## 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.

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 |
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Journal | Cogent mathematics and Statistics |

DOIs | |

Publication status | Published - 2018 Dec 7 |

## Subject classification (UKÄ)

- Probability Theory and Statistics
- Public Health, Global Health, Social Medicine and Epidemiology
- Other Biological Topics

## Free keywords

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