Mathematics Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/2793
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Item Application of Mathematical and Computational Models to Mitigate the Overutilization of Healthcare Systems(2017) Hu, Xia; Golden, Bruce; Barnes, Sean; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The overutilization of the healthcare system has been a significant issue financially and politically, placing burdens on the government, patients, providers and individual payers. In this dissertation, we study how mathematical models and computational models can be utilized to support healthcare decision-making and generate effective interventions for healthcare overcrowding. We focus on applying operations research and data mining methods to mitigate the overutilization of emergency department and inpatient services in four scenarios. Firstly, we systematically review research articles that apply analytical queueing models to the study of the emergency department, with an additional focus on comparing simulation models with queueing models when applied to similar research questions. Secondly, we present an agent-based simulation model of epidemic and bioterrorism transmission, and develop a prediction scheme to differentiate the simulated transmission patterns during the initial stage of the event. Thirdly, we develop a machine learning framework for effectively selecting enrollees for case management based on Medicaid claims data, and demonstrate the importance of enrolling current infrequent users whose utilization of emergency visits might increase significantly in the future. Lastly, we study the role of temporal features in predicting future health outcomes for diabetes patients, and identify the levels to which the aggregation can be most informative.Item A DECISION MODEL FOR STUDENT-ATHLETE ENTRY INTO THE NBA DRAFT(2014) Fisher, Narryn; Fu, Michael; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)We develop a Markov Decision Process model using the framework of an optimal stopping problem to describe whether or not a student-athlete should enter the National Basketball Association (NBA) draft early. Our model uses a simulation algorithm for estimating the draft value of a student-athlete to inform his decision as he evaluates whether or not he should enter the NBA draft and forgo his remaining college eligibility. The model incorporates the shift in player evaluation for the draft that is now heavily focused on a student athlete's potential rather than the talent that a student-athlete displays in the collegiate game. The algorithm generates two estimates, one biased high and one biased low, both asymptotically unbiased as the computational effort increases and converging to the student-athlete's draft value.Item An Agent-Based Modeling Approach to Reducing Pathogenic Transmission in Medical Facilities and Community Populations(2012) Barnes, Sean; Golden, Bruce; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The spread of infectious diseases is a significant and ongoing problem in human populations. In hospitals, the cost of patients acquiring infections causes many downstream effects, including longer lengths of stay for patients, higher costs, and unexpected fatalities. Outbreaks in community populations cause more significant problems because they stress the medical facilities that need to accommodate large numbers of infected patients, and they can lead to the closing of schools and businesses. In addition, epidemics often require logistical considerations such as where to locate clinics or how to optimize the distribution of vaccinations and food supplies. Traditionally, mathematical modeling is used to explore transmission dynamics and evaluate potential infection control measures. This methodology, although simple to implement and computationally efficient, has several shortcomings that prevent it from adequately representing some of the most critical aspects of disease transmission. Specifically, mathematical modeling can only represent groups of individuals in a homogenous manner and cannot model how transmission is affected by the behavior of individuals and the structure of their interactions. Agent-based modeling and social network analysis are two increasingly popular methods that are well-suited to modeling the spread of infectious diseases. Together, they can be used to model individuals with unique characteristics, behavior, and levels of interaction with other individuals. These advantages enable a more realistic representation of transmission dynamics and a much greater ability to provide insight to questions of interest for infection control practitioners. This dissertation presents several agent-based models and network models of the transmission of infectious diseases at scales ranging from hospitals to networks of medical facilities and community populations. By employing these methods, we can explore how the behavior of individual healthcare workers and the structure of a network of patients or healthcare facilities can affect the rate and extent of hospital-acquired infections. After the transmission dynamics are properly characterized, we can then attempt to differentiate between different types of transmission and assess the effectiveness of infection control measures.Item Dependence Structure for Levy Processes and Its Application in Finance(2008-06-06) chen, qiwen; Madan, Dilip B; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this paper, we introduce DSPMD, discretely sampled process with pre-specified marginals and pre-specified dependence, and SRLMD, series representation for Levy process with pre-specified marginals and pre-specified dependence. In the DSPMD for Levy processes, some regular copula can be extracted from the discrete samples of a joint process so as to correlate discrete samples on the pre-specified marginal processes. We prove that if the pre-specified marginals and pre-specified joint processes are some Levy processes, the DSPMD converges to some Levy process. Compared with Levy copula, proposed by Tankov, DSPMD offers easy access to statistical properties of the dependence structure through the copula on the random variable level, which is difficult in Levy copula. It also comes with a simulation algorithm that overcomes the first component bias effect of the series representation algorithm proposed by Tankov. As an application and example of DSPMD for Levy process, we examined the statistical explanatory power of VG copula implied by the multidimensional VG processes. Several baskets of equities and indices are considered. Some basket options are priced using risk neutral marginals and statistical dependence. SRLMD is based on Rosinski's series representation and Sklar's Theorem for Levy copula. Starting with a series representation of a multi-dimensional Levy process, we transform each term in the series component-wise to new jumps satisfying pre-specified jump measure. The resulting series is the SRLMD, which is an exact Levy process, not an approximation. We give an example of alpha-stable Levy copula which has the advantage over what Tankov proposed in the follow aspects: First, it is naturally high dimensional. Second, the structure is so general that it allows from complete dependence to complete independence and can have any regular copula behavior built in. Thirdly, and most importantly, in simulation, the truncation error can be well controlled and simulation efficiency does not deteriorate in nearly independence case. For compound Poisson processes as pre-specified marginals, zero truncation error can be attained.Item Simulation Optimization of Traffic Light Signal Timings via Perturbation Analysis(2006-07-12) Howell, William Casey; Fu, Michael C; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)We develop simulation optimization algorithms for determining the traffic light signal timings for an isolated intersection and a network of two-signalized intersections modeled as single-server queues. Both problem settings consider traffic flowing in one direction. The system performance is estimated via stochastic discrete-event simulation. In the first problem setting, we examine an isolated intersection. We use smoothed perturbation analysis to derive both left-hand and right-hand gradient estimators of the queue lengths with respect to the green/red light lengths within a signal cycle. Using these estimators, we are able to apply stochastic approximation, which is a gradient-based search algorithm. Next we extend the problem to the case of a two-light intersection, where there are two additional parameters that we must estimate the gradient with respect to: the green/red light lengths within a signal cycle at the second light and the offset between the two light signals. Also, the number of queues increases from two to five. We again derive both left-hand and right-hand gradient estimators of the all queue lengths with respect to the three aforementioned parameters. As before, we are able to apply gradient-based search based on stochastic approximation using these estimators. Next we reexamine the two aforementioned problem settings. However, this time we are solely concerned with optimization; thus, we model the intersections using three different stochastic fluid models, each incorporating different degrees of detail. From these new models, we derive infinitesimal perturbation analysis gradient estimators. We then implement these estimators on the underlying discrete-event simulation and are able to apply gradient-based search based on stochastic approximation using these estimators. We perform numerical experiments to test the performance of the three gradient estimators and also compare these results with finite-difference estimators. Optimization for both the one-light and two-light settings is carried out using the gradient estimation approaches.