i am using lsqnonlin method for estimating parameters and drawing graph.was is my graph correct or not?
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good morning sir
i got parameter values from lsqnonlin. i got figure for c_data vs fitting .
i have doubt sir .was the graph is correct or not?
if not i request you please modify sir
thank you sir
my code;
time = data(:,1);
c_data= data(:,2);
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)
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);
plot(time,c_data,time,C)
end
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/962165/image.jpeg)
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