A small number of individuals infected within a community can lead to the rapid spread of the disease throughout that community, leading to an epidemic outbreak. This is even more true for highly contagious diseases such as COVID-19, known to be caused by the new coronavirus SARS-CoV-2. Mathematical models of epidemics allow estimating several impacts on the population and, therefore, are of great use for the definition of public health policies. Some of these measures include the isolation of the infected (also known as quarantine), and the vaccination of the susceptible. In a possible scenario in which a vaccine is available, but with limited access, it is necessary to quantify the levels of vaccination to be applied, taking into account the continued application of preventive measures. This work concerns the simulation of the spread of the COVID-19 disease in a community by applying the Monte Carlo method to a Susceptible-Exposed-Infective-Recovered (SEIR) stochastic epidemic model. To handle the computational effort involved, a simple parallelization approach was adopted and deployed in a small HPC cluster. The developed computational method allows to realistically simulate the spread of COVID-19 in a medium-sized community and to study the effect of preventive measures such as quarantine and vaccination. The results show that an effective combination of vaccination with quarantine can prevent the appearance of major epidemic outbreaks, even if the critical vaccination coverage is not reached.

在一个社区内感染的少数人会导致该疾病在整个社区内迅速传播，从而导致流行病暴发。对于传染性很强的疾病，例如已知由新型冠状病毒SARS-CoV-2引起的COVID-19等传染性疾病，则更是如此。流行病的数学模型可以估算对人口的若干影响，因此，在定义公共卫生政策时非常有用。其中一些措施包括隔离感染者（也称为隔离区）和对易感者进行疫苗接种。在可能获得疫苗但获得途径有限的情况下，有必要对要应用的疫苗接种水平进行量化，同时要考虑到持续采取预防措施。这项工作涉及通过将蒙特卡洛方法应用于易感暴露传染恢复（SEIR）随机流行模型来模拟COVID-19疾病在社区中的传播。为了处理所涉及的计算工作，采用了一种简单的并行化方法并将其部署在小型HPC群集中。先进的计算方法可以真实地模拟COVID-19在中等规模社区中的传播情况，并可以研究预防措施（如检疫和疫苗接种）的效果。结果表明，即使未达到关键的疫苗接种覆盖率，疫苗接种与隔离的有效结合也可以防止重大流行病的出现。