Keywords
modeling, tuberculosis, epidemiology, SEIR, SIMULINK
Abstract
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.
Notes
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Graduation Date
2008
Advisor
Mohapatra, Ram N.
Degree
Master of Science (M.S.)
College
College of Sciences
Department
Mathematics
Degree Program
Mathematical Science
Format
application/pdf
Identifier
CFE0002030
URL
http://purl.fcla.edu/fcla/etd/CFE0002030
Language
English
Release Date
June 2008
Length of Campus-only Access
None
Access Status
Masters Thesis (Open Access)
STARS Citation
Atkins, Tracy, "Modeling Transmission Dynamics Of Tuberculosis Including Various Latent Periods" (2008). Electronic Theses and Dissertations. 3682.
https://stars.library.ucf.edu/etd/3682