### AIMS Mathematics

2020, Issue 3: 2646-2670. doi: 10.3934/math.2020172
Research article Special Issues

# Sensitivity analysis and optimal treatment control for a mathematical model of Human Papillomavirus infection

• Received: 07 December 2019 Accepted: 02 March 2020 Published: 16 March 2020
• MSC : 92C60, 92D30

• 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.

Citation: Kai Zhang, Yunpeng Ji, Qiuwei Pan, Yumei Wei, Yong Ye, Hua Liu. Sensitivity analysis and optimal treatment control for a mathematical model of Human Papillomavirus infection[J]. AIMS Mathematics, 2020, 5(3): 2646-2670. doi: 10.3934/math.2020172

### Related Papers:

• 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.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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