Open AccessMathematical analysis of a human papillomavirus transmission model with vaccination and screening
Author(s) -
Kai Zhang,
Xinwei Wang,
Hua Liu,
Yun Peng Ji,
Qiuwei Pan,
Yumei Wei,
Mengyu Ma
Publication year - 2020
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2020294
Subject(s) - vaccination , human papillomavirus , basic reproduction number , maximum principle , transmission (telecommunications) , herd immunity , optimal control , pontryagin's minimum principle , mathematics , mathematical model , hopf bifurcation , sensitivity (control systems) , computer science , mathematical optimization , biology , virology , medicine , bifurcation , statistics , physics , nonlinear system , engineering , population , telecommunications , environmental health , quantum mechanics , electronic engineering
We formulate a mathematical model to explore the transmission dynamics of human papillomavirus (HPV). In our model, infected individuals can recover with a limited immunity that results in a lower probability of being infected again. In practice, it is necessary to revaccinate individuals within a period after the first vaccination to ensure immunity to HPV infection. Accordingly, we include vaccination and revaccination in our model. The model exhibits backward bifurcation as a result of imperfect protection after recovery and because the basic reproduction number is less than one. We conduct sensitivity analysis to identify the factors that markedly affect HPV infection rates and propose an optimal control problem that minimizes vaccination and screening cost. The optimal controls are characterized according to Pontryagin's maximum principle and numerically solved by the symplectic pseudospectral method.