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

TL;DR

This paper presents a mathematical analysis of a spatially-heterogeneous in-host HIV model, proving positivity, boundedness, smoothness, and analyzing the long-term behavior of solutions.

Contribution

It introduces a new spatially-heterogeneous HIV model and provides rigorous mathematical proofs of solution properties and asymptotic behavior.

Findings

Solutions remain positive, bounded, and smooth over time.

The model exhibits specific local and global asymptotic behaviors.

The analysis extends understanding of spatial effects in HIV dynamics.

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.