Fitting a system of ODEs to data using lsqcurvefit to estimate system's parameters

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Maryam Alyahyai 2022-4-11

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https://ww2.mathworks.cn/matlabcentral/answers/1693450-fitting-a-system-of-odes-to-data-using-lsqcurvefit-to-estimate-system-s-parameters

评论： Maryam Alyahyai 2022-4-12

I have a problem in using lsqcurvefit to fit data. I am not very good in matlab. My problem is about paramater estimation of a system of ODEs. I tried to use the lsqcurvefit in a way similar to fminsearchbnd. I managed to get a good fit and acceptable estimation of the parameters when using fminsearchbnd. However, when using lsqcurvefit I ended up with errors! One of the error tha I couldn't fix is: "Error using lsqcurvefit (line 229) FUN must have two input arguments"

I have attached the code and the excel sheet for data.

Thanks in advance for your help.

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Alex Sha 2022-4-12

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Hi, Maryam Alyahyai, I have told in previous answer that the result had been obtained by using another package named "1stOpt", the codes are as below, very simple. For Matlab solution, you may refer to Star Strider's great replies.

Parameter mu, beta_1, beta_2, beta_3, lambda_1, lambda_2, lambda_3, gamma_1, gamma_2, sigma, delta;
ParameterDomain = [0.00001,0.9];
InitialODEValue t=1, S = 5215663,E = 3779,A = 2103,P = 1512,I = 86,R = 233,N = 5215663+3779+2103+1512+86+233;
Variable t,I;
ODEFunction
S'=mu-beta_1*A*S/N - beta_2*P*S/N  - beta_3*I*S/N-mu*S ;
E'=beta_1*A*S/N  + beta_2*P*S/N  + beta_3*I*S/N - (mu + lambda_1 + lambda_2 + lambda_3)* E ;
A'= lambda_1*E - (mu+gamma_1)*A;
P'= lambda_2*E - (mu+sigma)*P;
I'= lambda_3*E + sigma*P- (mu + gamma_2 + delta)* I;
R'= gamma_1*A + gamma_2*I - mu*R;
N'= -delta*I;
Data;
t=1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103;
I=86,144,98,106,102,74,115,93,51,82,143,74,99,36,85,69,98,168,55,154,112,175,174,148,298,322,284,404,157,193,292,372,327,424,463,513,400,348,255,636,811,603,1014,786,576,738,778,770,930,866,604,712,689,1067,1117,1006,1404,1043,745,810,739,852,896,905,1605,1318,1142,1366,1132,919,1197,910,1010,1124,1361,1374,1177,1072,1557,1262,1210,1518,1889,1083,1318,2164,1839,1679,1327,1619,1311,1157,1739,1487,1660,1099,1145,1067,1147,1053,846,665,590;