Chaos Versus Noisy Periodicity: Alternative Hypotheses for Childhood Epidemics

Abstract

Whereas case rates for some childhood diseases (chickenpox) often vary according to an almost regular annual cycle, the incidence of more efficiently transmitted infections such as measles is more variable. Three hypotheses have been proposed to account for such fluctuations. (i) Irregular dynamics result from random shocks to systems with stable equilibria. (ii) The intrinsic dynamics correspond to biennial cycles that are subject to stochastic forcing. (iii) Aperiodic fluctuations are intrinsic to the epidemiology. Comparison of real world data and epidemiological models suggests that measles epidemics are inherently chaotic. Conversely, the extent to which chickenpox outbreaks approximate a yearly cycle depends inversely on the population size.

The epidemiology of varicella–zoster virus infections: a mathematical model

“…(i) Because the two variables, time since initial infection (r) and age (a), are strongly correlated, and because most initial infection occurs at a similar age, there is no way of clearly differentiating which of them is influencing the system. Thus, in our model we used a recrudescence function which was dependent on age in equation (4). If age is replaced by time since initial infection then the results in Figure 3 remain the same.…”

“…p(a.7) = +±501a. (4) Here, a is a background probability of zoster caused by other effects, as described above. If chance events, such as another illness which involves general damage to the immune system, play no part in the reactivation, then a would equal zero.…”

“…Other reports of this sort of transmission of the virus are common [4,61] and zoster was shown to have a statistically significant influence on levels of varicella in a boarding school [62]. However, in general it appears that zoster is a much less infectious disease than varicella [33] and its influence is in any case implicit in the calculation of the force of infection for varicella.…”

“…There is an extensive literature describing the dynamics of varicella incidence in terms of simple mathematical models [3,4], and HopeSimpson has formulated a qualitative model of the varicella-zoster system [5][6][7]. However, no attempt has yet been made to produce a quantitative model of infection with VZV infection which explicitly includes the dynamics of zoster.…”

The Sociobiologic Integrative Model (SBIM): Enhancing the Integration of Sociobehavioral, Environmental, and Biomolecular Knowledge in Urban Health and Disparities Research

“…Some researchers have looked to Chaos Theory and Complexity Theory as constructs to facilitate the understanding about health and its relationship to diverse processes and outcomes such as cardiac arrhythmias 22,23 and even urban epidemics. 24,25 Whereas this approach may have merit, it appears to be beyond the practical usefulness of many clinicians and scientists.…”