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SEIR_tvarinf_dynamics.m
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SEIR_tvarinf_dynamics.m
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%SEI-Isr-R Model to evaluate effect of test-isolation strategy
% Idea is to use the proposed model structure and to tweak the
% parameters/infectiousness function to determine the region in which a
% test-isolation strategy would be reasonably effective for SARS-CoV-2 (and
% compare it to SARS-CoV-1
% Model structure:
% dS/dt = -beta(tau)*S*I;
% dE/dt = beta(tau)*S*I-gamma*E;
% dI/dt = gamma*E - alpha*delta*I -sigma*I
% dIsr/dt = alpha*delta*I;
% dR/dt = sigma*I;
%June 8 2020
close all; clear all; clc;
%% Make plot of time-dependent infectivity
dt = 0.1;
tend = 200;
tvec = 0:dt:tend;
tvec = tvec';
a = 2.12; % from He et al
b = 1/0.69; % from He et al
beta0 = 2.5;
w_tau = gampdf(tvec, a,b);
tsym = 2.3;
figure;
plot([0, 0], [0 0.28*beta0], 'k--')
hold on
plot(tvec-tsym, beta0.*w_tau, '-', 'LineWidth', 2)
legend('symptom onset')
legend('boxoff')
ylim([0 0.28*beta0])
xlim([ -tsym 11])
set(gca,'FontSize',16,'LineWidth',1.5)
xlabel ('Days after symptom onset')
ylabel ('Infectiousness')
title('SARS-CoV-2')
D = sum(w_tau.*dt.*tvec)
AUC=sum(w_tau)*dt*beta0
%% Run SEIR model with & without isolation
% Set IC to a single exposure
S0 = 999;
E0 = 0;
I0 = 1;
Isr0 = 0;
R0 = 0;
y0 = [S0, E0, I0, Isr0, R0];
N = sum(y0);
beta0 = 2.5; % initial rate of infection
gamma = 1/3; % 1/gamma = duration exposed but not detectable or infectious
alpha = 0; % alpha = proportion who will become symptomatic and seek testing
infend = 14; % time to be considered "recovered"
trem = 0+tsym; % time from infeciton to be removed
params = [beta0, gamma, alpha, infend, trem];
tau_params = horzcat(a,b);
D = a/b;
dt = 0.1;
tvec = 0:dt:tend;
disease = 'COVID';
%% Run ideal isolated and non-isolated scenarios
[y, B, new_inf, beta_t,inf_distrib, Reff] = fwd_SEIRD_model(params,tau_params, tvec, y0, dt, disease);
ihalf = find(y(:,1)<0.8*N, 1, 'first');
thalf = tvec(ihalf);
i1001 = find(y(:,3)>30, 1, 'first');
t1001 = tvec(i1001);
totinf = N-y(end,1);
totinf = N-y(end,1);
pctinf = 100*totinf/N;
inf = y(:,3)+y(:,4);
peakinf = 100*max(inf)/N;
colorsets1 = varycolor(500);
colorsets = varycolor(7);
figure;
for i = 1:500
plot(tvec, inf_distrib(:,i), '-','color', colorsets1(i,:), 'LineWidth', 2)
hold on
AUCi(round(i/100+1,0))=sum(inf_distrib(:,i));
%text(tauvec(i), inf_distrib(i, i), ['day ', num2str(i*dt)])
end
%legend('day 0', 'day 1', 'day 2', 'day 3', 'day 4', 'day 5', 'day 6')
%legend boxoff
xlim([ 0 14])
xlabel('infection time (\tau) (days)')
ylabel('Force of infection (I*\beta)')
title('Weighted infectiousness if no isolation')
set(gca,'FontSize',16,'LineWidth',1.5)
inf_distribNI=inf_distrib(:,500); % save for comparison figure
inf_distrib1 = inf_distrib;
figure;
subplot(2,2,1)
