Vaccination can sufficiently ameliorate the coronavirus disease-2019 (COVID-19). Investigating what factors influence vaccine uptake may benefit ongoing vaccination efforts (e.g. booster injections, annual vaccination). The present study expanded Protection Motivation Theory with possible factors including perceived knowledge, adaptive responses, and maladaptive responses to develop a proposed model investigating vaccine uptake among United Kingdom (UK) and Taiwan (TW) populations. An online survey collected responses from UK (n = 751) and TW (n = 1052) participants (August to September, 2022). The results of structural equation modeling (SEM) showed that perceived knowledge was significantly associated with coping appraisal in both samples (standardized coefficient β = 0.941 and 0.898; p < .001). Coping appraisal was correlated with vaccine uptake only in the TW sample (β = 0.319, p < .05). Multigroup analysis showed there were significant differences between the path coefficients of perceived knowledge to coping and threat appraisals (p < .001), coping appraisal to adaptive and maladaptive responses (p < .001), as well as threat appraisal to adaptive response (p < .001). Such knowledge may improve vaccine uptake in Taiwan. The potential factors for the UK population require further investigation.