The link provided has all the information needed to answer the questions. https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread-of-disease-the-contact-number

From this link answer the question below.

1 Show that i + s 1n8 is independent of time and use the fact that this quantity is c Ins the same at time t = 0 and as t > 00 to explain why 0 = tlim s 1. >oo