Fig. 1.

Numerical solution of the models, giving the susceptible S(t) (blue points), infected I(t) (red points) and removed R(t) (green points) populations as functions of time t in days; the corresponding colored lines give the approximate solutions obtained by the analytical expressions, Eq. (3). Left: The SIR model, with parameter values $\beta =0.25$ and $\gamma =1/10$; the parameter β is constant. Right: The SIR model with a time-dependent parameter β with exponential decay and parameter values ${\beta }_0=0.25,$$\gamma =1/20,$$\lambda =50$ (see text for details). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)