Attractors and entropy bounds for a nonlinear RDEs with distributed delay in unbounded domains
Dynamic transitions of generalized Kuramoto-Sivashinsky equation
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
Stephen Pankavich 1, and Christian Parkinson 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.
Keywords: longtime asymptotic behavior., nonlinear diffusion, HIV, Global existence.
Mathematics Subject Classification: Primary: 35K51, 92C17, 35Q92; Secondary: 35K45, 35K57, 92C50, 35B4.
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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Stephen Pankavich Christian Parkinson