-
Notifications
You must be signed in to change notification settings - Fork 0
/
plot_all.m
281 lines (228 loc) · 10.6 KB
/
plot_all.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
%% 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;
% numerical solver parameters;
parsT.dt = 1e-1;
parsT.t0 = 0;
parsT.tf = 12*30; % 12 months
ini_infected_1_base = 500;
ini_infected_2_base = 500;
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];
usa_vac_rate = 0.5/(6*30);
lambda = usa_vac_rate * parsM.Ntot;
%% reduction in fatalities for different mu (Fig. 2 a/b/c)
mu_vec = 0:0.01:1;
parsM.kappa = 10^(-6);
parsS.vaccination_rate_baseline = 1*lambda;
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);
figure;
plot(mu_vec, deaths_A/(parsM.Ntot/10^7), 'b','Linewidth', 3)
hold on
plot(mu_vec, deaths_B/(parsM.Ntot/10^7), 'r','Linewidth', 3)
%plot(mu_vec, deaths_A + deaths_B, '--', 'Linewidth', 3)
yline(deaths_A(1)/(parsM.Ntot/10^7), '--b', 'Linewidth', 3)
yline(deaths_B(1)/(parsM.Ntot/10^7), '--r', 'Linewidth', 3)
plot(mu_optimal_val ,deaths_A(idx)/(parsM.Ntot/10^7), 'o', 'MarkerSize',10,...
'MarkerEdgeColor','blue', 'Linewidth', 2)
plot(mu_optimal_val ,deaths_B(idx)/(parsM.Ntot/10^7), 'o', 'MarkerSize',10,...
'MarkerEdgeColor','red', 'Linewidth', 2)
plot(0.33 ,deaths_A(34)/(parsM.Ntot/10^7), 'd', 'MarkerSize',10,...
'MarkerEdgeColor','blue', 'Linewidth', 2)
plot(0.33 ,deaths_B(34)/(parsM.Ntot/10^7), 'd', 'MarkerSize',10,...
'MarkerEdgeColor','red', 'Linewidth', 2)
reduction_A_optimal = (deaths_A(1) - deaths_A(idx))/deaths_A(1)*100;
reduction_B_optimal = (deaths_B(1) - deaths_B(idx))/deaths_B(1)*100;
reduction_A_33 = (deaths_A(1) - deaths_A(34))/deaths_A(1)*100;
reduction_B_33 = (deaths_B(1) - deaths_B(34))/deaths_B(1)*100;
fatalities_A = compose('%.1f',reduction_A_optimal);
str1 = {fatalities_A{1},'\% reduction in A'};
str1 = strjoin(str1, {'\b'});
fatalities_B = compose('%.1f',reduction_B_optimal);
str2 = {fatalities_B{1},'\% reduction in B'};
str2 = strjoin(str2, {'\b'});
% print fatality reduction
%text(0, 0, str1, 'FontSize', 20, Interpreter='latex')
%text(0, 10000, str2, 'FontSize', 20, Interpreter='latex')
xlim([0, 0.5])
axis square
legend('Fatalities in A ','Fatalities in B','Fatalities in A (no sharing)',...
'Fatalities in B (no sharing)','Fatalities in A (optimal)',...
'Fatalities in B (optimal)','Fatalities in A (33\% sharing)',...
'Fatalities in B (33\% sharing)','Interpreter','latex')
xlabel('$\mu$ (Fraction donated)','Interpreter','latex')
ylabel('Fatalities per $10^7$ over 1 year','Interpreter','latex')
set(gca,'FontSize',20);
legend boxoff
title('$\kappa = 10^{-6}$')
%% graphs for optimal strats
% heatmap showing optimal mu for different kappa and vaccination rates (Fig. 1)
load('vac_don_save_70_perc_10^7_pop.mat')
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);
figure;
%xvals = 0.5*lambda:0.1*lambda:1.5*lambda;
%xvals = {'0.5\lambda_0', '0.6\lambda_0','0.7\lambda_0','0.8\lambda_0','0.9\lambda_0'...
% ,'\lambda_0','1.1\lambda_0','1.2\lambda_0','1.3\lambda_0','1.4\lambda_0','1.5\lambda_0'};
%yvals = {10^(-8), 10^(-7),10^(-6),10^(-5), 10^(-4), 10^(-3),...
