AIMS Mathematics, 2020, 5(3): 2646-2670. doi: 10.3934/math.2020172.

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

1 School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, P. R. China
2 Biomedical Research Center, Northwest Minzu University, Lanzhou, P. R. China
3 Department of Gastroenterology and Hepatology, Erasmus MC-University Medical Center, Rotterdam, The Netherlands
4 Department of Genetics, Inner Mongolia Maternal and Child Care Hospital, Hohhot, Inner Mongolian Autonomous Region, P. R. China
5 Experimental Teaching Department, Northwest Minzu University, Lanzhou 730030, P. R. China

Special Issues: Mathematical modeling in medicine

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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Keywords HPV-disease; forward bifurcation; sensitivity analysis; optimal control; numerical simulations

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. AIMS Mathematics, 2020, 5(3): 2646-2670. doi: 10.3934/math.2020172

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