目的 研究一類具有飽和接觸率且潛伏期、染病期均傳染的非線性SEIRS流行病傳播數學模型動力學性質，方法 利用Lasalle不變集原理和Routh Hurwitz判據探討系統的漸近性態，結果 得到了疾病絕滅與持續的閾值———基本再生數,證明了無病平衡點的全域漸近穩定性和地方病平衡點的區域漸近穩定性,揭示了潛伏期傳染的影響，結論 潛伏期有傳染的疾病,不但要注意控制染病期的病人,還要注意控制潛伏期的病人，只有這樣,才能有效地控制疾病的蔓延，
clear all; clc;
close all;
load('Infectious_data', 'T', 'X'); % load data generated by ODE45
load('prediction'); % Data from NN
X = X';
% Generate training data
train_size = 20; % size of trainning data
x_idx = randperm(1000);
T_train = T(x_idx(1:train_size));
X_train = X(:,x_idx(1:train_size));
Y_train = X(:,x_idx(1:train_size)+1);
%% DMD Main
% Dynamic mode decomposition: Classic
Ad = Y_train * pinv(X_train);
[U,S,~] = svd(X_train,'econ');
eig_tru = sum(diag(S)>=0.01*max(diag(S))); % Truncate eigenvalues to reduce noise
U = U(:,1:eig_tru);
Ad_til = U'*Ad*U;
[W,D] = eig(Ad_til);
Omega = diag(log(diag(D)));
Phi = U*W;
c = W \ U' * X(:,1);
X_DMD = zeros(size(X,1),length(T));
for t = 0:length(T)-1
X_DMD(:,t+1) = Phi*expm(Omega*t)*c;
end
%% Koopman Main
% Define feature according to Brusselator
Psi = @(x) [x(1); x(2); x(3); x(4); x(5); x(6); x(7); x(1)*x(3); x(1)*x(4); x(1)*x(5)];
Psi_X = [];
Psi_Y = [];
for i = 1:train_size
Psi_X = [Psi_X,Psi(X_train(:,i))];
Psi_Y = [Psi_Y,Psi(Y_train(:,i))];
end
完整代碼添加QQ1575304183
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