a4, you will salyee a model of disesie spread in a population, called the SIR model. This system Wots models the spread of an endemic discase that confers immunity. The dependent variables in roseat individuals that are ntisoeptible to the diseave (S), infected by it ( 1), or recovered/remosed of thene variables change over time t, the independent variable. N=S+I+R is the total number in the popalation. and initial conditions are: Y,F(t,Y),Y0 to write (1) in the standard form {=r(t,)(0)=e prob1, tse your improved Euler's method to nolve the system from part (a) appraximately, parameter values given in the table. of the improved Euler's method is W^0=Y0Wi+1=W1+2h[F(ti,Wi)+F(t1+1,Wi+hF(t1,Wi))],i=0,,n1 ipproximations that you get for S(t),I(t) and R(t)=NS(t)I(t) for times in [0,T] on the and add a legend. Problem 3 : An SIR model for disease spread of \& In this problem, yoi will arialyoe a model of disesse spread in a pogralation, calfed the SIR model. This system of three eyuathons models tbe mpread of an endernic diseose that oonfers immunity. The dependent variables itu the modn represent individuale that arn aborptithe 6 the dasose (S), infected by it (1), or rocoverod/remosed (R). All three of these variables chanme ore time t, the independent variable. N=S+I+R is the total atumber of indivinguls in the populstion. The ciuatiots and initial craulitious ars: (1) dtdS=(NS)SI,0tTS(0)=S0dtdt=St(+)t,0tTt(0)=I0 (a) Identify Y5Y(t,Y1,Y0 to write (1) in the atrndard forn {Y=1(t1)Y(0)=Y0 (b) In In your prob1, ase your improved Euler's method to nolve the ayatem from part. (a) approximately: asouming the parmmeter values given in the table. 'The definition of the improwed Einler's method is {W^9=Y0WS+1=Wi+2h[F(ti,W4)+F(ti1,Wt+hF(ti,Wi))],i=0,,n1 Present the epprosimations that you net for S(t),I(t) and R(t)=NS(t)I(t) for times in [0,T] on the name figure and add a logend