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New approach to dynamical Monte Carlo methods: application to an epidemic model

Author

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  • Aiello, O.E.
  • da Silva, M.A.A.

Abstract

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 forth order Runge–Kutta Method in a region of deterministic solution. We also show that purely local interactions reproduce a poissonian-like process at mesoscopic level. The simulations for this case are checked self-consistently using a stochastic version of the Euler Method.

Suggested Citation

  • Aiello, O.E. & da Silva, M.A.A., 2003. "New approach to dynamical Monte Carlo methods: application to an epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 327(3), pages 525-534.
    • Handle: RePEc:eee:phsmap:v:327:y:2003:i:3:p:525-534
    DOI: 10.1016/S0378-4371(03)00504-1
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    Cited by:

    1. Giannini, Massimo, 2004. "Job Search Mechanism and Individual Behaviour," Economics & Statistics Discussion Papers esdp04017, University of Molise, Department of Economics.
    2. Centres, P.M. & Perez-Morelo, D.J. & Guzman, R. & Reinaudi, L. & Gimenez, M.C., 2024. "Diffusion model for the spread of infectious diseases: SIR model with mobile agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    3. Massimo Giannini, 2006. "Job Search Mechanism and Individual Behaviour," Computational Economics, Springer;Society for Computational Economics, vol. 27(1), pages 89-113, February.
    4. Zhang, Zhonghua & Wu, Jianhua & Suo, Yaohong & Song, Xinyu, 2011. "The domain of attraction for the endemic equilibrium of an SIRS epidemic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(9), pages 1697-1706.

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