for i = 1:length(y0)
plot(tvec, 100*y(:,i)./N, '-', 'LineWidth',2)
%plot(tvec, 100*y(:,i)./N, '-', 'color', colorsets(i+5,:), 'LineWidth',2)
hold on
end
%plot(thalf, 80, 'k*', 'LineWidth', 4)
%text(thalf+5, 80, [num2str(round(thalf,0)), ' days to 20% infected'], 'FontSize', 14)
%text(tvec(end-150),y(end-150,1), [num2str(round(pctinf,0)), '% infected'], 'FontSize',14)
%ylim([ 0 0.1*N])
legend( 'S','E', 'I', 'I_{sr}', 'R', 't_{20% infected}', 'Location', 'NorthWest')
legend boxoff
xlabel('epidemic time (days)')
ylabel('% of population')
set(gca,'FontSize',16,'LineWidth',1.5)
%title(['No isolation'])
title(['No isolation, total infected = ', num2str(round(pctinf,0)),'%'])
%ylim([0 3.5e4])
subplot(2,2,2)
plot(tvec,new_inf./dt,'-', 'color',colorsets(6,:),'LineWidth', 2)
hold on
%plot(tvec, new_exp, 'm-', 'lineWidth', 2)
%plot(t, effI, 'LineWidth', 2)
%legend( 'new infections per day')
%legend boxoff
xlabel('epidemic time (days)')
ylabel('New infections per day')
set(gca,'FontSize',16,'LineWidth',1.5)
%title('Percent growth rate per day')
ylim([ 0 400])
title(['No isolation ', num2str(round(peakinf,0)),'% infected at peak'])
% subplot(2,2,2)
% plot(tvec,Rt1,'-', 'color',colorsets(6,:),'LineWidth', 2)
% hold on
% plot(tvec, beta0*ones(length(tvec),1), 'k--', 'LineWidth', 2)
% %plot(tvec, new_exp, 'm-', 'lineWidth', 2)
% %plot(t, effI, 'LineWidth', 2)
% %legend( 'new infections per day')
% %legend boxoff
% %xlim([ 0 50])
% xlabel('epidemic time (days)')
% ylabel('R_t')
% set(gca,'FontSize',16,'LineWidth',1.5)
% %title('Percent growth rate per day')
% title(['No isolation ', num2str(round(peakinf,0)),'% infected at peak'])
%ylim([0 4e4])
alpha2 = 0.8; % alpha = proportion who will become symptomatic and seek testing
infend = 14; % time to be considered "recovered"
trem = tsym; % time from infeciton to be removed
params2 = [beta0, gamma, alpha2, infend, trem];
[y, B, new_inf, beta_t,inf_distrib, Reffp] = fwd_SEIRD_model(params2,tau_params, tvec, y0, dt,disease);
ihalf = find(y(:,1)<0.8*N, 1, 'first');
thalf = tvec(ihalf);
i100 = find(y(:,3)>30, 1, 'first');
t100 = tvec(i100);
totinf = N-y(end,1);
pctinf = 100*totinf/N;
inf = y(:,3)+y(:,4);
peakinf = 100*max(inf)/N;
subplot(2,2,3)
for i = 1:length(y0)
plot(tvec, 100*y(:,i)./N, '-', 'LineWidth',2)
%plot(tvec, 100*y(:,i)./N, '-', 'color', colorsets(i,:), 'LineWidth',2)
hold on
end
%plot(thalf, 80, 'k*', 'LineWidth', 4)
%text(thalf+5, 80, [num2str(round(thalf,0)), ' days to 20% infected'], 'FontSize', 14)
%text(tvec(end-150),y(end-150,1), [num2str(round(pctinf,0)), '% infected'], 'FontSize',14)
%ylim([ 0 0.1*N])
legend( 'S','E', 'I', 'I_{sr}', 'R', 't_{20% infected}', 'Location', 'NorthWest')
legend boxoff
xlabel('epidemic time (days)')
ylabel('Number of individuals')
set(gca,'FontSize',16,'LineWidth',1.5)
%title('Perfect symptomatic isolation')
title(['Perfect symptomatic isolation, total infected= ', num2str(round(pctinf,0)),'%'])
