Mathematical analysis of an in-host model of viral dynamics with spatial heterogeneity

Stephen  Pankavich; Christian  Parkinson

doi:10.3934/dcdsb.2016.21.1237

Article Contents

2016, Volume 21, Issue 4: 1237-1257. Doi: 10.3934/dcdsb.2016.21.1237

This issue Previous Article Dynamic transitions of generalized Kuramoto-Sivashinsky equation Next Article Attractors and entropy bounds for a nonlinear RDEs with distributed delay in unbounded domains

Mathematical analysis of an in-host model of viral dynamics with spatial heterogeneity

Stephen Pankavich^1, and
Christian Parkinson^1,

1.
Colorado School of Mines, 1500 Illinois St, Golden, CO 80401

Received: April 30, 2015

Revised: November 30, 2015

Published: May 2016

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Abstract

We consider a spatially-heterogeneous generalization of a well-established model for the dynamics of the Human Immunodeficiency Virus-type 1 (HIV) within a susceptible host. The model consists of a nonlinear system of three coupled reaction-diffusion equations with parameters that may vary spatially. Upon formulating the model, we prove that it preserves the positivity of initial data and construct global-in-time solutions that are both bounded and smooth. Finally, additional results concerning the local and global asymptotic behavior of these solutions are also provided.

Keywords:

Mathematics Subject Classification: Primary: 35K51, 92C17, 35Q92; Secondary: 35K45, 35K57, 92C50, 35B40.

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