and the choice of how long we keep

and the choice of how long we keep the wake values before switching to the leading front values is made automatically to ensure the smoothest curve, which is the most physical. An exact solution, if it could be found, would have a smooth behaviour, but it is difficult to obtain as our calculations are possible only under the approximation that the second derivative can be neglected. This approximation fails near the
maximum. Hence we make a smooth junction of the front and wake solutions. To illustrate this, we show more values of the trailing and leading solutions on one of the curves of Fig. 5, which is the case for which the junction is the least smooth. The comparison of infection waves from SIR and SEIR models ((3)–(6)) is shown in Fig. 7. We can see that the peak of infection wave in the SEIR model is less than the peak of infection wave in the SIR model. The length of the outburst in the SEIR model is also less than the length of the outburst in the SIR model.