Sensitivity analysis and optimal treatment control for a mathematical model of Human Papillomavirus infection
Kai Zhang, Yunpeng Ji, Qiuwei Pan, Yumei Wei, Yong Ye, Hua Liu
Abstract
Human papillomavirus (HPV) is one of the most common sexually transmitted viruses, and is a causal agent of cervical cancer. We aimed to develop a mathematical model of HPV natural history and qualitatively analyzed the stability of disease-free equilibrium, non-existence of limit cycle and existence of forward bifurcation. We performed sensitivity analysis to identify key epidemiological parameters. The Partial Rank Correlation Coefficient (PRCC) values for basic reproduction number shows that controlling contact rate plays an important role in disturbing equilibrium of HPV infection. Moreover, the increase of medical level is the most effective measure to prevent new HPV infections. Optimal treatment problem is solved and theoretical analysis is verified by numerical simulation.