Numerical modeling of T-cell dynamics by reaction-diffusion problems

The paper proposes a numerical model for T-cell dynamics, based on a reaction-diffusion problem originated by adding a diffusion term in the model introduced in [1] and based on ordinary differential equations. The model here introduced is specifically intended to provide a mathematical description of the homeostasis of T-cells, mainly due to a quorum-sensing mechanism. The introduced reaction-diffusion problem is then discretized by means of a finite difference numerical scheme. Numerical experiments supporting the approach are provided.