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main.m
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main.m
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%% Parameters
% model parameters
parsM.Tinc = 4; % length of incubation period (days)
parsM.Tinf = 6; % duration patient is infectious (days)
parsM.etaI = 0.1; % *true* transmission effectivenesss, note transmission rate beta ~ etaI*contactRate
parsM.mu = 1e-2; % case fatality ratio
parsM.c_baseline = 5; % baseline contact rate (/day)
parsM.Ntot = 1e7; % total number of population (neglect death)
parsM.numSVar = 10; % number of state variables
parsM.numCVar = 1; % number of control variables
% contact rates - c_S, c_E, c_I, c_R, c_V
parsM.cA = [parsM.c_baseline; parsM.c_baseline; parsM.c_baseline/2; ...
parsM.c_baseline; parsM.c_baseline];
parsM.cB = [parsM.c_baseline; parsM.c_baseline; parsM.c_baseline/2; ...
parsM.c_baseline; parsM.c_baseline];
parsM.kappa = 0;
parsM.total_vaccines = 0.7*parsM.Ntot;
% simulation params
parsS.idx = 1;
parsS.step = 0.02;
usa_vac_rate = 0.5/(6*30); % USA ~6 months for 50% fully vaccinated
parsS.vaccination_rate_baseline = 1 * usa_vac_rate * parsM.Ntot;
% numerical solver parameters;
parsT.dt = 1e-1;
%% Simulation of outbreak
% outbreak simulation with true model
parsT.t0 = 0;
parsT.tf = 12*30; % 12 months
ini_infected_1_base = 500; % initial infected cases in A
ini_infected_2_base = 500; % initial infected cases in B
ini_infected_multiplier_vector = 1;
% costate boundary condition
lambda_tf = zeros(12,1);
lambda_tf(6) = 1; % grad of D_A
% initial subpopulations of A and B
initial_state.A = [parsM.Ntot - ini_infected_1_base, 0, ...
ini_infected_1_base, 0, 0, 0];
initial_state.B = [parsM.Ntot - ini_infected_2_base, 0, ...
ini_infected_2_base, 0, 0, 0];
%% kappa vector
kappa_iter =1;
kappa_vec = 0;
for i = 8:-1:2
for j = 1:9
kappa_vec(kappa_iter) = j * 10^(-i);
kappa_iter = kappa_iter +1;
end
end
kappa_vec(kappa_iter) = 10^(-1);
lambda = usa_vac_rate * parsM.Ntot;
vac_donated_coarse_opt = zeros(length(0.5*lambda:0.05*lambda:1.5*lambda),length(kappa_vec));
%% coarse search for start point
mu_vec = 0:0.03:1;
vac_rate_idx = 1;
if ~isfile('coarse_start_pt_10^7_pop.mat')
for vaccination_rate = 0.5*lambda:0.05*lambda:1.5*lambda
parsS.vaccination_rate_baseline = vaccination_rate;
vac_rate_idx
kappa_idx = 1;
for kappa = kappa_vec
parsM.kappa = kappa;
for i =1:length(mu_vec)
parsS.VA = parsM.total_vaccines * (1-(mu_vec(i)));
parsS.VB = parsM.total_vaccines * (mu_vec(i));
state_sol_test= state_solver(parsM, parsT, parsS,initial_state);
deaths_A(i) = state_sol_test.A(end,end);
deaths_B(i) = state_sol_test.B(end,end);
end
[min_death_A, idx] = min(deaths_A);
mu_optimal_val = mu_vec(idx);
vac_donated_coarse_opt(vac_rate_idx, kappa_idx) = mu_optimal_val;
kappa_idx = kappa_idx + 1;
end
save('coarse_start_pt_10^7_pop', 'vac_donated_coarse_opt')
vac_rate_idx = vac_rate_idx + 1;
end
save('coarse_start_pt_10^7_pop', 'vac_donated_coarse_opt')
end
%% gradient desc for optimal
load('coarse_start_pt_10^7_pop.mat')
vac_rate_idx = 1;
for vaccination_rate = 0.5*lambda:0.05*lambda:1.5*lambda
parsS.vaccination_rate_baseline = vaccination_rate;
vac_rate_idx
kappa_idx = 1;
%kappa_vec = [10^(-8), 10^(-7),10^(-6),10^(-5), 10^(-4), 10^(-3),...
