Abstract
Virus outbreaks have the potential to be a source of severe sanitarian and economic crisis. We propose a new methodology to study the influence of several parameter combinations on the dynamical behavior of simple epidemiological compartmental models. Using this methodology, we analyze the behavior of a simple vaccination model. We find that for susceptible-infected-recovered (SIR) models with seasonality and natural death rate, a new vaccination can reduce the chaoticity of epidemic trajectories, even with nonvaccinated adults. This strategy has little effect on the first infection wave, but it can stop subsequent waves.