SIRC RLS with additive ar noise

SIRC_noisyRLSQ.m

+clc
+%% System initalization
+% Population
+N = 1000;
+% Initial number of infected individuals
+I0 = 10;
+% Initial number of recovered individuals
+R0 = 0;
+% Initial number of carrier individuals
+C0 = 0;
+% Everyone else is susceptible
+S0 = N - I0 - R0 - C0;
+% Initial parameteres
+nu = 14;
+mu = 0.013;
+epsilon = 1.2;
+beta = 0.0002;
+gamma = 0.05;
+Gamma = 0.03;
+q = 0.8;
+
+time = 200;
+%t = linspace(0, time, time);
+
+y0 = [S0, I0, R0, C0];
+[t, y] = ode45(@(t, y) deriv(y, nu, mu, epsilon, beta, gamma, Gamma, q), [0 time], y0);
+
+
+%% Add noise
+
+[t_noisy, y_noisy] = ode45(@(t, y) noisy_deriv(y, nu, mu, epsilon, beta, gamma, Gamma, q), [0 time], y0);
+
+figure(1)
+plot(t_noisy, y_noisy);
+xlabel('Time(days)');
+ylabel('Number of individuals');
+legend('S', 'I', 'R', 'C');
+
+%% Recursive Least Square with ar additive noise
+
+h = 1.0;
+lambda0 = 0.99; % 0.95-0.99
+alpha = 0.8;
+N = length(y_noisy);
+
+% dSdt = nu - beta*I*S - epsilon*beta*C*S - mu*S;
+y_S = (y_noisy(2:end, 1) - y_noisy(1:end-1, 1)) / h;
+phi_S = zeros(N-1, 4);
+phi_S(:,1) = ones(N-1, 1);
+phi_S(:,2) = y_noisy(1:end-1, 2) .* y_noisy(1:end-1, 1);
+phi_S(:,3) = y_noisy(1:end-1, 4) .* y_noisy(1:end-1, 1);
+phi_S(:,4) = y_noisy(1:end-1, 1);
+
+[theta_S, p_S] = recursiveLSQ(phi_S, y_S, lambda0, alpha)
+figure(2)
+plot(theta_S);
+legend('nu', '-beta', '-epsilon*beta', '-mu')
+
+% dIdt = beta*I*S + epsilon*beta*C*S - (gamma + mu)*I;
+y_I = (y_noisy(2:end, 2) - y_noisy(1:end-1, 2)) / h;
+phi_I = zeros(N-1, 3);
+phi_I(:,1) = y_noisy(1:end-1, 2) .* y_noisy(1:end-1, 1);
+phi_I(:,2) = y_noisy(1:end-1, 4) .* y_noisy(1:end-1, 1);
+phi_I(:,3) = y_noisy(1:end-1, 2);
+
+[theta_I, p_I] = recursiveLSQ(phi_I, y_I, lambda0, alpha)
+figure(3)
+plot(theta_I);
+legend('beta', 'epsilon*beta', '-(gamma+mu)')
+
+% dRdt = gamma*(1-q)*I + Gamma*C - mu*R;
+y_R = (y_noisy(2:end, 3) - y_noisy(1:end-1, 3)) / h;
+phi_R = zeros(N-1, 3);
+phi_R(:,1) = y_noisy(1:end-1, 2);
+phi_R(:,2) = y_noisy(1:end-1, 4);
+phi_R(:,3) = y_noisy(1:end-1, 3);
+
+[theta_R, p_R] = recursiveLSQ(phi_R, y_R, lambda0, alpha)
+figure(4)
+plot(theta_R);
+legend('gamma*(1-q)', 'Gamma', '-mu')
+
+% dCdt = gamma*q*I - (Gamma + mu)*C;
+y_C = (y_noisy(2:end, 4) - y_noisy(1:end-1, 4)) / h;
+phi_C = zeros(N-1, 2);
+phi_C(:,1) = y_noisy(1:end-1, 2);
+phi_C(:,2) = y_noisy(1:end-1, 4);
+
+[theta_C, p_C] = recursiveLSQ(phi_C, y_C, lambda0, alpha)
+figure(5)
+plot(theta_C);
+legend('gamma*q', '-(Gamma+mu)')
+