Predicting attenuant and resonant 2-cycles in periodically forced discrete-time two-species population models.

Periodic environments may either enhance or suppress a population via resonant or attenuant cycles. We derive signature functions for predicting the responses of two competing populations to 2-periodic oscillations in six model parameters. Two of these parameters provide a non-trivial equilibrium and two provide the carrying capacities of each species in the absence of the other, but the remaining two are arbitrary and could be intrinsic growth rates.

Periodically forced discrete-time SIS epidemic model with disease induced mortality.

We use a periodically forced SIS epidemic model with disease induced mortality to study the combined effects of seasonal trends and death on the extinction and persistence of discretely reproducing populations. We introduce the epidemic threshold parameter, R0 , for predicting disease dynamics in periodic environments. Typically, R0 <1 implies disease extinction.

Disease-induced mortality in density-dependent discrete-time S-I-S epidemic models.

The dynamics of simple discrete-time epidemic models without disease-induced mortality are typically characterized by global transcritical bifurcation. We prove that in corresponding models with disease-induced mortality a tiny number of infectious individuals can drive an otherwise persistent population to extinction. Our model with disease-induced mortality supports multiple attractors.

SIS epidemic attractors in periodic environments.

The demographic dynamics are known to drive the disease dynamics in constant environments. In periodic environments, we prove that the demographic dynamics do not always drive the disease dynamics. We exhibit a chaotic attractor in an SIS epidemic model, where the demograhic dynamics are asymptotically cyclic.

Globally attracting attenuant versus resonant cycles in periodic compensatory Leslie models.

We use a periodically forced density-dependent compensatory Leslie model to study the combined effects of environmental fluctuations and age-structure on pioneer populations. In constant environments, the models have globally attracting positive fixed points. However, with the advent of periodic forcing, the models have globally attracting cycles.

Personal dust exposures at a food processing facility.

A field study was performed to quantify personal dust exposures at a food processing facility. A review of the literature shows very little exposure information in the food processing industry. The processing area consisted of a series of four rooms, connected by a closed-loop ventilation system, housed within a larger warehouse-type facility.

Signature function for predicting resonant and attenuant population 2-cycles.

Populations are either enhanced via resonant cycles or suppressed via attenuant cycles by periodic environments. We develop a signature function for predicting the response of discretely reproducing populations to 2-periodic fluctuations of both a characteristic of the environment (carrying capacity), and a characteristic of the population (inherent growth rate). Our signature function is the sign of a weighted sum of the relative strengths of the oscillations of the carrying capacity and the demographic characteristic.