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We propose and study an epidemiological model on a social network that takes into account heterogeneity of the population and different vaccination strategies. In particular, we study how the COVID-19 epidemics evolves and how it is contained by different vaccination scenarios by taking into account data showing that older people, as well as individuals with comorbidities and poor metabolic health, and people coming from economically depressed areas with lower quality of life in general, are more likely to develop severe COVID-19 symptoms, and quicker loss of immunity and are therefore more prone to reinfection. Our results reveal that the structure and the spatial arrangement of subpopulations are important epidemiological determinants. In a healthier society the disease spreads more rapidly but the consequences are less disastrous as in a society with more prevalent chronic comorbidities. If individuals with poor health are segregated within one community, the epidemic outcome is less favorable. Moreover, we show that, contrary to currently widely adopted vaccination policies, prioritizing elderly and other higher-risk groups is beneficial only if the supply of vaccine is high. If, however, the vaccination availability is limited, and if the demographic distribution across the social network is homogeneous, better epidemic outcomes are achieved if healthy people are vaccinated first. Only when higher-risk groups are segregated, like in elderly homes, their prioritization will lead to lower COVID-19 related deaths. Accordingly, young and healthy individuals should view vaccine uptake as not only protecting them, but perhaps even more so protecting the more vulnerable socio-demographic groups. [ABSTRACT FROM AUTHOR]