Pierre Philippe, University of Montreal, Montreal, QC, Canada

Abstract: The dominant paradigm in epidemiology is characterized by the absence of a theory of disease that is capable of informing epidemiologic praxis and challenging conventional linear statistical reasoning. This paper has two main objectives: first, it is a reflection over the pathologic process (transition from health to disease state) in line with the nonlinear dynamic paradigm of self-organized critical systems. According to the latter, dynamic processes are characterized by phase transitions, emergence, robustness, far-from-equilibrium dynamics, punctuated equilibria, historically-based mechanic, nonlinearity, irreversibility, and heterogeneity. Further, complex adaptive systems have outcomes with inverse power law (IPL) fits. The article second objective is to test the theory of self-organized critical systems along two paths of epidemiologic investigations. The first path takes the form of a study in waiting times (WT) and attempts to show that their distribution complies with an IPL. The second application shows that hierarchies of patients (generated by cluster analysis) with a complex disease process (diabetes) featuring coupling of their component units (biologic markers of glucose handling) also fit an IPL. The IPL fit is compared with that of a lognormal, the more likely benchmark model for WTs. It is concluded that both the WTs and hierarchies of patients can be interpreted in terms of self-organized critical systems with possible fractal significance. The paper culminates with a theory of disease emphasizing the properties of self-organized complex systems in the epidemiologic context.

Keywords: complex systems, nonlinear dynamics, epidemiology, paradigm, inverse power law, fractal, incubation period, waiting times