A reaction-diffusion within-host HIV model with cell-to-cell transmission

Area of Science:

• Mathematical Biology
• Epidemiology
• Virology

Background:

• Within-host HIV dynamics are complex, influenced by cell mobility and spatial factors.
• Cell-to-cell transmission is a key mechanism in HIV spread.

Purpose of the Study:

• To develop and analyze a reaction-diffusion HIV model incorporating cell mobility and spatial heterogeneity.
• To establish the basic reproduction number as a threshold for viral persistence.
• To investigate traveling wave solutions and their speeds in unbounded domains.

Main Methods:

• Reaction-diffusion modeling
• Schauder fixed point theorem
• Limiting argument
• LaSalle's invariance principle
• One-side Laplace transform
• Numerical simulations

Main Results:

• The basic reproduction number ([Formula: see text]) determines the stability of the virus-free steady state.
• Explicit formulas for [Formula: see text] and wave speed were derived for homogeneous and unbounded domains.
• Numerical simulations suggest asymptotic spreading speed can exceed minimum wave speed.
• Spatial heterogeneity and cell mobility significantly impact spread risk estimations.

Conclusions:

• Cell mobility and spatial heterogeneity are crucial factors in accurately modeling HIV spread.
• Ignoring these factors can lead to under- or overestimation of viral spread risk.
• The proposed model provides a more realistic framework for understanding within-host HIV dynamics.