%title(['Perfect symptomatic isolation ', num2str(round(pctinf,0)), '% infected total'])
%ylim([0 3.5e4])
subplot(2,2,4)
plot(tvec,new_inf/dt, '-', 'color', colorsets(6,:),'LineWidth', 2)
hold on
%plot(tvec, new_exp, 'm-', 'lineWidth', 2)
%plot(t, effI, 'LineWidth', 2)
%legend( 'new infections per day')
%legend boxoff
xlabel('epidemic time (days)')
ylim ([0 400])
ylabel('New infections per day')
set(gca,'FontSize',16,'LineWidth',1.5)
title(['Perfect symptomatic isolation ',num2str(round(peakinf,0)),'% infected at peak'])
% subplot(2,2,4)
% plot(tvec,Rt2,'-', 'color',colorsets(6,:),'LineWidth', 2)
% hold on
% plot(tvec, beta0*ones(length(tvec),1), 'k--', 'LineWidth', 2)
% %plot(tvec, new_exp, 'm-', 'lineWidth', 2)
% %plot(t, effI, 'LineWidth', 2)
% %legend( 'new infections per day')
% %legend boxoff
% xlabel('epidemic time (days)')
% ylabel('R_t')
% %xlim ([0 50])
% set(gca,'FontSize',16,'LineWidth',1.5)
% title(['Perfect symptomatic isolation ',num2str(round(peakinf,0)),'% infected at peak'])
%% Plot of individuals at each stage of infection and
figure;
plot(tvec, inf_distrib1(:,i1001), 'b-', 'LineWidth',5)
hold on
plot(tvec, inf_distrib(:,i100), 'r-', 'LineWidth', 5)
% for i = 1:500
% plot(tvec, inf_distrib1(:,i), 'b-', 'LineWidth',5)
% plot(tvec, inf_distrib(:,i), 'r-', 'LineWidth', 5)
% hold on
% %text(tauvec(i), inf_distrib(i, i), ['day ', num2str(i*dt)])
% end
%legend('day 0', 'day 1', 'day 2', 'day 3', 'day 4', 'day 5', 'day 6')
%legend boxoff
AUCNI = sum(inf_distrib1(:,500)).*dt;
AUCPSI = sum(inf_distrib(:,500)).*dt;
legend( ['no isolation, t=', num2str(t1001),' days'], ['perfect symptomatic isolation, t=', num2str(t100),' days'])
%legend(['no isolation, AUC= ',num2str(round(AUCNI,0))], ['perfect symptomatic isolation, AUC= ', num2str(round(AUCPSI,0))])
legend boxoff
xlim([ 0 14])
xlabel('infection stage (\tau)(days)')
ylabel('Number of individuals x relative infectiousness')
title('Comparison of weighted infectiousness at 30 infections')
set(gca,'FontSize',16,'LineWidth',1.5)
%% Adjust one parameter at a time form the perfect symptomatic removal scenario
% Effect of increasing the time to removal
trem = tsym+0;
alpha = 0.8;
params = [beta0, gamma, alpha, infend, trem];
% Time to remove
figure;
tremvec = [tsym:1:4+tsym];
alphavec = [0:0.2:0.8];
alphavec = fliplr(alphavec);
paramsi = params;
colorsets2 = varycolor(length(tremvec));
for i = 1:length(tremvec)
paramsi(5) = tremvec(i);
[y, B, new_inf, R_t, new_exp, Reff] = fwd_SEIRD_model(paramsi,tau_params, tvec, y0, dt, disease);
tot_inf = sum(y(:,3));
S_t(:,i) = y(:,1);
new_infi(:,i) = new_inf;
i20 = find(y(:,1)<0.8*N, 1, 'first');
t20(i) = tvec(i20);
pct_infected(i) = 100.*(1-(S_t(end,i)./N));
inf = y(:,3)+y(:,4);
peakinf(i) = 100*max(inf)/N;
Reffi(i) = Reff;
end
subplot(3,3,1)
for i = 1:length(tremvec)
