SIRC_RLSQ modificaticon

SIRC_RLSQ.m

@@ -12,7 +12,7 @@ C0 = 0;
 S0 = N - I0 - R0 - C0;
 % Initial parameteres
 nu = 14;
-mu = 0.015;
+mu = 0.013;
 epsilon = 1.2;
 beta = 0.0002;
 gamma = 0.05;
@@ -31,31 +31,11 @@ xlabel('Time(days)');
 ylabel('Number of individuals');
 legend('S', 'I', 'R', 'C');
 
-
-%% Add noise
-noise = wgn(size(t,1), 4, 0, 42);
-y_noise = y + noise;
-
-figure(2)
-plot(t, y_noise);
-xlabel('Time(days)');
-ylabel('Number of individuals');
-legend('S', 'I', 'R', 'C');
-
-
-[t_noisy, y_noisy] = ode45(@(t, y) noisy_deriv(y, nu, mu, epsilon, beta, gamma, Gamma, q), [0 time], y0);
-
-figure(3)
-plot(t_noisy, y_noisy);
-xlabel('Time(days)');
-ylabel('Number of individuals');
-legend('S', 'I', 'R', 'C');
-
-%% Recursive Least Square
+%% Recursive Least Square without noise
 
 h = 1.0;
 lambda0 = 0.95; % 0.95-0.99
-alpha = 0.7;
+alpha = 0.5;
 N = length(y);
 
 % dSdt = nu - beta*I*S - epsilon*beta*C*S - mu*S;
@@ -67,22 +47,21 @@ phi_S(:,3) = y(1:end-1, 4) .* y(1:end-1, 1);
 phi_S(:,4) = y(1:end-1, 1);
 
 [theta_S, p_S] = recursiveLSQ(phi_S, y_S, lambda0, alpha)
-figure(4)
-plot(1:size(theta_S, 1), theta_S);
+figure(2)
+plot(theta_S);
 legend('nu', '-beta', '-epsilon*beta', '-mu')
 
-% dIdt = beta*I*S + epsilon*beta*C*S - gamma*I - mu*I;
+% dIdt = beta*I*S + epsilon*beta*C*S - (gamma + mu)*I;
 y_I = (y(2:end, 2) - y(1:end-1, 2)) / h;
-phi_I = zeros(N-1, 4);
+phi_I = zeros(N-1, 3);
 phi_I(:,1) = y(1:end-1, 2) .* y(1:end-1, 1);
 phi_I(:,2) = y(1:end-1, 4) .* y(1:end-1, 1);
 phi_I(:,3) = y(1:end-1, 2);
-phi_I(:,4) = y(1:end-1, 2);
 
 [theta_I, p_I] = recursiveLSQ(phi_I, y_I, lambda0, alpha)
-figure(5)
-plot(1:size(theta_I, 1), theta_I);
-legend('beta', 'epsilon*beta', '-gamma', '-mu')
+figure(3)
+plot(theta_I);
+legend('beta', 'epsilon*beta', '-(gamma+mu)')
 
 % dRdt = gamma*(1-q)*I + Gamma*C - mu*R;
 y_R = (y(2:end, 3) - y(1:end-1, 3)) / h;
@@ -92,19 +71,18 @@ phi_R(:,2) = y(1:end-1, 4);
 phi_R(:,3) = y(1:end-1, 3);
 
 [theta_R, p_R] = recursiveLSQ(phi_R, y_R, lambda0, alpha)
-figure(6)
-plot(1:size(theta_R, 1), theta_R);
+figure(4)
+plot(theta_R);
 legend('gamma*(1-q)', 'Gamma', '-mu')
 
-% dCdt = gamma*q*I - Gamma*C - mu*C;
+% dCdt = gamma*q*I - (Gamma + mu)*C;
 y_C = (y(2:end, 4) - y(1:end-1, 4)) / h;
-phi_C = zeros(N-1, 3);
+phi_C = zeros(N-1, 2);
 phi_C(:,1) = y(1:end-1, 2);
 phi_C(:,2) = y(1:end-1, 4);
-phi_C(:,3) = y(1:end-1, 4);
 
 [theta_C, p_C] = recursiveLSQ(phi_C, y_C, lambda0, alpha)
-figure(7)
-plot(1:size(theta_C, 1), theta_C);
-legend('gamma*q', '-Gamma', '-mu')
+figure(5)
+plot(theta_C);
+legend('gamma*q', '-(Gamma+mu)')