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

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


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