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URN etd-0731109-153618 Statistics This thesis had been viewed 2496 times. Download 1672 times. Author Man-ling Hsu Author's Email Address No Public. Department Math Year 2008 Semester 2 Degree Master Type of Document Master's Thesis Language zh-TW.Big5 Chinese Page Count 48 Title Mathematical Models for the Evolution of AIDS Symptoms Keyword cell mortality inhibitor epidemic model AIDS AIDS epidemic model inhibitor cell mortality Abstract It has been hundreds of years, since mathematical models were applied to the study of epidemic disease. From the time when AIDS was inspected, a lot of researchers in the related fields including biology, medicine and mathematics, were interested in and tried to deal with this kind of epidemic. Up to now, there have been many reports involving in AIDS; however, most of these reports concerned only the spread of the epidemic disease in the population, and rarely concerned patients’ condition.
This thesis was based on mechanism for AIDS. By figuring out the cell concentration of healthy T-cell density, infected T-cell density and HIV density, patients could be identified whether they were infected with AIDS. Without taking the medical issue such as the incubation period into deep consideration, the study constructed one AIDS mathematical model without treatment and two mathematical models with treatment.
Because these mathematical models are written in nonlinear differential equations, it is usually not easy to find the analytical solution. Therefore, we adopted numerical methods to find out the approximating solutions. From the graphs of these approximating solutions, we found that the equilibrium states of mathematical models were asymptotically stable and also discovered some crucial approaches to control AIDS symptoms. For instantce, if the infection coefficient or the amount of HIV released from an infected T cell could be decreased, then AIDS symptoms would be under control.
Advisor Committee Lu-han Chuang - advisor
Fuh-gwo Wang - co-chair
Yung-cheng Wang - co-chair
Files Date of Defense 2009-07-17 Date of Submission 2009-07-31