Epidemic processes with vaccination and immunity loss studied with the BLUES function method

The BLUES function method is applied to the epidemiological SIRS model with vaccination, described by coupled nonlinear ordinary differential equations. Accurate analytic approximations are obtained for the time evolution of the susceptible and infected population fractions. The results are compared with those obtained with alternative methods, notably Adomian decomposition, variational iteration and homotopy perturbation. In contrast with these methods, the BLUES iteration converges rapidly, globally, and captures the exact asymptotic behaviour for long times. The time of the infection peak is calculated using the BLUES approximants and the results are compared with numerical solutions.