Threshold dynamics in a within-host infection model with Crowley–Martin functional response considering periodic effects

In this work, we investigate the threshold dynamics of a within host viral infection model that incorporates a Crowley–Martin functional response together with periodically varying parameters. For this nonautonomous system, we establish the essential analytic properties, namely existence and uniqueness of solutions, positivity, and uniform boundedness of the periodic trajectories. A key component of the analysis is the basic reproduction number ${\mathcal{R}}_0$, formulated as the spectral radius of an associated integral operator. This quantity acts as the decisive threshold governing the global behavior of the system: if ${\mathcal{R}}_0<1$, all solutions converge to the virus free $\omega$ periodic orbit, whereas ${\mathcal{R}}_0>1$ guarantees uniform persistence and the existence of at least one strictly positive periodic solution. Numerical experiments are provided to illustrate these threshold driven transitions and to complement the theoretical findings.