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abstract: There have been many studies on the dynamics of infectious diseases considering the age structure of the population. This study analyzes the dynamics when the population is stratified by size. This kind of models are useful in the spread of a disease in fisheries where size matters, for microorganism populations or even human diseases that are driven by weight. A simple size structured SIR model is introduced for which a threshold condition, R0, equilibria and stability are established in special cases. Hethcote's approach is used to derive, from first principles, a parallel ODE size-structure system involving n-size classes.The specific case of n = 2 is partially analyzed. Constant effort harvesting is added to this model with the purpose of exploring the role of controls and harvesting. Different harvesting policies are proposed and analyzed through simulations. / Dissertation/Thesis / Ph.D. Applied Mathematics for the Life and Social Sciences 2012

This thesis examines news articles to see if obesity has been framed as a moral panic by looking at how the coverage understands the causes of obesity and its solutions. A qualitative textual analysis of 100 articles and 28 images from Time and Newsweek was done spanning 1986 to 2012. I found that the obesity "epidemic" was first discussed as problem of individual responsibility and that the best cure was medicine. The narrative shifted to childhood obesity around 2004 and cited parents as the responsible party while suggesting family bonding as a solution to childhood obesity. I find that the media dialogue around obesity points to individuals rather than systemic factors as the cause of obesity and, in so doing, takes the focus off of social and economic inequalities that are also factors in the obesity epidemic.

Master of Science / Department of Mathematics / Pietro Poggi-Corradini / This thesis contains three chapters split into two parts. In the first chapter, the discrete p-modulus of families of walks is introduced and discussed from various perspectives. Initially, we prove many properties by mimicking the theory from the continuous case and use Arne Beurling's criterion for extremality to build insight and intuition regarding the modulus. After building an intuitive understanding of the p-modulus, we proceed to switch perspectives to that of convex analysis. From here, uniqueness and existence of extremal densities is shown and a better understanding of Beurling's criterion is developed before describing an algorithm that approximates the value of the p-modulus arbitrarily well. In the second chapter, an exclusively edge-based approach to the discrete transboundary modulus is described. Then an interesting application is discussed with some preliminary numerical results. The final chapter describes four different takes of the Susceptible-Infected (SI) epidemic model on graphs and shows them to be equivalent. After developing a deep understanding of the SI model, the epidemic hitting time is compared to a variety of different graph centralities to indicate successful alternative methods in identifying important agents in epidemic spreading. Numerical results from simulations on many real-world graphs are presented. They indicate the effective resistance, which coincides with the 2-modulus for connecting families, is the most closely correlated indicator of importance to that of the epidemic hitting time. In large part, this is suspected to be due to the global nature of both the effective resistance and the epidemic hitting time. Thanks to the equivalence between the epidemic hitting time and the expected distance on an randomly exponentially weighted graph, we uncover a deeper connection- the effective resistance is also a lower bound for the epidemic hitting time, showing an even deeper connection.

Many healthcare providers report not feeling confident when prescribing opioids, which represents an educational gap in the clinical setting that must be addressed to improve patient care and outcomes (Dowell, Haegerich, & Chou, 2016b). Healthcare providers attribute this lack of confidence in opioid prescribing to insufficient training on the tools provided to them to ensure safe prescribing habits. Thus, healthcare providers do not feel confident in managing patients’ chronic pain. A healthcare provider’s time spent with their patient is limited and therefore, needs to be utilized efficiently. In order to achieve effective time management, healthcare providers need to be experts on chronic pain management and self-assured with their practice in relation to opioids. This practice improvement project focused on increasing healthcare providers’ knowledge and confidence when prescribing opioids for chronic pain and managing chronic pain. An educational intervention with health professionals working in federally qualified health centers in North Dakota was implemented via Skype. The intervention allowed healthcare providers to be up-to-date on the most recent evidence-based literature and guidelines regarding this topic. Throughout this practice improvement project, healthcare providers were educated on the latest Centers for Disease Control (CDC) and Prevention Guideline for Prescribing Opioids for Chronic Pain, provided resources for their clinical practice, and given an opportunity to evaluate their own knowledge and confidence. The implementation of the practice improvement project was comprised of an educational session. To assess the participants’ knowledge, a pre-test was provided prior to the educational session and a post-test was given following the educational session. Furthermore, a self-confidence evaluation survey was administered, which utilized a Likert scale. Lastly, the clinic’s policies and pain agreements related to pain and opioids were reviewed and discussed. The results of the project indicated an overall increase in the participants’ knowledge and self-confidence. In addition, the project promoted awareness of the clinic’s current pain agreement and the likelihood of a future implementation of a policy regarding chronic pain management. The educational session was beneficial in promoting the use of evidence-based research and guidelines in the primary care setting.

