Stability analysis and optimal control of a SVICR HPV model with vaccination and cancerous delay

Cervical cancer is a prevalent cancer, caused by persistent HPV infection and poses a severe danger to public health worldwide. The transition from HPV infection to cervical cancer is a protracted process, typically spanning many years, and is hereby referred to as the cancerous delay. To take into account the impact of the cancerous delay in transmission between HPV and cervical cancer, we develop a delayed model that correlates HPV and cervical cancer to investigate the transmission behavior of HPV. Firstly, we demonstrate the existence and stability of equilibria. Then, we identify the existence of Hopf bifurcation, which is induced by the cancerous delay, and discuss its properties, subsequently estimate the duration of delay which maintains the stability of bifurcating periodic solutions. Additionally, we introduce and evaluate an optimal control model. Then, we modify the forward-backward sweep method for the non-delayed model which further addresses the optimal control problem for the delayed model. The results reveal that a comprehensive strategy combining pharmacological interventions with non-pharmacological approaches is the most effective method for controlling the disease. Ultimately, we utilize numerical simulations to substantiate the validity of our theoretical results.