Chaos, population biology, and epidemiology: some research implications

In this article I aim to provide some feeling of the new paradigm of disease causation (chaos) as it applies to the field of population biology and epidemiology. A secondary objective is to show, with the aid of qualitative methods, how one can approach chaos in time-series data. The multifactorial stochastic paradigm of causation is contrasted with the new deterministic approach. This approach is embedded in the theory of nonlinear system dynamics. Chaos implies that randomness is intrinsic to a nonlinear deterministic system; this is true despite the extent of knowledge of the intervening causes and, ultimately, despite determinism. Three research avenues are discussed in depth from the standpoint of chaos theory. First, the topic of sporadic epidemics is dealt with. I argue that the space-time clustering of cases from a starting epidemic is due to a sudden and high increase of the contact rate beyond a threshold. Interaction rather than main effects and nonlinear rather than linear dynamics are involved. Second, the incubation period of disease is studied. I advocate that an individual-level deterministic process underlies Sartwell's model of the incubation period. This accounts for the robustness of the model vis-à-vis confounding variables. Third, monozygotic twinning is analyzed. Assumed by some to be a random process, monozygotic twinning proves to be dynamically different from dizygotic or single-maternity processes; its dynamics can actually be chaotic. Throughout the provided examples, the point is made that chancelike phenomena are primarily concerned with chaos theory. For biological problems showing recurrent inconsistencies by stochastic modeling, dynamic modeling should be envisaged. Inconsistencies can suggest that the relevant factors are out of the model and that they are related deterministically. Finally, spectral analysis and attractors in the phase space are presented; these tools can aid the population biologist in tracing out chaos from time-series data sets. Several time-series data sets are simulated according to a simple nonlinear difference equation that bears some relationship to the basics of the dynamics of infections in the population. I show how the series can be analyzed and interpreted. Much research remains to be carried out until the nonlinear effects of risk factors can be validated. The undertaking is worth the effort, as a new paradigm of causation is at stake.