how to draw separate graphs

Good afternoon sir,

Sir I have taken lsqnonlin method to estimate parameters and draw the graphs for prediction.Here i have to draw graphs for 2,3,4 columns but it shows only one column for predictions.sir i request please tell me how to draw graphs for 3rd and 4th columns and also please tell me how to separate graphs.please give me 3 to 5 lines code if possible.

Thanking you sir

the code and graph are

code:

data = [  1  1  0  0
    2  1  0  0
    3  1  0  0
    4  2  0  0
    5  3  0  0
    6  3  0  0
    7  3  0  0
    8  3  0  0
    9  3  0  0
    10  3  0  0
    11  3  0  0
    12  3  0  0
    13  3  0  0
    14  3  0  0
    15  3  1  0
    16  3  1  0
    17  3  1  0
    18  3  2  0
    19  3  2  0
    20  3  2  0
    21  3  2  0
    22  3  3  0
    23  3  3  0
    24  3  3  0
    25  3  3  0
    26  3  3  0
    27  3  3  0
    28  3  3  0
    29  3  3  0
    30  3  3  0
    31  3  3  0
    32  3  3  0
    33  5  3  0
    34  6  3  0
    35  28  3  0
    36  30  3  0
    37  31  3  0
    38  34  3  0
    39  39  3  0
    40  48  3  0
    41  63  4  0
    42  71  4  0
    43  81  4  1
    44  91  10  1
    45  102  10  2
    46  112  13  2
    47  126  14  2
    48  146  15  3
    49  171  15  3
    50  198  20  4
    51  256  23  4
    52  334  23  4
    53  403  23  7
    54  497  25  9
    55  571  40  10
    56  657  43  11
    57  730  50  16
    58  883  75  19
    59  1019  85  24
    60  1139  102  27
    61  1326  137  41
    62  1635  150  47
    63  2059  169  53
    64  2545  191  69
    65  3105  230  83
    66  3684  286  96
    67  4293  329  118
    68  4777  394  134
    69  5350  469  161
    70  5915  565  181
    71  6728  635  227
    72  7599  786  249
    73  8453  972  290
    74  9211  1086  332
    75  10454  1198  359
    76  11485  1365  396
    77  12371  1509  423
    78  13432  1767  449
    79  14354  2040  487
    80  15725  2466  522
    81  17305  2854  560
    82  18544  3273  593
    83  20081  3976  646
    84  21373  4370  682
    85  23040  5012  722
    86  24448  5496  781
    87  26283  5938  825
    88  27890  6523  881
    89  29458  7103  939
    90  31360  7739  1008
    91  33065  8429  1079
    92  34866  9059  1154
    93  37262  10021  1231
    94  39826  10852  1323
    95  42778  11763  1463
    96  46434  12845  1566
    97  49405  14140  1694
    98  53007  15301  1785
    99  56351  16776  1889
    100  59690  17887  1986]

time = data(:,1);
c_data = data(:,[2,3,4]);
beta0 = 0.5;
alpha0 = 0.004;
gamma0 = 0.1;
upsilon0 = 0.13;
epsilon0= 0.07;
lamda0= 0.1;
sigma0= 0.07;
kappa0= 0.03;
nu0 = 0.0001;	
xi0 = 0.0002;
lb =[0,0,0,0,0,0,0,0,0,0]; ub = [1,1,1,1,1,1,1,1,1,1];
p0 = [beta0; alpha0; gamma0;  upsilon0; epsilon0; lamda0; sigma0; kappa0; nu0; xi0 ];
options = optimoptions(@lsqnonlin,'Algorithm','trust-region-reflective');
[p,resnorm,RESIDUAL,exitflag,OUTPUT,LAMBDA,Jacobian] = lsqnonlin(@(p) immanuel(p,time,c_data),p0,lb,ub,options );
disp(p)
Cdata_minus_Cv =immanuel(p,time,c_data);
Cv = c_data-Cdata_minus_Cv;
plot(time,[c_data,Cv])
function  C=immanuel(p,time,c_data)
c0 = [1217378052,100,10,5,3,3,1,1];
[T,Cv]=ode45(@DifEq,time,c0);
    function dC=DifEq(time,c)
        N = 1390000000;
        pi = 150;
        zeta = 0.1;
        eta = 0.2;
        theta = 0.3;
        iota = 0.3;
        delta = 0.1;
        rho = 0.5;
        mu = 0.0000425;
        beta = p(1);
        alpha =p(2);
        gamma = p(3);
        upsilon =p(4);
        epsilon = p(5);
        lamda = p(6);
        sigma = p(7);
        kappa = p(8);
        nu = p(9);	
        xi = p(10);
        dcdt = zeros(8,1);
        dcdt(1) = pi -beta*(zeta*c(3)+eta*c(4)+theta*c(5)+iota*c(6))*(c(1)/N) -mu*c(1);
        dcdt(2) = beta*(zeta*c(3)+eta*c(4)+theta*c(5)+iota*c(6))*(c(1)/N) -(delta+mu)*c(2); 
        dcdt(3) = rho*delta*c(2)-(lamda+gamma+nu+mu)*c(3);
        dcdt(4) = (1-rho)*delta*c(2)-(sigma+kappa+mu)*c(4);
        dcdt(5) = lamda*c(3) + sigma*c(4)-(alpha+upsilon+mu)*c(5);
        dcdt(6) = alpha*c(6)  + kappa*c(4)- (epsilon+xi+mu)*c(6);
        dcdt(7) =  gamma*c(3) + upsilon*c(5) + epsilon*c(6);
        dcdt(8) = nu*c(3)  + xi*c(6);
        dC = dcdt;
    end
C=c_data-Cv(:,2);
end

Graph:

[Star Strider]

What columns of the 8 created by the differential equations do you want to fit?

