Document Type


Date of Degree


Degree Name

PhD (Doctor of Philosophy)

Degree In

Applied Mathematical and Computational Sciences

First Advisor

Hethcote, Herbert W

Second Advisor

Hyman, James M


In Chapter 1, we study the effects of behavioral changes in a smallpox attack model. Response strategies to a smallpox bioterrorist attack have focused on interventions such as isolation, contact tracing, quarantine, ring vaccination, and mass vaccination. We formulate and analyze a mathematical model in which some individuals lower their daily contact activity rates once an epidemic has been identified in a community. We use computer simulations to analyze the effects of behavior change alone and in combination with other control measures. We demonstrate that the spread of the disease is highly sensitive to how rapidly people reduce their contact activity.

In Chapter 2, we study mixing patterns between age groups using social networks. The course of an epidemic through a population is determined by the interactions among individuals. To capture these elements of reality, we use the contact network simulations for the city of Portland, Oregon that were developed as part of the TRANSIMS/EpiSims project to study and identify mixing patterns. We analyze contact patterns between different age groups and identify those groups who are at higher risk of infection. We describe a new method for estimating transmission matrices that describe the mixing and the probability of transmission between the age groups. We use this matrix in a simple differential equation model for the spread of smallpox. Our differential equation model shows that the epidemic size of a smallpox outbreak could be greatly affected by the level of residual immunity in the population.

In Chapter 3, we study the effects of mixing patterns in the presence of population heterogeneity. We investigate the impact that different mixing assumptions have on the spread of a disease in an age-structured differential equation model. We use realistic, semi-bias and bias mixing matrices and investigate the impact that these mixing patterns have on epidemic outcomes when compared to random mixing. Furthermore, we investigate the impact of population heterogeneity such as differences in susceptibility and infectivity within the population for a smallpox epidemic outbreak. We find that different mixing assumptions lead to differences in disease prevalence and final epidemic size.


2, xi, 112 pages


Includes bibliographical references (pages 107-112).


Copyright 2005 Sara Yemimah Del Valle