Epidemic Model & Control The Infection$-$Quarantine dynamics of a pandemic are as follows: BST ia N $-$I$+$U $(1)$ Q$=-$U $-$ Q $(2)$I$,$ Q represent infected, quarantine states. $$ B$,7$ are the transmission, recovery rates. $$S$,$ N are the susceptible and total population. Initially S $=$ N$.$ The values of the parameters are given to be: B $=0\mathrm{.}2,7=0\mathrm{.}1.$ Following is an output feedback strategy to suppress the infection: $$ At any given instance t$,$ an intervention is made by identifying and se$-$ lecting U $=-$al individuals for removal from I and moving them into isolation Q$,$ where a is the rate of test and quarantine. Problem $2$ This question is on frequency response control and carries $3\mathrm{.}5+9$ points. $1.$ Find the transfer function I$/$U$,$ is the system stable? $2.$ Design a lead compensator Kst to stabilize the infections with a band$-$ width of at least $2.$