已知含有9个微分的微分方程组，带参数，根据已知数据，拟合曲线，得参数最优解

adogpp · 发表于 2020-12-8 11:21

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% syms s(t) e(t) i1(t) p(t) h(t) f(t) iph(t) %定义符号变量
% syms Beta IoTa Beta_2 Kappa Rho_1 Rho_2 Gamma_a Gamma_i Gamma_r Delta_i Delta_p Delta_h 希腊字母参数
N = 11000000/250;
%dS/dt
dy(1)=-Beta*(y(3)/N)*y(1)-Iota*Beta*(y(6)/N)*y(1)-Beta_2*(y(4)/N)*y(1);
%dE/dt
dy(2)=Beta*(y(3)/N)*y(1)+Iota*Beta*(y(6)/N)*y(1)+Beta_2*(y(4)/N)*y(1)-Kappa*y(2);
%dI/dt
dy(3)=Kappa*Rho_1*y(2)-(Gamma_a+Gamma_i)*y(3)-Delta_i*y(3);
%dP/dt
dy(4)=Kappa*Rho_2*y(2)-(Gamma_a+Gamma_i)*y(4)-Delta_p*y(4);
%dA/dt
dy(5)=Kappa*(1-Rho_1-Rho_2)*y(2);
%dH/dt
dy(6)=Gamma_a*(y(3)+y(4))-Gamma_r*y(6)-Delta_h*y(6);
%dR/dt
dy(7)=Gamma_i*(y(3)+y(4))+Gamma_r*y(6);
%dF/dt
dy(8)=Delta_i*y(3)+Delta_p*y(4)+Delta_h*y(6);%
%d(I+P+H)/dt
dy(9)=dy(3)+dy(4)+dy(6);
%y(9)数据
y9data1 = [6,  12,  19,  25,  31,  38,  44,  60,  80,  131,  131,  259,  467,  688,  776 ...,
      1776,  1460,  1739,  1984,  2101,  2590,  2827,  3233,  3892,  3697,  3151 ...,
      3387,  2653,  2984,  2473,  2022,  1820,  1998,  1506,  1278,  2051,  1772 ...,
      1891,  399,  894,  397,  650,  415,  518,  412,  439,  441,  435,  579,  206 ...,
      130,  120,  143,  146,  102,  46,  45,  20,  31,  26,  11,  18,  27,  29,  39,  39];
%y(8)数据
y8data1= [0,  0,  0,  0,  0,  0,  0,  0,  4,  4,  4,  8,  15,  15,  25,  26,  26 ...,
38,  43,  46,  45,  57,  64,  66,  73,  73,  86,  89,  97,  108,  97,  254 ...,
121,  121,  142,  106,  106,  98,  115,  118,  109,  97,  150,  71,  52,  29 ...,
44,  37,  35,  42,  31,  38,  31,  30,  28,  27,  23,  17,  22,  11,  7,  14 ...,
10,  14,  13,  13];