The longer someone delays getting vaccinated, the less likely they are to get vaccinated at all. In our new study, we explore how this long-lasting vaccine hesitancy can impact how an epidemic unfolds.
Using data from the COVID-19 vaccination campaign in Portugal, we analysed vaccination waiting times (i.e. time between being eligible for vaccination and getting the vaccine) over a 5-month period for a cohort of people above 65 years.
The vaccination waiting times displayed a heavy-tail distribution, meaning that while many individuals received the vaccine quickly at the beginning of the campaign, a substantial fraction delayed their vaccination for extended periods. A heavy-tail distribution differs from the exponential distribution assumed in traditional models by predicting that delays are not uniformly unlikely but instead get more likely over time, with some individuals remaining unvaccinated far longer than expected.
That’s why we developed a fractional order SIR model, incorporating fractional derivatives. Our model quantified the effect of the hesitancy and showed that the hesitancy can have a strong persistent effect. Essentially, the longer an individual stays unvaccinated, the longer they are likely to remain that way. We show that this behaviour greatly impacts the dynamics of disease spread of COVID-19.
Our study highlights the value of exploring alternative models, such as fractional-order models, in epidemiological contexts with specific characteristics, such as the dynamics of vaccine hesitancy. We show that traditional models may fail to capture the nuances of scenarios where events are not independent of the past (i.e. memory effects). This approach also opens the door to applying fractional-order models to other contexts where memory effects or heavy-tail distributions play a critical role.
It has been great to work together with our Portuguese collaborators. Congrats to all the authors!
Read the full paper here.