Reference no: EM131522527

Find $p(1)$, $p(2)$, $p(3)$ and $p(4)$ which fit $N = [9.045015676e6 1.899453292e7 1.989903449e7 5.427009406e7 ...

9.045015676e7 2.532604389e8 3.979806897e8 4.341607524e8 ...

4.432057681e8 5.246109092e8 6.150610660e8];$

by use fminsearch code in Matlab.

\begin{equations}

dydt(1) = 0.515*y(1)*(1-y(1)*1e-9)/(1 + 8.164*y(1))- p(1)*y(3)*y(1)- p(2)*y(4)*y(1)- p(3)*y(5)*y(1)+ p(4)*y(6)*y(1) - 0.01525*y(2);

dydt(2) = -0.69*y(2) + 10*(heaviside(t-10) - heaviside(t-10.2));

dydt(3) =0.09*y(3)*y(5)*(1-(1/100000000)*y(3)-(1/100000000)*y(4))-0.03*y(3)+0.008*y(5)-(1/10000000)*y(3)*y(1)+0.00594*y(3)*y(2);

dydt(4) =0.09*y(4)*y(5)*(1-(1/100000000)*y(3)-(1/100000000)*y(4))-0.03*y(4)+0.008*y(6)-(1/10000000)*y(4)*y(1)+0.00594*y(2)*y(4);

dydt(5) = 0.02*y(5)*(1-(1/1000000000)*y(5)-(1/1000000000)*y(6))-0.07*y(5)+0.001*y(3)+0.09*y(6)-(1/10000000)*y(5)*y(1)+0.01*y(5)*y(2);

dydt(6) = 0.02*y(6)*y(4)*(1-(1/1000000000)*y(5)-(1/1000000000)*y(6))-0.11*y(6)+0.001*y(4)+0.05*y(5)+(1/10000000)*y(6)*y(1)-0.01*y(6)*y(2);

\end{equations}