Computational simulation of the COVID-19 epidemic with the SEIR stochastic model

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.