Global Stability of HPV Transmission on Scale-Free Networks

This paper develops a dynamic model of two-stage recovery on scale-free networks to analyze the infection pathways of human papillomavirus (HPV) leading to cervical cancer, incorporating heterogeneous contact patterns. The framework stratifies the demographic cohort across four distinct compartments: susceptible (S), HPV-infected (I 1 ), precancerous lesions (I 2 ), and cervical cancer (I 3 ), with degree-based differential equations governing transmission dynamics. Theoretical analysis demonstrates that the basic reproduction number R 0 serves as a critical threshold: when R 0 < 1, the disease-free equilibrium is globally asymptotically stable, ensuring disease eradication; when R 0 > 1, the dynamical system asymptotically approaches a globally stable endemic equilibrium, with proven permanence. Numerical simulations also validate the theoretical results. Research indicates that under scale-free network structures, priority should be given to implement targeted screening high-contact groups, leveraging their central role in transmission dynamics to block HPV diffusion. The results of this study emphasize the critical role of early screening, targeted interventions for high-contact groups, and optimized treatment protocols to mitigate HPV-related cervical cancer.