SENSITIVITY ANALYSIS OF A SYSTEM OF AN ODE USING NORMALIZED SENSITIVITY FUNCTION

I want to perform the sensitivity analysis on the parameters of an ODE SIR model using normalized sensitivity function. I used the following code below. When it was run, I got this error: "undefined functionnor variable ‘p’, error in epidemic1 line8, F=ode45(@epidemic,ic,p)". How can I resolve it to get the plots?
My interest is to get the figure (3) i.e. The plot of nomalized sensitivity functions against time
function epidemic1()

clc

beta=0.4; gamma=0.04;
p1 = [beta gamma];
ic = [995;5;0];
F = ode45(@epidemic,ic,p);

sol1 = solve(F,0,80)

figure(1)
plot(sol1.Time,sol1.Solution,’-o’)
legend(‘S’,’I’,’R’)
title([‘SIR Populations over Time’,’$beta=0.4$, $gamma=0.04$’],’Interpreter’,’latex’)
xlabel(‘Time’,’Interpreter’,’latex’)
ylabel(‘Population’,’Interpreter’,’latex’)

Figure(2)
p2 = [0.2 0.1];
F.Parameters = p2;
F.Sensitivity = odeSensitivity;
sol2 = solve(F,0,80)

plot(sol2.Time,sol2.Solution,’-o’)
legend(‘S’,’I’,’R’)
title([‘SIR Populations over Time’,’beta=0.2$, $gamma=0.1$’],’Interpreter’,’latex’)
xlabel(‘Time’,’Interpreter’,’latex’)
ylabel(‘Population’,’Interpreter’,’latex’)

U11 = squeeze(sol2.Sensitivity(1,1,:))’.*(p2(1)./sol2.Solution(1,:));
U12 = squeeze(sol2.Sensitivity(1,2,:))’.*(p2(2)./sol2.Solution(1,:));
U21 = squeeze(sol2.Sensitivity(2,1,:))’.*(p2(1)./sol2.Solution(2,:));
U22 = squeeze(sol2.Sensitivity(2,2,:))’.*(p2(2)./sol2.Solution(2,:));
U31 = squeeze(sol2.Sensitivity(3,1,:))’.*(p2(1)./sol2.Solution(3,:));
U32 = squeeze(sol2.Sensitivity(3,2,:))’.*(p2(2)./sol2.Solution(3,:));

Figure(3)
t = tiledlayout(3,2);
title(t,[‘Parameter Sensitivity by Equation’,’$beta=0.2$, $gamma=0.1$’],’Interpreter’,’latex’)
xlabel(t,’Time’,’Interpreter’,’latex’)
ylabel(t,’% Change in Eqn’,’Interpreter’,’latex’)
nexttile
plot(sol2.Time,U11)
title(‘$beta$, Eqn. 1′,’Interpreter’,’latex’)
ylim([-5 5])
nexttile
plot(sol2.Time,U12)
title(‘$gamma$, Eqn. 1′,’Interpreter’,’latex’)
ylim([-5 5])
nexttile
plot(sol2.Time,U21)
title(‘$beta$, Eqn. 2′,’Interpreter’,’latex’)
ylim([-5 5])
nexttile
plot(sol2.Time,U22)
title(‘$gamma$, Eqn. 2′,’Interpreter’,’latex’)
ylim([-5 5])
nexttile
plot(sol2.Time,U31)
title(‘$beta$, Eqn. 3′,’Interpreter’,’latex’)
ylim([-5 5])
nexttile
plot(sol2.Time,U32)
title(‘$gamma$, Eqn. 3′,’Interpreter’,’latex’)
ylim([-5 5])
function dydt = epidemic(t,y,p)
dydt = [0;0;0];
S = y(1);
I = y(2);
R = y(3);
N = S + I + R;

dSdt = -beta*(I*S)/N;
dIdt = beta*(I*S)/N – gamma*I;
dRdt = gamma*I;

end
endI want to perform the sensitivity analysis on the parameters of an ODE SIR model using normalized sensitivity function. I used the following code below. When it was run, I got this error: "undefined functionnor variable ‘p’, error in epidemic1 line8, F=ode45(@epidemic,ic,p)". How can I resolve it to get the plots?
My interest is to get the figure (3) i.e. The plot of nomalized sensitivity functions against time
function epidemic1()

clc

beta=0.4; gamma=0.04;
p1 = [beta gamma];
ic = [995;5;0];
F = ode45(@epidemic,ic,p);

sol1 = solve(F,0,80)

Figure(2)
p2 = [0.2 0.1];
F.Parameters = p2;
F.Sensitivity = odeSensitivity;
sol2 = solve(F,0,80)

dSdt = -beta*(I*S)/N;
dIdt = beta*(I*S)/N – gamma*I;
dRdt = gamma*I;

end
end I want to perform the sensitivity analysis on the parameters of an ODE SIR model using normalized sensitivity function. I used the following code below. When it was run, I got this error: "undefined functionnor variable ‘p’, error in epidemic1 line8, F=ode45(@epidemic,ic,p)". How can I resolve it to get the plots?
My interest is to get the figure (3) i.e. The plot of nomalized sensitivity functions against time
function epidemic1()

clc

beta=0.4; gamma=0.04;
p1 = [beta gamma];
ic = [995;5;0];
F = ode45(@epidemic,ic,p);

sol1 = solve(F,0,80)

Figure(2)
p2 = [0.2 0.1];
F.Parameters = p2;
F.Sensitivity = odeSensitivity;
sol2 = solve(F,0,80)

dSdt = -beta*(I*S)/N;
dIdt = beta*(I*S)/N – gamma*I;
dRdt = gamma*I;

end
end sensisitivity analysis, ode, normalized sensitivity MATLAB Answers — New Questions

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