

M3 - Article

SN - 2574-2558

JO - Cogent mathematics and Statistics

JF - Cogent mathematics and Statistics

ER -

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

Abstract

Subject classification (UKÄ)

Free keywords

UN SDGs

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