Pandemics can significantly impact public health and society, for instance, the 2009 H1N1<br />and the 2003 SARS. In addition to analyzing the historic epidemic data, computational simulation of epidemic propagation processes and disease control strategies can help us understand the spatio-temporal dynamics of epidemics in the laboratory. Consequently, the public can be better prepared and the government can control future epidemic outbreaks more effectively. Recently, epidemic propagation simulation systems, which use high performance computing technology, have been proposed and developed to understand disease propagation processes. However, run-time infection situation assessment and intervention adjustment, two important steps in modeling disease propagation, are not well supported in these simulation systems. In addition, these simulation systems are computationally efficient in their simulations, but most of them have<br />limited capabilities in terms of modeling interventions in realistic scenarios.<br />In this dissertation, we focus on building a modeling and simulation environment for epidemic propagation and propagation control strategy. The objective of this work is to<br />design such a modeling environment that both supports the previously missing functions,<br />meanwhile, performs well in terms of the expected features such as modeling fidelity,<br />computational efficiency, modeling capability, etc. Our proposed methodologies to build<br />such a modeling environment are: 1) decoupled and co-evolving models for disease propagation, situation assessment, and propagation control strategy, and 2) assessing situations and simulating control strategies using relational databases. Our motivation for exploring these methodologies is as follows: 1) a decoupled and co-evolving model allows us to design modules for each function separately and makes this complex modeling system design simpler, and 2) simulating propagation control strategies using relational databases improves the modeling capability and human productivity of using this modeling environment. To evaluate our proposed methodologies, we have designed and built a loosely coupled and database supported epidemic modeling and simulation environment. With detailed experimental results and realistic case studies, we demonstrate that our modeling environment provides the missing functions and greatly enhances many expected features, such as modeling capability, without significantly sacrificing computational efficiency and scalability. / Ph. D.

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The purpose of this study is to closely analyze opioid overdose response efforts on county, state, and federal levels in designated Appalachian regions in order to better understand program methodology standards that ensure success in combating the opioid epidemic. The study exists to answer the question: What approaches have worked best in combating the opioid epidemic and should be implemented in any future potential solutions? The research data scope involved comparison of existing data from county reports, government agencies, and response efforts to best identify program decline rates of opioid usage by the following indicators; declines in opioid overdose deaths, drug distribution per capita, deaths attributing to synthetic opioid overdose, and decline in neonatal abstinence syndrome births. All sources used are publicly available and depict de-identifiable population health information. When compiling research, important background information including how to define the opioid epidemic, root cause identification, and existing response effort methodologies were addressed. While hard to define, the opioid epidemic refers to a public health crisis by which Appalachian individuals unproportionally die at the hands of opioid overdose in comparison to the rest of the country; which is evident and alarming. This opioid crisis has many social and economic causes relating to the demographic majority of Appalachian regions, as well as occurrences that jumpstart a quick decline. The existing response effort methodologies of county, state, and federal programs are expensive and challenging to implement with only some success. There are also many facets to addressing the opioid epidemic including government initiatives, federal or state agencies, non-profit agencies, educational facilities, public health initiatives, and faith-based organizations. While the complexity of response efforts can be beneficial to have many options for addressing the issue, it can also quickly muddle the most effective methods to success. However, the most notable programs that saw a quick decline in overdose death rates included those that coordinated multiple types of entities such as schools, health departments, and correctional departments. Other successful programs reinstituted training and education both with regional providers on appropriate opioid prescriptions; and to the community on proper use, handling, and disposal of opioids. The most effective methods to reduce the health disparities relating to the opioid epidemic in Appalachian regions are extensive collaboration and re-education across the communities most deeply affected by the crisis. Any future response efforts should address these key success indicators.

This dissertation introduced several issues concerning the analysis of diseases by showing how modeling and simulation could be used to assist in creating health policy by estimating the effects of such policies. The first question posed was how would education, vaccination and a combination of these two programs effect the possible outbreak of meningitis on a college campus. After creating a model representative of the transmission dynamics of meningitis and establishing parameter values characteristic of the University of Central Florida main campus, the results of a deterministic model were presented in several forms. The result of this model was the combination of education and vaccination would eliminate the possibility of an epidemic on our campus. Next, we used simulation to evaluate how quarantine and treatment would affect an outbreak of influenza on the same population. A mathematical model was created specific to influenza on the UCF campus. Numerical results from this model were then presented in tabular and graphical form. The results comparing the simulations for quarantine and treatment show the best course of action would be to enact a quarantine policy on the campus thus reducing the maximum number of infected while increasing the time to reach this peak. Finally, we addressed the issue of performing the analysis stochastically versus deterministically. Additional models were created with the progression of the disease occurring by chance. Statistical analysis was done on the mean of 100 stochastic simulation runs comparing that value to the one deterministic outcome. The results for this analysis were inconclusive, as the results for meningitis were comparable while those for influenza appeared to be different.

Scalability is an important problem in epidemiological applications that simulate complex intervention scenarios over large datasets. Indemics is one such interactive data intensive framework for High-performance computing (HPC) based large-scale epidemic simulations. In the Indemics framework, interventions are supplied from an external, standalone database which proved to be an effective way of implementing interventions. Although this setup performs well for simple interventions and small datasets, performance and scalability of complex interventions and large datasets remain an issue. In this thesis, we present IndemicsXC, a scalable and massively parallel high-performance data engine for Indemics in a supercomputing environment. IndemicsXC has the ability to implement complex interventions over large datasets. Our distributed database solution retains the simplicity of Indemics by using the same SQL query interface for expressing interventions. We show that our solution implements the most complex interventions by intelligently offloading them to the supercomputer nodes and processing them in parallel. We present an extensive performance evaluation of our database engine with the help of various intervention case studies over synthetic population datasets. The evaluation of our parallel and distributed database framework illustrates its scalability over standalone database. Our results show that the distributed data engine is efficient as it is parallel, scalable and cost-efficient means of implementing interventions. The proposed cost-model in this thesis could be used to approximate intervention query execution time with decent accuracy. The usefulness of our distributed database framework could be leveraged for fast, accurate and sensible decisions by the public health officials during an outbreak. Finally, we discuss the considerations for using distributed databases for driving large-scale simulations. / Master of Science