Deterministic and Stochastic Models for HIV-1 Dynamics

by Amy Creel

Faculty mentor: Dr. Leo Lee

In this research project, I investigated deterministic and stochastic versions of a model for Human Immunodeficiency Virus Type 1 (HIV-1) dynamics. First, the deterministic model is introduced, and numerical techniques are used to obtain an approximate solution to the system. Then, a stochastic model is developed from the deterministic system. Patient data is introduced, and the Monte Carlo Method is used to find an approximate solution to the stochastic system. The results of this project demonstrate the behavior of HIV-1 in an infected patient under the effects of reverse transcriptase and protease inhibitors, and the introduction of randomness to the system of equations allows us to account for the randomness that occurs biologically within the model, thereby making our results more biologically sound.

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