Dissertation
MATHEMATICAL MODELING IN VIRAL DYNAMICS AND DRUG CONTROL: A CASE STUDY OF HIV-1 VIRUS
Washington State University
Doctor of Philosophy (PhD), Washington State University
01/2021
DOI:
https://doi.org/10.7273/000005446
Handle:
https://hdl.handle.net/2376/119355
Abstract
Mathematical modeling has long given insight in understanding the initiation, progression, and dynamics of diseases and infection.The primary focus of this research is to investigate cost-effective strategies for chemotherapy in HIV and the emergence of drug resistance in HIV by mathematical modeling and analysis. The optimal control problem is formulated based on an existing HIV latency model by incorporating the termination level in terms of viral loads, latently, and productively infected T cells.
The necessary condition for this optimal system is derived using the Pontryagin's maximum principle. Numerical simulation is carried out using Runge-Kutta 4 method for the forward-backward sweep. Our results suggest that introducing the termination viral load into the control provides a better strategy in developing HIV chemotherapy. On the other hand, we develop a continuous-time Markov chain (CTMC) model, which is derived based on an ordinary differential equation model proposed by Kitayimbwa et al. (J Math Biol, 67:1111-1139, 2013), to study the emergence of drug resistance in HIV. An analytic estimate of the probability of disease extinction of the CTMC model near the disease-free equilibrium is obtained by a multitype branching process approximation. The analytical predictions are validated by numerical simulations. Our result shows that, unlike the deterministic dynamics where the basic reproduction number serves as a sharp threshold parameter (i.e., the disease dies out if the reproduction number is less than 1 and persists if it is greater than 1), the stochastic model indicates that there is always a positive probability of disease extinction in patients.
The findings of this research provide insight into HIV therapeutic strategies, such as the importance of the size of the latent cell reservoir in the treatment of HIV.
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Details
- Title
- MATHEMATICAL MODELING IN VIRAL DYNAMICS AND DRUG CONTROL: A CASE STUDY OF HIV-1 VIRUS
- Creators
- Damilola Omolola Olabode
- Contributors
- Xueying Wang (Advisor)Libin Rong (Committee Member)Nikolaos Voulgarakis (Committee Member)Mark F Schumaker (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Mathematics and Statistics
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 133
- Identifiers
- 99900592156301842
- Language
- English
- Resource Type
- Dissertation