Sensitivity Analysis And Optimal Control Of HPV Models With Treatment And Vaccines

Human papilloma virus is one of the most common sexually transmitted viruses.It is the cause of cervical cancer and other genital cancer.After long-term HPV infection,precancerous lesions will occur in the infected site,and then develop into cancer.In this paper,a HPV model considering treatment and vaccination was established.Next,the basic regeneration number was calculated,and the stability analysis and parameter sensitivity analysis were carried out.Finally,the optimal control problems such as the cost of vaccination is analyzed by using optimal control theory.Considering that the infected individuals can be cured,and the convalescent individuals with limited immunity have lower possibility of reinfection,the HPV transmission dynamics model is established based on the different infectivity of patients in different stages.The stability of disease-free equilibrium and the existence of forward bifurcation are qualitatively studied.Latin hypercube sampling and partial rank correlation coefficient were used to analyze the sensitivity of the parameters in the basic reproduction number and infection variables to determine the key factors affecting the transmission of HPV.The results showed that the control of contact rate played an important role in the suppression of HPV transmission.In addition,improving the medical level is the most effective measure to prevent and control HPV infection.Finally,the optimal control problem of minimizing the vaccination cost and the number of patients is considered.In order to maintain the long-term effect of immunization against HPV infection,it is necessary to revaccinate after vaccination for a period of time to make people immune to HPV infection for a long time.The possibility of endemic disease can be reduced by strengthening the protection after cure.Then sensitivity analysis is carried out to determine the key factors that may affect the transmission of HPV.The optimal control problem of minimizing the cost of vaccination and screening is considered.Theoretical analysis and corresponding numerical simulation are carried out.