A model for HPV-related cervical cancer dynamics with saturated terms: an optimal control problem using chemotherapy, immunotherapy, and antibody drugs

In this study, we formulate a within-host mathematical model of human papillomavirus (HPV) infection that captures the dynamics of susceptible epithelial cells, infected cells, free virions, cytotoxic T lymphocytes (CTLs), neutralizing antibodies, and cancerous cells. The model incorporates immune mechanisms, including CTL-mediated killing of infected cells and antibody-driven neutralization of virions, as well as therapeutic interventions. Building on this framework, we apply optimal control theory using three treatment strategies: (i) chemotherapy intensity, which enhances infected-cell death and reduces virion production, (ii) CTL stimulation (immunotherapy) intensity, which augments the CTL source term, and (iii) antibody therapy, which strengthens humoral immunity. We first identify the equilibria of the system and test their stability. The disease-free equilibrium is stable when the basic reproduction number is $R_0<1$, meaning the infection cannot persist in the population. When $R_0>1$, the endemic equilibrium (EE) becomes feasible and is globally asymptotically stable. Finally, the optimal control approach shows that a combined treatment strategy-chemotherapy, immune cell (CTL) boosting, and antibody therapy can significantly minimize viral load and cancer cell growth. This integrated approach demonstrates how traditional chemotherapy and immune-based therapies can complement each other, offering a more effective pathway for managing HPV.