plot(tvec, S_t(:,i)/N, '-', 'color', colorsets2(i,:), 'LineWidth',2)
hold on
%text(tvec(20*i), S_t(20*i), ['t_{isolate post symptoms}=', num2str(tremvec(i)-3)], 'FontSize', 14)
end
legend( '0 days', '1 day', '2 days', '3 days', '4 days')
legend boxoff
xlabel('epidemic time (days)')
ylabel('Proportion not infected')
set(gca,'FontSize',14,'LineWidth',1.5)
%title(' infections over time')
ylim([0 1])
subplot(3,3,2)
for i = 1:length(tremvec)
plot(tvec, new_infi(:,i)./dt, '-', 'color', colorsets2(i,:), 'LineWidth',2)
hold on
%text(tvec(20*i), 100*new_infi(20*i, i)/N, ['t_{isolate post symptoms}=', num2str(tremvec(i)-3)], 'FontSize', 14)
end
legend( '0 days', '1 day', '2 days', '3 days', '4 days')
legend boxoff
xlabel('epidemic time (days)')
ylabel('New infections per day')
set(gca,'FontSize',14,'LineWidth',1.5)
%title('Effect of removal time on growth rate')
subplot(3,3,3)
for i = 1:length(tremvec)
plot(tremvec(i)-tsym, Reffi(i), '*','color', colorsets2(i,:), 'LineWidth', 10)
hold on
end
%legend( '0 days', '1 day', '2 days', '3 days', '4 days', '5 days','Location', 'NorthWest')
%legend boxoff
%ylim([15 60])
ylim([1 3])
xlabel('Days after symptom onset an individual is isolated')
ylabel('R_{eff}')
set(gca,'FontSize',14,'LineWidth',1.5)
% subplot(3,3,3)
% for i = 1:length(tremvec)
% plot(tremvec(i)-tsym, peakinf(i), '*','color', colorsets2(i,:), 'LineWidth', 10)
% hold on
% end
% %legend( '0 days', '1 day', '2 days', '3 days', '4 days', '5 days','Location', 'NorthWest')
% %legend boxoff
% %ylim([15 60])
% xlabel('Days after symptom onset an individual is isolated')
% ylabel('Peak % infected at any time')
% set(gca,'FontSize',14,'LineWidth',1.5)
% %title('Effect of removal time peak infections')
% Effect of reducing the % removed
trem = tsym;
alpha = 0.8;
params = [beta0, gamma, alpha, infend, trem];
% Time to remove
paramsi = params;
for i = 1:length(alphavec)
paramsi(3) = alphavec(i);
[y, B, new_inf, R_t, new_exp, Reff] = fwd_SEIRD_model(paramsi,tau_params, tvec, y0, dt, disease);
tot_inf = sum(y(:,3));
S_t(:,i) = y(:,1);
new_infi(:,i) = new_inf;
i20 = find(y(:,1)<0.8*N, 1, 'first');
t20(i) = tvec(i20);
pct_infected(i) = 100.*(1-(S_t(end,i)./N));
inf = y(:,3)+y(:,4);
peakinf(i) = 100*max(inf)/N;
Reffi(i) = Reff;
end
subplot(3,3,4)
for i = 1:length(alphavec)
plot(tvec, S_t(:,i)/N, '-', 'color', colorsets2(i,:), 'LineWidth',2)
hold on
%text(tvec(20*i), S_t(20*i), ['t_{isolate post symptoms}=', num2str(tremvec(i)-3)], 'FontSize', 14)
end
legend( '80%', '60%', '40%', '20%', '0%')
legend boxoff
xlabel('epidemic time (days)')
ylabel('Proportion not infected')
set(gca,'FontSize',14,'LineWidth',1.5)
%title(' infections over time')
ylim([0 1])
subplot(3,3,5)
for i = 1:length(alphavec)
plot(tvec, new_infi(:,i)./dt, '-', 'color', colorsets2(i,:), 'LineWidth',2)
hold on
%text(tvec(20*i), 100*new_infi(20*i, i)/N, ['t_{isolate post symptoms}=', num2str(tremvec(i)-3)], 'FontSize', 14)
