Dynamical Monte Carlo method for stochastic epidemic models

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 so...

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Bibliographic Details
Published in:arXiv.org 2003-01
Main Authors: Aiello, O E, M A A da Silva
Format: Article
Language:English
Subjects:
Computer simulation
Differential equations
Epidemics
Immunity
Markov processes
Monte Carlo simulation
Runge-Kutta method
Stochastic models
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Summary: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 Introducing local stochastic interactions, the Runge-Kutta method is no longer applicable.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.
ISSN:2331-8422