A Kinetic Theory Approach to Pedestrian Motion and Onset of Disease Spreading

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dc.contributor.advisorQuaini, Annalisa
dc.contributor.committeeMemberOtt, William
dc.contributor.committeeMemberTimofeyev, Ilya
dc.contributor.committeeMemberSharma, Natasha S.
dc.creatorKim, Daewa 1988-
dc.date.accessioned2019-09-13T01:07:47Z
dc.date.available2019-09-13T01:07:47Z
dc.date.createdMay 2019
dc.date.issued2019-05
dc.date.submittedMay 2019
dc.date.updated2019-09-13T01:07:47Z
dc.description.abstractThis dissertation shows a kinetic approach for pedestrian dynamics. First, we model the evacuation of a crowd from bounded domains. The interactions of a person with other pedestrians and the environment, which includes walls, exits, and obstacles, are modeled by using tools of game theory and are transferred to the crowd dynamics. The model allows to weight between two competing behaviors: the search for less congested areas and the tendency to follow the stream unconsciously in a panic situation. For the numerical approximation of the solution to our model, we apply an operator splitting scheme which breaks the problem into two pure advection problems and a problem involving the interactions. We compare our numerical results against the data reported in a recent empirical study on evacuation from a room with two exits. For medium and medium-to-large groups of people, we achieve good agreement between the computed average people density, flow rate, and the respective measured quantities. Through a series of numerical tests, we also show that our approach is capable of handling evacuation from a room with one or more exits with variable size, with and without obstacles, and can reproduce lane formation in bidirectional flow in a corridor. Next, we consider a crowd model known as ASCRIBE that can also track the level of emotional contagion in evacuation scenarios. We propose a modification of this model to track disease contagion. Finally, we couple the disease contagion model with the one dimension kinetic approach for pedestrian dynamics to simulate the initial spreading of an infectious disease.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginborn digital
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/10657/4456
dc.language.isoeng
dc.rightsThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).
dc.subjectPedestrian dynamics
dc.subjectKinetic Theory Approach
dc.subjectContagion Model
dc.titleA Kinetic Theory Approach to Pedestrian Motion and Onset of Disease Spreading
dc.type.dcmiText
dc.type.genreThesis
thesis.degree.collegeCollege of Natural Sciences and Mathematics
thesis.degree.departmentMathematics, Department of
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Houston
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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