Abstract / Summary
Abstract Intracellular production times vary across infected cells, whereas standard within-host virus models often represent the eclipse phase by a single fixed delay. We replace the fixed lag in a diffusive virus-immune model by weak and strong gamma-distributed memories and use the linear-chain technique to obtain finite-dimensional reaction-diffusion systems. Positivity and equilibrium preservation are established, mode-dependent characteristic polynomials are derived, and explicit Routh-Hurwitz stability criteria are formulated. At the mean delay $T = 21.034$ T = 21.034 corresponding to the Hopf threshold of the reference discrete-delay model, the homogeneous mode remains strictly stable for both gamma kernels: the spectral abscissa is approximately −0.0358 for the weak kernel and −0.0243 for the strong kernel, whereas the discrete-delay formulation is at a near-zero crossing. Numerical continuation in the gamma order shows that the dominant real part moves slowly toward zero as the kernel becomes more concentrated. Time-domain and phase-plane simulations confirm that distributed memory damps the oscillatory feedback, with the broader weak kernel producing the strongest attenuation. These results identify the variance and shape of intracellular memory, independently of its mean, as dynamically relevant stability parameters and show how temporal dispersion can suppress delay-induced Hopf instability.