Abstract
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.
Highlights
Uterine cervical cancer is a worldwide health problem but it is especially concerning in developing countries
It is estimated that the probability of a person being infected with human papillomavirus (HPV) in their lifetime reaches 70 to 80% [2], and the total infection rate in the global population is as high as 11.7% [3]
We found that the possibility of HPV transmission to lead to endemic disease can be reduced by strengthening the protection after cure
Summary
Uterine cervical cancer is a worldwide health problem but it is especially concerning in developing countries. The risk of invasive cervical cancer occurs earlier than of most adult cancers, peaking or reaching a plateau between about 35 and 55 years of age [13] This distribution is because cervical cancers originate mainly from HPV infections transmitted sexually in late adolescence and early adulthood [14]. Sharomi and Malik [21] developed a two-sex HPV vaccination model to study the effect of vaccine compliance on HPV infection and cervical cancer. Omame [22] developed a two-sex deterministic model for HPV that assessed the impact of treatment and Mathematical Biosciences and Engineering. Elbasha [23] presented a two-sex, deterministic model for assessing the potential impact of a prophylactic HPV vaccine with several properties. Through extensive numerical simulations with MATLAB, we obtained results to verify our conclusions
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