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Mathematical Modeling of Drug Delivery Methods for HIV Treatment

By joshua rushlow

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My name is Joshua Rushlow, and I am a senior chemistry major, mathematics minor, at Millersville University. I plan to attend a doctoral program in chemistry after I graduate from MU. My project is studying the drug delivery methods for the treatment of Staphylococcus aureus. This project is focused on Drug delivery methods for treating patients, especially those with compromised immune systems due to human immunodeficiency virus (HIV), are widely studied to provide doctors with a variety of options. Intravenous treatment, which delivers medicine instantaneously to the bloodstream, allows for low dosage and quick treatment, while methods like pills or injections offer a slower, controlled delivery of drugs. Both methods have their benefits and cases where they are most suitable.
In this study, differential equation calculations were used to analyze both instantaneous and time-dependent methods of drug delivery. The critical dose, the relationship between drug amount and the number of virus cells present, and the function for time of treatment were all considered. The time-dependent methods were also analyzed for a dosage that would provide an initial decrease in virus amount before the virus grows exponentially, even if it is less than the critical dose.

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