The systems of equations created by Blower et al. (1995) and Jia et al. (2007) designed to model the dynamics of Tuberculosis are solved using the computer software SIMULINK. The results are first employed to examine the intrinsic transmission dynamics of the disease through two models developed by Blower et al. (1995). The "simple transmission model" was used primarily to give insight to the behavior of the susceptible, latent, and infectious groups of individuals. Then, we consider a more detailed transmission model which includes several additional factors. This model captures the dynamics of not only the susceptible, latent and infectious groups but also the non-infectious cases and the recovered cases. Using the SIMULINK results, it can be shown that the intrinsic dynamics of the disease contribute to the rise and decline of the disease seen in historical accounts. Next, the simulation results are used to study the equilibrium points of the disease which can be obtained by varying the parameters and therefore changing the value for the basic reproduction ratio (R0 ). Our model uses the system of equations developed by Jia et al. (2007). The SIMULINK results are used to visually confirm the hypothesis proposed by Jia et al. (2007) that the equilibrium behavior of the system when R0 > 1 is globally asymptotically stable.
| Identifer | oai:union.ndltd.org:ucf.edu/oai:stars.library.ucf.edu:etd-4682 |
| Date | 01 January 2008 |
| Creators | Atkins, Tracy |
| Publisher | STARS |
| Source Sets | University of Central Florida |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Electronic Theses and Dissertations |
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