% 10^(-2), 10^(-1)};
%yvals = {'R_0 = 40','R_0 = 60','R_0 = 80','R_0 = 100'};
xvals = 0.5:0.05:1.5;
xvals = xvals * 100/360;
yvals = kappa_vec;
h = heatmap(xvals, yvals, vac_don_save','CellLabelColor','none');
%h = heatmap(vac_don_save','CellLabelColor','none');
h.Colormap = parula;
xlabel('Percentage vaccinated daily ($\%$)','Interpreter', 'latex')
ylabel('Coupling coefficient, $\kappa$','Interpreter', 'latex')
set(gca,'FontSize',20);
h.XDisplayLabels = compose('%.2f',str2double(h.XDisplayLabels));
for i = 1:3:63
yvals_cells{1, i} = yvals(i);
yvals_cells{1, i + 1} = "";
yvals_cells{1, i + 2} = "";
end
for i = 2:2:21
xvals_cells{1, i-1} = xvals(i-1);
xvals_cells{1, i} = "";
end
xvals_cells{1, 21} = xvals(21);
yvals_cells{1, 64} = yvals(64);
h.YDisplayLabels = yvals_cells;
h.NodeChildren(3).XAxis.Label.Interpreter = 'latex';
h.NodeChildren(3).YAxis.Label.Interpreter = 'latex';
h.NodeChildren(3).Title.Interpreter = 'latex';
h.NodeChildren(3).YDir='normal';
figure; % draw contour lines for heatmap of mu = 33 perc and 0
contour(vac_don_save', [0.33, 0.33],'--k', 'LineWidth',3)
hold on
contour(vac_don_save', [3*10^(-3),3*10^(-3)],'--r', 'LineWidth',3)
xticks(1:2:21)
xticklabels(xvals(1:2:21)*360)
title('No sharing', 'Interpreter', 'latex')
title('$33\%$ sharing', 'Interpreter', 'latex')
xlabel('Percentage vaccinated yearly ($\%$)','Interpreter', 'latex')
ylabel('Coupling coefficient, $\kappa$','Interpreter', 'latex')
set(gca,'FontSize',20);
%
% figure;
% yyaxis right
% plot(1:7, -20:20:100)
% yticks(-20:20:100)
% yticklabels({'-20\%','0\%','20\%','40\%','60\%','80\%','100\%'})
% set(groot,'defaultAxesTickLabelInterpreter','latex');
% set(gca,'FontSize',20);
% ax = gca;
% ax.YAxis(2).Color = 'k';
%% compute optimal v/s no share - change in fatalities in A and B (create matrix)
%load('strategy_compare.mat') % for 10^6 pop
load('strategy_compare_10^7_pop.mat')
% fatality change optimal
fatality_reduction_optimal.A = 100*(fatalities_all.baseline.A - fatalities_all.optimal.A)./fatalities_all.baseline.A;
fatality_reduction_optimal.B = 100*(fatalities_all.baseline.B - fatalities_all.optimal.B)./fatalities_all.baseline.B;
fatality_reduction_third.A = 100*(fatalities_all.baseline.A - fatalities_all.third.A)./fatalities_all.baseline.A;
fatality_reduction_third.B = 100*(fatalities_all.baseline.B - fatalities_all.third.B)./fatalities_all.baseline.B;
fatality_reduction_half.A = 100*(fatalities_all.baseline.A - fatalities_all.half.A)./fatalities_all.baseline.A;
fatality_reduction_half.B = 100*(fatalities_all.baseline.B - fatalities_all.half.B)./fatalities_all.baseline.B;
%% hybrid strat
% heatmap comparing hybrid strat (max(1/3, optimal)) with optimal
fatality_hybrid = fatalities_all.third;
fatality_reduction_hybrid_compare_optimal = fatality_reduction_third;
fatality_reduction_hybrid = fatality_reduction_third;
for i =1:length(vac_don_save(:, 1))
for j = 1:length(vac_don_save(1,:))
if vac_don_save(i, j) > 1/3
