Complex dynamics of a time periodic nonlocal and time-delayed model of reaction-diffusion equations for modeling CD4+T cells decline

Pyroptosis, an intensively inflammatory form of programmed cell death triggered during abortive HIV infection, is associated with the release of inflammatory cytokines. The inflammatory cytokines can attract more CD4(+) cells to be infected. Based on the new biological perspective, a time periodic reaction-diffusion equation model with spatial heterogeneity and latent period is developed to investigate whether or not pyroptosis can explain CD4(+) T cells decline during HIV infection. Threshold dynamics is explored in terms of the basic reproduction number R-0. It is shown that the infection-free periodic solution is globally attractive if R-0 < 1, while there exists positive infection periodic solution and the virus is uniformly persistent if R-0 > 1, which might be a new finding for viral infection dynamical models. Theoretical analyses and simulations for the spatially homogeneous model demonstrate rich dynamics, including the occurrence of Turing instability, which may result in Hopf bifurcation and spatially inhomogeneous pattern formations. It turns out that the new model issues some new challenges due to the enhancement infection term in the global stability problem and Turing instability analysis for the high dimensional system. Our results reveal that the inflammatory cytokines can make the CTLs level increase, which is a new phenomenon not presented in the existing literature. (C) 2019 Elsevier B.V. All rights reserved.