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In-host modeling of the spatial dynamics of HIV

Parkinson, Christian
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Advisor
Pankavich, Stephen
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Date
Date Issued
2015
Date Submitted
Keywords
math modeling
 diffusion
 math biology
 HIV
 PDEs
 HIV infections -- Mathematical models
 Finite differences
 Differential equations, Partial
 Differential equations, Parabolic
 Diffusion
 Computer simulation
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2010-2019 - Mines Theses & Dissertations
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In-host modeling of the spatial dynamics of HIV
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https://hdl.handle.net/11124/17136
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Abstract
The well-known three-compartment model which describes the spatially homogeneous dynamics of HIV in-vivo is adapted to account for spatial heterogeneity by considering diffusion of populations and spatially varying parameters. The new system of nonlinear parabolic PDEs is analyzed in detail. Specifically, local and global existence, uniqueness and high-order regularity of solutions is proven. We also determine the global asymptotic behavior of the model in certain biologically relevant regimes and compare our findings with the analogous results for the spatially homogeneous model. In doing so, we diss existence and stability of viral extinction and viral persistence steady states in different cases. Finally, the system is simulated using a semi-implicit finite difference method with the goal of verifying the analysiscus.
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