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Finite Symmetries in Agent-Based Epidemic Models

1
Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP), Universidade de São Paulo (USP), Avenida Bandeirantes 3900, 14040-901 Ribeirão Preto, São Paulo, Brazil
2
Instituto Nacional de Ciência e Technologia de Sistemas Complexos (INCT-SC), Rua Dr. Xavier Sigaud 150, Urca, 22290-180 Rio de Janeiro, Brazil
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2019, 24(2), 44; https://doi.org/10.3390/mca24020044
Received: 1 March 2019 / Revised: 10 April 2019 / Accepted: 21 April 2019 / Published: 23 April 2019
(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)
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Abstract

Predictive analysis of epidemics often depends on the initial conditions of the outbreak, the structure of the afflicted population, and population size. However, disease outbreaks are subjected to fluctuations that may shape the spreading process. Agent-based epidemic models mitigate the issue by using a transition matrix which replicates stochastic effects observed in real epidemics. They have met considerable numerical success to simulate small scale epidemics. The problem grows exponentially with population size, reducing the usability of agent-based models for large scale epidemics. Here, we present an algorithm that explores permutation symmetries to enhance the computational performance of agent-based epidemic models. Our findings bound the stochastic process to a single eigenvalue sector, scaling down the dimension of the transition matrix to o ( N 2 ) . View Full-Text
Keywords: Markov processes; computational methods; epidemic models; complex systems; nonlinear dynamics Markov processes; computational methods; epidemic models; complex systems; nonlinear dynamics
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Nakamura, G.M.; Monteiro, A.C.P.; Cardoso, G.C.; Martinez, A.S. Finite Symmetries in Agent-Based Epidemic Models. Math. Comput. Appl. 2019, 24, 44.

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