Nonlinear Analysis of Guillain Barré Time Series to Elucidate Its Epidemiology

The etiology of Guillain Barré Syndrome (GBS) is not fully clarified, and there is a lack of agreement concerning its putative epidemic character. The low incidence rate of this disease is a disadvantage for employing the traditional statistical methods used in the analysis of epidemics. The objective of this paper is to clarify the GBS epidemic behavior applying a nonlinear time series identification approach. The authors obtained one time series of GBS and nine series of classical infectious epidemics (5 national and 4 international). These data were processed with advanced techniques of statistical time series analysis. This paper shows that GBS behaves similar to the other time series of classical epidemic studied. It corresponds to a nonlinear dynamics, with a point attractor. The spectral analysis pointed to an annual periodicity, and preference for the warmest month of the year was found. These results might suggest that Guillain Barré Syndrome has an epidemic behavior. The adequacy of nonlinear methods for analyzing the dynamics of epidemics, particularly those with low incidence rate, such as GBS was revealed. 1. Introduction The Guillain Barré Syndrome is an acute autoimmune neuropathy. It’s epidemiology is a broadly approached topic in the literature, but there are still aspects where opinions diverge or are even diametrically opposed [1]. The epidemiological behavior of GBS is one of the most controversial issues. Some authors report outbreaks or “striking fluctuations” in the incidence and confirm that it behaves periodically and shows seasonal variation [2–11]. The occurrence of outbreaks and the presence of periodicity and seasonal preference of the incidence are aspects that suggest an epidemic behavior. Nevertheless, some authors have found that incidence of this syndrome is stable throughout the year and even for longer periods of observation and deny any seasonal variation or periodicity [12–17]. The endemic channel and other statistical tools for epidemiological surveillance show limitations when the epidemic analyzed has a low level of endemicity or when fluctuations of the incidence, which could be considered as outbreaks are not numerically large, as occuring in GBS. Some models have been proposed to study the dynamics of epidemics, but these techniques cannot adequately describe behavior of a series with more complex dynamics [18–21]. The modeling of “biological systems” through nonlinear mathematics (“Chaos theory”) has proven to be useful in the understanding of complexity and especially in epidemics [22–36]. However, we have