In response to your question, Doc, I think that the objective of the study, the population, reality, resources, and context will shape the design of the study. Someone might choose to use a qualitative design if their objective is to understand in words while another may choose the quantitative design to understand in terms of numbers. On the other hand, another person may choose to mix both quali and quanti together to understand both perspectives altogether. Either way, from my experience, the aim/objective and research question(s) should guide the design to be chosen.
I agree with Yetunde. However, assessing the acceptance of HPV vaccine could be better done with a quantitative analysis but It would be more helpful to understand the barriers to HPV vaccine uptake by exploring the perceptions or perspective of the study population and outlining recommendations to scale up vaccination hence, a mixed method could be preferable from my humble opinion.
In other words, you can describe or quantify the proportion of participants willing and unwilling to accept HPV vaccine and investigate the influential factors, and furthermore use a qualitative study design to understand the concerns of the participants about HPV vaccine. For example, the proportion of those who may be hesitant to vaccinate could be explained by behavioral, cultural, accessibility or lack of health promotion, giving meaningful insights for recommendations.
Should you be willing to collaborate then I am available.
You can employ a combination of quantitative and qualitative research methods to gain a comprehensive understanding of various factors influencing acceptance of HPV vaccine. It's best to seek support from a statistician in order to design your study in the most approriate way to answer you study objective.