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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Solution of deterministic-stochastic epidemic models by dynamical Monte Carlo method

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Aièllo, O. E. ; Haas, V. J. ; Silva, M. A. A. da ; Caliri, A.
Total Authors: 4
Document type: Journal article
Source: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS; v. 282, n. 3/4, p. 546-558, July 2000.
Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics

This work is concerned with dynamical Monte Carlo (MC) method and its application to models originally formulated in a continuous-deterministic approach. Specifically, a susceptible-infected-removed-susceptible (SIRS) model is used in order to analyze aspects of the dynamical MC algorithm and achieve its applications in epidemic contexts. We first examine two known approaches to the dynamical interpretation of the MC method and follow with tilt: application of one of them in the SIRS model. The working method chosen is based on the Poisson process where hierarchy of events, properly calculated waiting time between events, and independence of the events simulated, are the basic requirements. To verify the consistence of the method, some preliminary MC results are compared against exact steady-state solutions and other general numerical results (provided by Runge-Kuna method): good agreement is found. Finally, a space-dependent extension of the SIRS model is introduced and treated by MC. The results are interpreted under and in accordance with aspects of the herd-immunity concept. (AU)