6. (10 points) An SIR model is a simplied model of the spread of an infectious disease. We assume that the epidemic proceeds among a wellvmixed population over a sufciently short period that births, deaths, and immigration can be ignored. Infective individuals average 2) contacts per day sufficient to spread the disease; of these contacts, a fraction S (r) of them are susceptible. The parameter It depends on the infectious period. (For example, if time is measured in days and infectives can transmit the disease on average for a week, then It : 1/ 7.) Suppose that all infectives eventually recover and acquire permanent immunity. If 5(1'), I0), and RU) dene the fraction of the population that is susceptible, infective, and recovered, respectively, then under these assumptions, the SIR model can be written as S'{r) = bS(r)I(r) Hr) = bS(r)I(t)k1(r) R'{r) : MU). Below are graphs showing the progress over a 150vday period of two epidemics that have the same values of b (i.e., in each epidemic, infectives average equal numbers of contacts per day suicient to spread the disease). The susceptible, infective, and recovered fractions of the population are shown in the blue, red, and green curves, respectively. Which epidemic has the longer infectious period? Justify your answer. (No justication, no credit.) 0 50 100 150 o 50 100 150