fatality_hybrid.A(i,j) = fatalities_all.optimal.A(i,j);
fatality_hybrid.B(i,j) = fatalities_all.optimal.B(i,j);
fatality_reduction_hybrid_compare_optimal.A(i,j) = 0;
fatality_reduction_hybrid_compare_optimal.B(i,j) = 0;
fatality_reduction_hybrid.A(i,j) = fatality_reduction_optimal.A(i,j);
fatality_reduction_hybrid.B(i,j) = fatality_reduction_optimal.B(i,j);
else
fatality_reduction_hybrid_compare_optimal.A(i,j) = (fatality_hybrid.A(i,j)-fatalities_all.optimal.A(i,j))/fatalities_all.optimal.A(i,j);
fatality_reduction_hybrid_compare_optimal.B(i,j) = (fatality_hybrid.B(i,j)-fatalities_all.optimal.B(i,j))/fatalities_all.optimal.B(i,j);
end
end
end
%% actual fatalities in no-share, optimal and hybrid
% no-share Fig. S1 (a)
plot_heatmap(xvals, yvals, fatalities_all.baseline.A, 0, 8*10^4);
plot_heatmap(xvals, yvals, fatalities_all.baseline.B, 0, 8*10^4);
% optimal Fig. S1 (b)
plot_heatmap(xvals, yvals, fatalities_all.optimal.A, 0, 8*10^4);
plot_heatmap(xvals, yvals, fatalities_all.optimal.B, 0, 8*10^4);
% hybrid Fig. S1 (c)
plot_heatmap(xvals, yvals, fatality_hybrid.A, 0, 8*10^4);
plot_heatmap(xvals, yvals, fatality_hybrid.B, 0, 8*10^4);
%% compare hybrid to optimal Fig. S2
plot_heatmap(xvals, yvals, 100*fatality_reduction_hybrid_compare_optimal.A, 0, 100);
plot_heatmap(xvals, yvals, -100*fatality_reduction_hybrid_compare_optimal.B, 0, 100);
%% graph of optimal reduction and hybrid reduction for a and b for vac rate of 50, 75, 100% per year
for i = 1:5:11
figure;
semilogx(kappa_vec, fatalities_all.baseline.A(i,:), ':b', 'Linewidth', 3)
hold on
semilogx(kappa_vec, fatalities_all.baseline.B(i,:), ':r', 'Linewidth', 3)
semilogx(kappa_vec, fatalities_all.optimal.A(i, :),'b','Linewidth', 2)
semilogx(kappa_vec, fatalities_all.optimal.B(i, :),'r','Linewidth', 2)
plot(kappa_vec, fatality_hybrid.A(i, :), '--b','Linewidth', 3)
plot(kappa_vec, fatality_hybrid.B(i, :), '--r','Linewidth', 3)
xline(10^(-4),'-.k','Linewidth', 2)
xticks([10^(-8),10^(-7),10^(-6),10^(-5),10^(-4),10^(-3),10^(-2),10^(-1)])
%yticks(-20:10:100)
legend('Fatalities in A (No-sharing)','Fatalities in B (No-sharing)','Fatalities in A (Optimal)','Fatalities in B (Optimal)',...
'Fatalities in A (Hybrid)','Fatalities in B (Hybrid)','Interpreter','latex')
legend boxoff
ax = gca;
ax.XAxisLocation = 'origin';
ylabel('Fatalities per $10^7$ in 1 year', 'Interpreter', 'latex')
%ylabel({'Excess';'deaths(\%)'}, interpreter='latex')
xlabel('Coupling coefficient, $\kappa$', 'Interpreter', 'latex')
ylim([0,10^5])
xlim([10^(-8), 10^(-1)])
set(gca,'FontSize',20);
text(10^(-5), 20, '$\hat{\mu} = 0.33$', 'FontSize', 20, Interpreter='latex')
text(10^(-5), 60, '$\hat{\mu} = \mu^*$', 'FontSize', 20, Interpreter='latex')
axis square
if i ==1
title('$50\%$ vaccinated in 1 year', 'Interpreter', 'latex')
elseif i == 6
title('$75\%$ vaccinated in 1 year', 'Interpreter', 'latex')
else
title('$100\%$ vaccinated in 1 year', 'Interpreter', 'latex')
end
end