Temporal duration and event size distribution at the epidemic threshold.
The epidemic event, seen as a nonequilibrium dynamic process, is studied through a simple stochastic system reminiscent of the classical SIR model. The system is described in terms of global and local variables and was mainly treated by means of Monte Carlo simulation; square lattices N×N, with N=23, 51, 100, 151, and 211 were used. Distinct extensive runs were performed and then classified as corresponding to epidemic or non-epidemic phase. They were examined with detail through the analysis of the event duration and event size; illustrations, such as density-like plots in the space of the model's parameters, are provided. The epidemic/non-epidemic phase presents smaller/larger relative fluctuations, whereas closer to the threshold the uncertainty reaches its highest values. Far enough from the threshold, the distribution φ(t) of the events time duration t shows a step-like appearance. However at the threshold line it shows an exponential behavior of the form φ (t) ∼ exp (-ωt); the same behavior is observed for the event size distribution. These results help to explain why the approach to epidemic threshold would be hard to anticipate with standard census data.
Departamento de Física e Matemática, Universidade de São Paulo, FFCLRP - 14040-900 Ribeirão Preto, SP - Brasil.
V J
VJ
Haas
A
A
Caliri
M A
MA
da Silva
Epidemic size; Monte Carlo; global/local variables; phase; scaling; threshold