Global Dynamics and Critical Decay of an SLBS Malware Model with Double Saturation

Contact constraints and stage-dependent recovery shape malware persistence, motivating a joint analysis of invasion thresholds and subsequent infection burden. This study develops a susceptible–latent–bursting–susceptible model with separate saturation factors, demographic turnover, and latent-only transmission. Explicit full-system Lyapunov functions establish global virus-free stability for reproduction number R0≤1 and global endemic attraction for R0>1 with a positive initial latent population. The initially latent-free boundary converges to the virus-free state. These conclusions allow for arbitrary initial total populations. An explicit coefficient links the forward transcritical branch to critical inverse-time decay. The slow infection eigenvalue also vanishes linearly at the threshold, explaining prolonged near-critical transients. Moreover, sensitivity identities show that the saturation factors separately regulate invasion and endemic burden, while faster bursting recovery enlarges the endemic latent reservoir and reduces bursting infection. Numerical comparisons in a synthetic reference setting reveal that, at matched R0=2, the double-saturation and bilinear models yield latent equilibrium fractions of 19.10% and 33.33%, respectively. Matching invasion also reverses the susceptible-saturation response obtained at fixed transmission. Consequently, the findings provide novel insights into how contact saturation and recovery jointly determine the relationship between invasion potential and persistent infection burden.