Dynamical Monte Carlo method for stochastic epidemic models

Details Dynamical Monte Carlo method for stochastic epidemic models Dynamical Monte Carlo method for stochastic epidemic models

2002-08-26

arxiv.org/abs/physics/0208089v2

Physics

Biological Physics

18 pages, 4 figures in ps format, regular article, Latex, written with Scientific WorkPlace 3.51

Scientific paper

In this work we introduce a new approach to Dynamical Monte Carlo methods to simulate markovian processes. We apply this approach to formulate and study an epidemic generalized SIRS model. The results are in excellent agreement with the fourth order Runge-Kutta method in a region of deterministic solution. Introducing local stochastic interactions, the Runge-Kutta method is no longer applicable. Thus, we solve the system described by a set of stochastic differential equations by a Dynamical Monte Carlo technique and check the solutions self-consistently with a stochastic version of the Euler method. We also analyzed the results under the herd-immunity concept.

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