Global stability of a class of fractional partial differential equations describing the dynamics of viral infection with therapy and adaptive immunity

In this article, we formulate a mathematical model based on fractional partial differential equations (FPDEs) to describe the spatiotemporal progression of viral infections, incorporating the effects of adaptive immunity and antiviral treatment. The model includes a regional fractional Laplace operator to account for the anomalous diffusion observed within the infected medium. We investigate the existence and uniqueness of equilibria and establish their global stability using Lyapunov functions tailored to the associated reaction systems. Moreover, numerical simulations are presented to illustrate the analytical results.