SIR Model: The Boarding School Example - SAMSI

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Boarding School Example: MATLAB Cost Code function [Cost]=SIRCost(param, t,Infected, YInit, N) % param: 2x1 vector of beta and gamma % t: time data % Infected: infected data % Cost: value of sum of squared errors beta=param(1); gamma=param(2); options=[]; [t,PredY]=ode15s(@SIRode, t, YInit, options, beta, gamma, N); PredInfected=PredY(:,2); DiffY=PredInfected’-Infected; DiffYsq=(DiffY).ˆ2; Cost=sum(DiffYsq); SIR Model: The Boarding School Example – p. 6/8
Boarding School Example: Script Using Fminsearch and ODE time=[1:1:14]; Infected=[3 6 25 73 222 294 258 237 191 125 69 27 11 4]; N=763; %Initial Conditions: Susceptible 760, Infected: 3, Recovered: 0 YInit=[760 3 0]; options=[ ]; ParamInit=[0.01 0.1]; % Choose initial guesses for β and γ [ParamOpt] = fminsearch(@SIRCost,ParamInit,options, time,Infected, YInit, N) betaOpt=ParamOpt(1); gammaOpt=ParamOpt(2); [t,PredY]=ode15s(@SIRode, time, YInit, options, betaOpt, gammaOpt, N); PredInfected=PredY(:,2); figure plot(time,Infected, ’*’, t, PredInfected, ’-’) xlabel(’Time (in Days)’) ylabel(’Number Infected’) legend(’Data’, ’Model’) SIR Model: The Boarding School Example – p. 7/8
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Page 3 and 4: Boarding School Example: The Data T
Page 5: Least Squares: Sum of Squares of Re

SIR Model: The Boarding School Example - SAMSI

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