# American Institute of Mathematical Sciences

June  2016, 21(4): 1237-1257. doi: 10.3934/dcdsb.2016.21.1237

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

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

Received  May 2015 Revised  December 2015 Published  March 2016

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.
Citation: Stephen Pankavich, Christian Parkinson. Mathematical analysis of an in-host model of viral dynamics with spatial heterogeneity. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1237-1257. doi: 10.3934/dcdsb.2016.21.1237
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