% 10^(-2), 10^(-1)];
for kappa = kappa_vec
parsM.kappa = kappa;
kappa
dv = 0.02;
dm = 0.004;
vac_donated = vac_donated_coarse_opt(vac_rate_idx, kappa_idx); % use coarse opt as start pt for gradient desc
grad_prev = 10^5;
grad = 10^5;
parsS.step = 0.02;
while abs(grad) > 0.1
parsS.VA = parsM.total_vaccines * (1-vac_donated);
parsS.VB = parsM.total_vaccines * vac_donated;
state_sol = state_solver(parsM, parsT, parsS, initial_state);
J1 = state_sol.A(end, end);
parsS.VA = parsM.total_vaccines * (1-(vac_donated + dv));
parsS.VB = parsM.total_vaccines * (vac_donated + dv);
state_sol_test = state_solver(parsM, parsT, parsS, initial_state);
J2 = state_sol_test.A(end,end);
grad_prev = grad;
grad = (J2-J1)/dv;
if grad*grad_prev < 0
parsS.step = parsS.step/2;
end
if abs(grad) > 1
grad = grad/abs(grad);
end
vac_donated = vac_donated - parsS.step*grad;
if vac_donated >= 0.5
vac_donated = 0.5;
break
end
if vac_donated <= 0
vac_donated = 0;
break
end
end
vac_don_save(vac_rate_idx, kappa_idx) = vac_donated;
kappa_idx = kappa_idx + 1;
end
save('vac_don_save_70_perc_10^7_pop', 'vac_don_save')
vac_rate_idx = vac_rate_idx + 1;
end
%%
figure(1)
for i = 1:vac_rate_idx-1
semilogx(kappa_vec, vac_don_save(i, :),'Linewidth', 3);
hold on
%val = ini_frac_min + (i-1)*ini_frac_delta;
%title("ini fraction = " + val )
%ylim([0, 0.4])
end
xlabel('Kappa', 'FontName', 'Times New Roman','FontSize',20,'Interpreter','latex');
ylabel('Optimal fraction', 'FontName', 'Times New Roman','FontSize',20, 'Interpreter','latex');
%%
save('vac_don_save_70_perc_10^7_pop.mat', 'vac_don_save')
%% comparison of baseline, 1/3, 1/2 and optimal strats
fatalities_baseline.A = 0 * vac_don_save; % no share strat
fatalities_baseline.B = fatalities_baseline.A;
fatalities_optimal = fatalities_baseline; % optimal share strat
fatalities_third_share = fatalities_baseline; % mu = 1/3 strat
fatalities_half_share = fatalities_baseline; % mu = 0.5 strat
vac_rate_vec = 0.5*lambda:0.05*lambda:1.5*lambda;
for i = 1:length(vac_rate_vec)
for j = 1:length(kappa_vec)
parsM.kappa = kappa_vec(j);
parsS.vaccination_rate_baseline = vac_rate_vec(i);
vac_donated = [0, 1/3, 1/2, vac_don_save(i, j)];
for k = 1:4
% setup for no share
parsS.VA = parsM.total_vaccines * (1-vac_donated(k));
parsS.VB = parsM.total_vaccines * vac_donated(k);
state_sol = state_solver(parsM, parsT, parsS, initial_state);
if k == 1 % no share
fatalities_baseline.A(i, j) = state_sol.A(end, end);
fatalities_baseline.B(i, j) = state_sol.B(end, end);
elseif k == 2 % 1/3 share
fatalities_third_share.A(i, j) = state_sol.A(end, end);
fatalities_third_share.B(i, j) = state_sol.B(end, end);
elseif k ==3 % 1/2 share
fatalities_half_share.A(i, j) = state_sol.A(end, end);
fatalities_half_share.B(i, j) = state_sol.B(end, end);
elseif k == 4 % optimal share
fatalities_optimal.A(i, j) = state_sol.A(end, end);
fatalities_optimal.B(i, j) = state_sol.B(end, end);
end
end
end
end
%%
fatalities_all.baseline = fatalities_baseline;
fatalities_all.optimal = fatalities_optimal;
fatalities_all.third = fatalities_third_share;
fatalities_all.half = fatalities_half_share;
save('strategy_compare_10^7_pop.mat', 'fatalities_all');