end
legend( '80%', '60%', '40%', '20%', '0%')
legend boxoff
xlabel('epidemic time (days)')
ylabel('New infections per day')
set(gca,'FontSize',14,'LineWidth',1.5)
%title('Effect of removal time on growth rate')
subplot(3,3,6)
for i = 1:length(alphavec)
plot(100*alphavec(i), Reffi(i), '*','color', colorsets2(i,:), 'LineWidth', 10)
hold on
end
%ylim([15 60])
ylim([1 3])
xlabel('Percent of cases isolated')
ylabel('R_{eff}')
set(gca,'FontSize',14,'LineWidth',1.5)
% subplot(3,3,6)
% for i = 1:length(alphavec)
% plot(100*alphavec(i), peakinf(i), '*','color', colorsets2(i,:), 'LineWidth', 10)
% hold on
% end
% %ylim([15 60])
% xlabel('Percent of cases isolated')
% ylabel('Peak % infected at any time')
% set(gca,'FontSize',14,'LineWidth',1.5)
%Ideal vs. Realistic scenario
tremvec = [tsym, 1.5+tsym, tsym];
alphavec = [0.8, 0.75*0.8, 0]; % assume you can isolate 75% of symptomatics
colorsets3 = [0 0 1;0 1 0; 1 0 0];
paramsi = params;
for i = 1:length(alphavec)
paramsi(3) = alphavec(i);
paramsi(5) = tremvec(i);
[y, B, new_inf, R_t, new_exp, Reff] = fwd_SEIRD_model(paramsi,tau_params, tvec, y0, dt, disease);
tot_inf = sum(y(:,3));
S_t(:,i) = y(:,1);
new_infi(:,i) = new_inf;
%ihalf = find(y(:,1)<0.5*N, 1, 'first');
%thalf(i) = tvec(ihalf);
pct_infected(i) = 100.*(1-(S_t(end,i)./N));
inf = y(:,3)+y(:,4);
peakinf(i) = 100*max(inf)/N;
Reffi(i) = Reff
end
% Ideal vs realistic
subplot(3,3,7)
for i = 1:length(alphavec)
plot(tvec, S_t(:,i)/N, '-','color', colorsets3(i,:), 'LineWidth', 2)
hold on
end
%legend('perfect', 'realistic','no isolation')
%legend boxoff
ylabel('Percent not infected')
xlabel('epidemic time (days)')
set(gca,'FontSize',14,'LineWidth',1.5)
%%title(['Ideal ', num2str(round(pct_infected(1),0)),'% infected vs realistic ', num2str(round(pct_infected(2),0)),'% infected scenarios'])
subplot(3,3,8)
for i=1:length(alphavec)
plot(tvec, new_infi(:,i)./dt, '-', 'color', colorsets3(i,:), 'LineWidth',2)
hold on
end
legend('perfect', 'realistic','no isolation')
legend boxoff
ylabel('New infections per day')
xlabel('epidemic time (days)')
set(gca,'FontSize',14,'LineWidth',1.5)
%title('Ideal vs. realistic vs. no isolation epidemic growth rate dynamics')
scenarios = {'perfect symptomatic isolation realistic no isolation'};
subplot(3,3,9)
for i = 1:length(alphavec)
bar( i, Reffi(i), 'FaceColor', colorsets3(i,:))
hold on
end
ylim([1 3])
%legend('perfect', 'realistic','no isolation')
%legend boxoff
set(gca,'FontSize',14,'LineWidth',1.5, 'XTickLabel', [])
ylabel ('R_{eff}')
%ylim([20 60])
% subplot(3,3,9)
% for i = 1:length(alphavec)
% bar( i, peakinf(i), 'FaceColor', colorsets3(i,:))
% hold on
% end
% %legend('perfect', 'realistic','no isolation')
% %legend boxoff
% set(gca,'FontSize',14,'LineWidth',1.5, 'XTickLabel', [])
% ylabel ('Peak % infected')
% %ylim([20 60])
%% What is the critical R0 to make realistic isolation reasonably effective?
