An Exploratory Study on the Simulation of Stochastic Epidemic Models

A small number of people infected with a contagious disease in a large community can lead to the rapid spread of the disease by many of the people in that community, leading to an epidemic. Mathematical models of epidemics allow estimating several impacts on the population, such as the total and maximum number of people infected, as well as the duration and the moment of greatest impact of the epidemic. This information is of great use for the definition of public health policies. This work is concerned with the simulation of the spread of infectious diseases in small to medium communities by applying the Monte Carlo method to a Susceptibles-Infectives-Recovered (SIR) stochastic epidemic model. To minimize the computational effort involved, a simple parallelization approach was adopted and deployed in a small HPC cluster. The simulations conducted show that an epidemic outbreak can occur even if the initial number of infected people is small, and that this probability decreases significantly with the vaccination of a population subset.