Stability Analysis of the Immune System Induced by Chemotaxis.

This paper investigates the stability and instability of a generalized reaction-diffusion-advection system, which describes a cross-talk between antigens and immune cells via chemokines in the immune system. Based on the spectral analysis, energy estimates, and bootstrap techniques, we first consider a linearized problem around the positive constant equilibrium and show how the reaction term and chemotactic strength affect the stability and instability of the linearized problem. Then we go a further step to study the stability and instability for the nonlinear system based on the linearized results. Moreover, the numerical simulations are carried out to support our analytically theoretical results. Our results not only extend the previous ones of [S. Lee et al., J. Math. Biol., 75 (2017), pp. 1101-1131] but also involve some new conclusions.