$3$

M $408$Q Worksheet $4$: More SIR

Consider the evolution of a product that follows the usual SIR model, except that, now, rejected people become potentials again after an average of c days, after which they can become active users again. $($This variation is sometimes called the SIRS model, as people move from the S category to the I category to the R category and then back to S$.)$

Question $5.$ Modify the usual SIR equations to re$$ect this new feature. Your equations will involve unspeci$$ed parameters a$,$ b$,$ and c$.$

a$)$

b$)$

c$)$

d$)$

Question $6.$ Do you expect there to be more or fewer active users than with the regular SIR model?

a$)$ We should have MORE active users, since once individuals re$-$enter the susceptible class, they can become active users again, adding to the number of active users.

b$)$ We should have MORE active users, since susceptible users will stay active users longer.

c$)$ We should have FEWER active users, since there will be more users entering the rejected user stage.

d$)$ We should have FEWER active users, since once the individuals re$-$enter the susceptible class, they will be less inclined to try the product again.