Files and links (1)
PDFOpen Access (License Unspecified), Open Access
Dissertation
Determination of threshold conditions for non-linear stochastic partnership model for heterosexually transmitted diseases with stages
Doctor of Philosophy (Ph.D.), Drexel University
2000
DOI:
https://doi.org/10.17918/00000737
Abstract
To properly understand the modeling structure of an epidemic, it is imperative to understand and capture the characteristics impacting the epidemic's behavior in the population. A stochastic model with sufficient parameters describing the behavior of the epidemic was used. By embedding non-linear difference equations in the stochastic process in discrete time, a more thorough understanding of the epidemic was achieved. To visually enhance the investigation of the epidemic's behavior, comparison of trajectories of the deterministic model and those computed from the samples Monte Carlo realizations were made. In this modeling of the heterosexual disease, it is important for the mathematical/statistical structure to accommodate sexual and other contacts among members of the population. In this structure, biased partnership selection may arise. Threshold conditions are sensitive functions of this and other parameters in the model. To derive threshold conditions, non-linear differential equations were derived from the non-linear difference equations. Threshold conditions were determined by investigation of the stability of the Jacobian matrix for the embedded system of non-linear differential equations. Threshold conditions for the model were formulated and the sensitivity of these conditions were analyzed under slight deviations of the parameter space. Provided are numerous examples of this methodology applied to the HIV/AIDS epidemic in the heterosexual community. Comparison of the behavior of the two modeling structures, stochastic and deterministic, with respect to the threshold conditions were also investigated.
Metrics
21 File views/ downloads
8 Record Views
Details
- Title
- Determination of threshold conditions for non-linear stochastic partnership model for heterosexually transmitted diseases with stages
- Creators
- Robert J. Gallop
- Contributors
- Charles J. Mode (Advisor)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- x, 206 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Mathematics and Computer Science [Historical]; Drexel University
- Other Identifier
- 991014970194704721