Statistical analysis of a stochastic automata model for the spread of disease among mobile individuals

Persistent Link:
http://hdl.handle.net/10150/284283
Title:
Statistical analysis of a stochastic automata model for the spread of disease among mobile individuals
Author:
Fosser, Cecilia
Issue Date:
2000
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
We present techniques that allow for the statistical identification of the infection front and for the microscopic control of macroscopic statistics in a simple stochastic lattice automata model for the spread of an infectious disease through a mobile host population. The individual based model consists of susceptible and infected individuals that are free to move about a regular lattice. These individuals interact with each other when located at the same node of the lattice, and susceptible individuals become infected with a probability of infection that is dependent on the number of infected individuals present. By using statistics from the healthy population alone, we present a method by which the spread of an infection in the model can be located spatially, even in a low-density population. A parameter which governs the local mobility rules of the model is shown to be functionally related to the non-dimensional statistical values of skewness and flatness for various macroscopic quantities. We show formal convergence to reaction-diffusion equations from the lattice Boltzmann equations of the model via a Hilbert expansion. The validity of both the lattice Boltzmann equations and the reaction-diffusion equations is shown in a low-density population regime.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Biology, Biostatistics.; Mathematics.; Statistics.; Health Sciences, Public Health.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Applied Mathematics
Degree Grantor:
University of Arizona
Advisor:
Levermore, C. David

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleStatistical analysis of a stochastic automata model for the spread of disease among mobile individualsen_US
dc.creatorFosser, Ceciliaen_US
dc.contributor.authorFosser, Ceciliaen_US
dc.date.issued2000en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractWe present techniques that allow for the statistical identification of the infection front and for the microscopic control of macroscopic statistics in a simple stochastic lattice automata model for the spread of an infectious disease through a mobile host population. The individual based model consists of susceptible and infected individuals that are free to move about a regular lattice. These individuals interact with each other when located at the same node of the lattice, and susceptible individuals become infected with a probability of infection that is dependent on the number of infected individuals present. By using statistics from the healthy population alone, we present a method by which the spread of an infection in the model can be located spatially, even in a low-density population. A parameter which governs the local mobility rules of the model is shown to be functionally related to the non-dimensional statistical values of skewness and flatness for various macroscopic quantities. We show formal convergence to reaction-diffusion equations from the lattice Boltzmann equations of the model via a Hilbert expansion. The validity of both the lattice Boltzmann equations and the reaction-diffusion equations is shown in a low-density population regime.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectBiology, Biostatistics.en_US
dc.subjectMathematics.en_US
dc.subjectStatistics.en_US
dc.subjectHealth Sciences, Public Health.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorLevermore, C. Daviden_US
dc.identifier.proquest9992113en_US
dc.identifier.bibrecord.b41170623en_US
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