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Epidemics and pandemics are a field of scientific research since ancient times. The intensity of the repeated phenomena demonstrates their cyclicality in time. The ongoing COVID-19 pandemic, also known as the coronavirus pandemic, confirmed observations made in previous disease outbreaks. Epidemics are mainly characterized by two factors: (a) the population dynamics and (b) the nature of the disease. This article uses continuous mathematical models, on the basis of a scalable compartmental approach, characterized by systems of ordinary differential equations under the condition that individuals can freely move from one compartment to another. Numerous experiments were carried out to examine the impact of quarantine and vaccination policies, separately or in combination, on cumulative viral load, a measure adopted to reflect the cumulative viral burden of an infected population for a given time period. Current findings demonstrate that quarantine may play a crucial role in controlling an epidemic at its early stages, as well as the importance of early and widespread implementation of a vaccination program. The suggested approach may be utilized to study specific quarantine and vaccination scenarios, by manipulating various parameters such as the duration and extent of social distancing measures or the effectiveness and compliance to vaccination policies, and thus assist in decision making.