Overview

Temporal Exposure Response Surface (TERS) is a visualization tool used in time series analysis to link exposure and health outcome. This three-dimensional plot can reveal major characteristics of an infectious outbreak associated with level of exposure: magnitude, duration and shape of epidemic curve. In fact, we were able to detect a secondary spread of infections in the susceptible subpopulations, as well as shorter average incubation time in the elderly compared to general population. We analyzed the impact on people over age 65 of a record-breaking 1993 outbreak of the Cryptosporidium parvum in Milwaukee, which resulted from a failure in the city's water filtration system. Using the TERS tool we were able to detect that the daily rates of gastrointestinal illness increased by 0.44 events per 100,000 persons for every additional 10 years of age. Compared with younger adults, older persons were at greater risk of becoming quite ill from the exposure, of picking it up from other people instead of just from drinking the water, and developing symptoms more quickly (see full paper).

Seasonality assessment is an essential step for proper characterization of health outcomes. It is a well known fact that many infections have a pronounced seasonal pattern. We define seasonality as the systematic periodic fluctuations within the course of a year that can be characterized by the magnitude, timing, and duration of a seasonal increase. Variations in seasonal characteristics in temporal, spatial, or demographical context provide important clues to factors influencing disease patterns (see full paper - PDF ).Seasonality can be observed if linked to environmental or methodological parameters.

Simulation Modeling is a computational experimental technique in which researchers try to isolate and encode the local rules that govern a system of individual behaviors, and use these formulations to experiment with alterations to the system, comparing the resulting complex outcomes. Very complicated systems can arise from very simple sets of rules and the study of how small changes in these rules affect the resulting emergent system has applications on every level of biological and medical research. While mathematical in nature, this is not a theoretical methodology, but rather a method of empirical research that uses a mathematical framework for the investigation. We are using these methods to investigate the roles of individual social behavior on disease transmission patterns and, more broadly, how societal organization can affect population-level pathogen robustness. As a result, we are able to draw conclusions about the disease dynamics (see abstract), health effects (link to come in future), economic costs and efficacy of public health control policies (link to come in the future) involved in outbreak, epidemic and endemic disease scenarios.

Analytic Mathematical Modeling is the formulation of mathematical theories to describe the behavior of an entire system at once. Rather than focusing on local rules (as with simulation modeling) analytic modeling frequently tries to describe the global outcome in ways that ‘simplify out’ the local conditions. These methods can be applied on any scale of investigation and from any field of applied mathematics, though they traditionally involve ‘dynamical systems’ – systems of partial differential equations (as in the Kermack-McKendrick SIR models). Our theoretical models have involved the modeling of populations as composites of etiologically distinct sub-populations (publication in process) to better isolate and/or predict the spread patterns among demographic/social subgroups within single and across multiple populations.