reaction–diffusion

Spatiotemporal dynamics of RNA viruses in the presence of immunity and treatment: case of SARS-CoV-2

In this paper, we develop a mathematical model using partial differential equations to investigate the behavior of RNA viruses in the presence of antiviral treatment.  The developed model includes both cell-to-cell and virus-to-cell modes of transmission.  Initially, we establish the well-posedness of the model by demonstrating the existence and uniqueness of solutions, as well as their positivity and boundedness.  Additionally, we identify and analyze the stable equilibrium states, their global stability depending on specific threshold parameters, using Lyapunov functi

A new Lattice Boltzmann method for a Gray–Scott based model applied to image restoration and contrast enhancement

The aim of this work is to propose a new numerical approach to image restoration and contrast enhancement based on a reaction-diffusion model (Gray–Scott model).  For noise removal, a Lattice Boltzmann technique is used.  This method is usually used in fluid dynamics experiments.  Since pixels motion can be compared to fluids motion, the presented technique also indicates a good performance in processing noisy images.  The efficiency and performance of the proposed algorithm are verified by several numerical experiments.