Problem 1:The SIR epidemic model assumes that on average, an infected (and infectious) individual encounters a people per unit time. The susceptible population diminishes as they are infected (i.e. as they encounter infectious people).dSdt=-aSINote that quarantining would decrease the constant a, which is needed to control the spread of the disease. Also, the infected population increases with rate a, and decreases as people recover with the recovery rate k.dIdt=aSI-kIFinally, the recovered population increases with the recovery rate k.dRdt=kI(a) Show that I(t) does not increase if S(0) is less than or equal to ka.(b) Find and interpret the equilibria.(c) Set parameters a=0.003,k=0.5,I(0)=1,S(0)=700,R(0)=0. Use Euler's method to plot S,R,I on the same set of axes. Estimate the time at which the number of infected people is at a maximum, and the time at which the number of infected people decreases to zero. Make a plot of the trajectories (S,I).