Spatiotemporal dynamics of immune responses to viral infection and re-infection

Abstract

To test the hypothesis that the chemotactic movement of immune cells is pivotal in controlling within-host viral infection and re-infection, we formulate a chemotaxis model with multiple chemokines and spatial heterogeneity to investigate spatiotemporal dynamics of immune responses. The system admits globally bounded classical solutions in one-dimensional space, and the global classical solvability is derived in a high-dimensional space. We discuss the existence and local stability of four equilibria in the homogeneous case. By constructing Lyapunov functionals, we prove the global stability and the convergence rates of equilibria. Numerical simulations verify the theoretical results and provide additional insights. With stronger chemotaxis, the fluctuation of viral load in the early stage of viral infection is significantly reduced and enters a stable state faster, which indicates that chemotaxis can inhibit viral infection. During re-infection, the chemotactic movement of memory CTLs is more important than that of effector CTLs, and vice versa in initial infection. Furthermore, spatial heterogeneity, due to different patients or organs, should inevitably be considered to guarantee the success of clinical treatments.