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 ) .
Highlights
In recent years, the emergence of Zika and Ebola viruses have attracted much attention from the scientific community after reports of their aggressive effects, respectively, microcephaly in newborns [1] and high mortality rate [2,3,4]
agent-based epidemic models (ABEM) describe the stochastic dynamics of disease-spreading processes in networks
By exploiting cyclic permutation symmetries, relevant elements of the dynamics are confined to a single permutation sector, significantly reducing computational efforts
Summary
The emergence of Zika and Ebola viruses have attracted much attention from the scientific community after reports of their aggressive effects, respectively, microcephaly in newborns [1] and high mortality rate [2,3,4]. The susceptible-infected-susceptible model (SIS) is the simplest ABEM It considers only two health states for agents, infected |1 or susceptible |0 , and the occurrence of the following events during a time interval δt [10,11]. In the SIS model, recovery events result from actions of one-body operators, σk−nk ≡ σk−, on configuration vectors. The vectors |μp satisfy the eigenvalue equation P|μp = e−2iπp/N|μp They are useful to identify symmetries, as they never change link distributions, only node labels. Tcan be written using |μp and, more importantly, transitions between eigenvectors with distinct eigenvalues are prohibited This feature leads to a block diagonal form to the matrix representation of T
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