Also, this does not make sense:

C=c_data-Cv(:,2);

since ‘C’ should be the 3 columns of the solved differential equations that you want to fit to the data, nothing else, for example:

C = Cv(:,[2 4 8]);

or whatever of them you want to fit.

[mallela ankamma rao]

Thanks for your reply sir.

sir if it is not correct please tell how to correct this. i want only graphing part for fitted values

with this code i estimated the parameter values but how to draw graph for curve fitting

in given data 1st column is days

2nd column is confirmed

3rd column is recovered

4th column is deased

i want curve fit for these columns.i request you please modify my code and give correct code for curve fitting sir.

[Torsten]

What do the 2nd, 3rd and 4th column of the matrix "data" represent ?

Should they be fitted against any of the columns of the vector Cv obtained from the ODE integration ?

As is - as Star Strider said - the statement

C=c_data-Cv(:,2);

doesn't make sense since c_data has 4 columns, Cv(:,2) is only one column.

[mallela ankamma rao]

Thanks for your reply sir

i understood your explanation about the graph. i am requesting you how to overcome that please give any suggestions or relating code. can i change with C = c_data - Cv?

[mallela ankamma rao]

i have to write like this for 3rd and 4th columns also. please anyone give some code for curve fitting

[Torsten]

I know that English is not your native language, but just try to answer the two questions I asked:

What do the 2nd, 3rd and 4th column of the matrix "data" represent ?

Should they be fitted against any of the columns of the vector Cv obtained from the ODE integration ?

[mallela ankamma rao]

sir this project is mathematical modeling on covid 19.

here 1st column represents days,2nd columns represents confirmed cases,3rd columns represents recovered cases and 4th column represents death cases which are taken from WHO.

In python i knew how to draw how to take curve fitting prediction data against the observed data.

please see code below which belongs to python

fig.add_trace(go.Scatter(x=tspan, y=data[:, 0], mode='markers', name='Observed confirmed', line = dict(dash='dot')))

fig.add_trace(go.Scatter(x=tspan, y=data[:, 1], mode='markers', name='Observed recovered', line = dict(dash='dot')))

fig.add_trace(go.Scatter(x=tspan, y=data[:, 2], mode='markers', name='Observed death', line = dict(dash='dot')))

fig.add_trace(go.Scatter(x=tspan, y=final[:, 0], mode='lines+markers', name='Fitted confirmed'))

fig.add_trace(go.Scatter(x=tspan, y=final[:, 1], mode='lines+markers', name='Fitted recovered'))

fig.add_trace(go.Scatter(x=tspan, y=final[:, 2], mode='lines+markers', name='Fitted death'))

fig.update_layout(title='SEIaIsQHR: Observed vs Fitted',

xaxis_title='Day',

yaxis_title='Counts',

title_x=0.5,

width=1000, height=500)

I need code like this model sir. please help how to draw plot

[Torsten]

Before you plot results, we should first make sure that your code is correct - that's why I insist.

At the moment, you subtract the vector Cv(:,2) from each column of the matrix c_data. Thus, lsqnonlin assumes that columns 2, 3 and 4 of your matrix "data" are repetitions of an experiment and that all three columns should be approximated by Cv(:,2) using one set of parameters. But I think this must be wrong since the values for the three columns differ significantly in size.

So again my question: Is it correct that you want lsqnonlin minimize [c_data(:,1)-Cv(:,2);c_data(:,2)-Cv(:,2);c_data(:,3)-Cv(:,2)] simultaneously ?

[mallela ankamma rao]

Thanks for your reply sir.

C = [c_data(:,1)-Cv(:,2);c_data(:,2)-Cv(:,2);c_data(:,3)-Cv(:,2)]

i have tried this sir but i did not get answer.

ERROR:

Arrays have incompatible sizes for this operation.

C=c_data-Cv(:,[2,3,4]);

is it correct sir?. I got only curve fitting for 2nd and 3rd column but i did not get curve fit for 4th column.please tell me how to modify this sir.

Answer 1

[Image Analyst]

Have you looked at nexttile or subplot? These will set up separate axes so that you can draw each curve in its own separate axes.

[mallela ankamma rao]

thanks for your reply sir

i did not see subplot .first i have to fix C = c_data - Cv. but i dont know how to fix sir.

Answer 2

[Image Analyst]

In hindsight, we know that the curves look like a series of Gaussians:

https://www.worldometers.info/coronavirus/

I'm attaching a demo that will fit your data to a specified number of Gaussians.

[Image Analyst]

I'm also attaching a demo that will fit a set of data to a single set of data increasing with exponential growth.

along with a fit I did years ago on COVID when it was just getting started.

[mallela ankamma rao]

Thanks alot for your reply sir.I will try sir