Please help, I don't understand the error. How I can make it correct?

%%%%this function is defined, to input the model equation into matlab, 
% to be called on later for fitting the function takes three inputs
function SIRmodel(t,y,par)
lambda=par(1);
gamma=par(2);
S=y(1);
I=y(2);
R=y(3);
N=S+I+R;
Sdot=-lambda*I*S;
Idot=lambda*I*S-gamma*I;
Rdot=gamma*I;
f=[Sdot Idot Rdot];
end
%%%% i use the ode45 to solve the differential equation
function sol=SIRSol(par,IC,t)
DeHandle=@(T,Y) SIRModel(t,y,par);
[~,Y]=ode45(DeHandle,t,IC);
sol=Y';
end
%%%%first tke 20 randomly chosen time points
numpts=20;
tdata=[0 sort(20*rand(1,numpts))];
%%%% then we generate normally distribute noise:

width=0.1;
ndataSIR=20*[0 randn(0,width,[1,numpts]); 0 randn(0,width,[1,numpts]);  0 randn(0,width,[1,numpts])];
lambda=0.01;
%%%%i add the noise term to the model outputs
gamma=0.1;
par=[lambda gamma];
IC=[50 1 0];
%%%visualize the data
SIRData=SIRSol(Par, IC, tdata)+ndataSIR;
SIRData=[0 1 0 ; 1 1 1]*SIRData;
figure()
plot(tdata,SIRData(1,:),'r*');
hold on;
plot(tdata,SIRData(2,:),'o');
%%%i define the least-square error term

SIRparSol=@(par) sum(sum((SIRparSol ([par(1) par(2)],IC,t);
sumsquaresSIR=@(par) sum(sum((SIRparSol (par , tdata)-SIRData).2));
%%%call fminsearch with an initial guess
[SIRtheta,fval,exitflag]=fminsearch(SumSquaresSIR,[8 0.02]);
SIRsol=SIRparSol(SIRtheta,tsol);
figure;
plot(tdata, SIRData, '.')
hold on;
plot(tsol, SIRsol,'--');

[qaisar badshah]

ndataSIR=20*[0 normrnd(0,width,[1,numpts]); 0 normrnd(0,width,[1,numpts]); 0 normrnd(0,width,[1,numpts])];

Answer 1

[Sulaymon Eshkabilov]

There are a few crucial points overlooked in your code.

(1) Placement of input entries

(2) Placement of functions (SIRSol, SIRmodel, SIRparSOL) and from where they are called to run

(3) Syntaxes how to call/execute the functions.

Here is a simple example how to structure such functions and call them respectively. E.g.:

x0 = 0;
xend=13;
Ndata = 200;
[x, y] = Main(x0, xend, Ndata);
DEMO_data = Plot_ALL(x, y);

function [x, y] = Main(x1, x2,N)
x = linspace(x1, x2, N);
y = sin(x);
end

function H=Plot_ALL(x, y)
H=plot(x, y, 'ro--', 'DisplayName', 'x vs. y');
grid on
end

Answer 2

[Kevin Holly]

The line here need to be fixed:

ndataSIR=20*[0 randn(0,width,[1,numpts]); 0 randn(0,width,[1,numpts]);  0 randn(0,width,[1,numpts])];

You have width as an input. The input variable to randn need to be an integer (here width = 0.1). Even if that is fixed, [1,numpts] is not scalar and won't be accepted as an input. What are you trying to do on this line? Did you mean to use randn as opposed to rand? rand could accept 0.1, but I'm not sure what you are trying to do.

[qaisar badshah]

i want to generate normaly distribute noise.

so i replace it with

ndataSIR=20*[0 normrnd(0,width,[1,numpts]); 0 normrnd(0,width,[1,numpts]); 0 normrnd(0,width,[1,numpts])];

but still it shows error

[qaisar badshah]

Error using SIRModel

Too many output arguments.

Error in SIRSol>@(t,y)SIRModel(t,y,par) (line 2)

DeHandle=@(t,y) SIRModel(t,y,par);

Error in odearguments (line 87)

f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 113)

[neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...

Error in SIRSol (line 3)

[~,Y]=ode45(DeHandle,t,IC);

Error in lastSIR (line 9)

SIRData=SIRSol(par, IC, tdata)+ndataSIR;

[qaisar badshah]

thank you, Kevin Holly.

[Kevin Holly]

%%%%first tke 20 randomly chosen time points
numpts=20;
tdata=[0 sort(20*rand(1,numpts))];
%%%% then we generate normally distribute noise:
width= 0.1; % width needs to be an integer for it to be an input into randn, so i changed it to 1
ndataSIR=20*[0 normrnd(0,width,[1,numpts]); 0 normrnd(0,width,[1,numpts]);  0 normrnd(0,width,[1,numpts])];

lambda=0.01;
%%%%i add the noise term to the model outputs
gamma=0.1;
par=[lambda gamma];
IC=[50 1 0];
%%%visualize the data
SIRData=SIRSol(par, IC, tdata)+ndataSIR;

Unrecognized function or variable 'y'.

Error in solution>@(T,Y)SIRModel(t,y,par) (line 46)
DeHandle=@(T,Y) SIRModel(t,y,par);

Error in odearguments (line 92)
f0 = ode(t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 107)
odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

Error in solution>SIRSol (line 47)
[~,Y]=ode45(DeHandle,t,IC);

SIRData=[0 1 0 ; 1 1 1]*SIRData;
figure()
plot(tdata,SIRData(1,:),'r*');
hold on;
plot(tdata,SIRData(2,:),'o');
%%%i define the least-square error term
SIRparSol=@(par) sum(sum((SIRparSol([par(1) par(2)],IC,t))));
sumsquaresSIR=@(par) sum(sum((SIRparSol(par, tdata)-SIRData)*0.2));
%%%call fminsearch with an initial guess
[SIRtheta,fval,exitflag]=fminsearch(SumSquaresSIR,[8 0.02]);
SIRsol=SIRparSol(SIRtheta,tsol);
figure;
plot(tdata, SIRData, '.')
hold on;
plot(tsol, SIRsol,'--');

%%%%this function is defined, to input the model equation into matlab, to be called on later for fitting the function takes three inputs
function SIRmodel(t,y,par)
    lambda=par(1);
    gamma=par(2);
    S=y(1);
    I=y(2);
    R=y(3);
    N=S+I+R;
    Sdot=-lambda*I*S;
    Idot=lambda*I*S-gamma*I;
    Rdot=gamma*I;
    f=[Sdot Idot Rdot];
end
%%%% i use the ode45 to solve the differential equation

This function here uses a variable y that is undefined. Do you know what y should be?

function sol=SIRSol(par,IC,t)
    DeHandle=@(T,Y) SIRModel(t,y,par);
    [~,Y]=ode45(DeHandle,t,IC);
    sol=Y';
end