Epidemiologists engage in the study of the distribution and determinants of health-related states or events in human populations. Eventually, they will apply that study to prevent and control problems and contingencies associated with the health of the population. Due to the spread of new pathogens and the emergence of new bio-terrorism threats, it has become imperative to develop new and expand existing techniques to equip public health providers with robust tools to predict and control health-related crises. In this dissertation, I explore the effects caused in the disease dynamics by the differences in individuals’ physiology and social/behavioral characteristics. Multiple computational and mathematical models were developed to quantify the effect of those factors on spatial and temporal variations of the disease epidemics. I developed statistical methods to measure the effects caused in the outbreak dynamics by the incorporation of heterogeneous demographics and social interactions to the individuals of the population. Specifically, I studied the relationship between demographics and the physiological characteristics of an individual when preparing for an infectious disease epidemic.

Optimization of relief networks in humanitarian logistics often exemplifies the need for solutions that are feasible given a hard constraint on time. For instance, the distribution of medical countermeasures immediately following a biological disaster event must be completed within a short time-frame. When these supplies are not distributed within the maximum time allowed, the severity of the disaster is quickly exacerbated. Therefore emergency response plans that fail to facilitate the transportation of these supplies in the time allowed are simply not acceptable. As a result, all optimization solutions that fail to satisfy this criterion would be deemed infeasible. This creates a conflict with the priority optimization objective in most variants of the generic vehicle routing problem (VRP). Instead of efficiently maximizing usage of vehicle resources available to construct a feasible solution, these variants ordinarily prioritize the construction of a minimum cost set of vehicle routes. Research presented in this dissertation focuses on the design and analysis of efficient computational methods for optimizing high-consequence variants of the VRP for relief networks. The conflict between prioritizing the minimization of the number of vehicles required or the minimization of total travel time is demonstrated. The optimization of the time and capacity constraints in …