% perfect, realistic, none
tremvec = [tsym, 1.5+tsym, tsym];
alphavec = [0.8, 0.75*0.8, 0]; % assume you can isolate 75% of symptomatics
colorsets3 = [0 0 1;0 1 0; 1 0 0];
R0vec = [0.5 0.625 0.75 0.875 1].*beta0;
R0vec = linspace(0, 1.2, 100).*beta0;
paramsi = params;
for j = 1:length(R0vec)
paramsi(1) = R0vec(j);
for i = 1:length(alphavec)
paramsi(3) = alphavec(i);
paramsi(5) = tremvec(i);
[y, B, new_inf, R_t, new_exp, Reff] = fwd_SEIRD_model(paramsi,tau_params, tvec, y0, dt, disease);
tot_inf = sum(y(:,3));
S_t(:,i) = y(:,1);
new_infi(:,i) = new_inf;
%ihalf = find(y(:,1)<0.5*N, 1, 'first');
%thalf(i) = tvec(ihalf);
pct_infected(i,j) = 100.*(1-(S_t(end,i)./N));
inf = y(:,3)+y(:,4);
peakinf(i,j) = 100*max(inf)/N;
Reffi(i,j) = Reff;
end
end
%%
pct_trans = linspace(0.5, 1.2, 100);
ind = find(pct_infected(2,:)>=20,1, 'first');
Rcrit = R0vec(ind);
pct_red_crit = pct_trans(ind);
Reffcrit = Reffi(2, ind);
i2 = find(pct_infected(1,:)>=20, 1, 'first');
Rcritperf = R0vec(i2);
pct_red_perf_crit = pct_trans(i2);
Reffperf = Reffi(1,i2);
i5 = find(pct_infected(3,:)>=20, 1, 'first');
Rcritno = R0vec(i5);
pct_red_no_crit = pct_trans(i5);
Reffno = Reffi(1,i5);
i3 = find(Reffi(2,:)>=1, 1, 'first');
Rcrit3 = R0vec(i3);
i4 = find(Reffi(1,:)>=1, 1, 'first');
Rcrit4 = R0vec(i4);
figure;
for i = 1:3
plot(R0vec, pct_infected(i,:), 'color', colorsets3(i,:), 'LineWidth', 2)
hold on
end
hold on
plot( R0vec, 20*ones(length(R0vec),1), 'k--', 'LineWidth', 2)
%plot([Rcrit Rcrit], [0 20], 'k--', 'LineWidth', 2)
text(Rcrit, 23, ['Realistic R_{crit} =' num2str(round(Rcrit,1))], 'FontSize', 12)
%plot([Rcritperf Rcritperf], [0 20], 'k--', 'LineWidth',2)
text(Rcritperf, 23, ['Perfect R_{crit} =' num2str(round(Rcritperf,1))], 'FontSize', 12)
plot([beta0 beta0], [0 20], 'k--', 'LineWidth', 2)
text(beta0, 23, ['COVID-19 R_0 =' num2str(round(beta0,1))], 'FontSize', 12)
%plot([Rcritno Rcritno], [0 20], 'k--', 'LineWidth',2)
text(Rcritno-0.1, 17, ['No isolation R_0 =' num2str(round(Rcritno,1))], 'FontSize', 12)
legend ('perfect', 'realistic', 'no isolation', 'Location', 'NorthWest')
legend boxoff
xlabel ('R_0')
xlim([1 R0vec(end)])
title('Critical R_0 for symptomatic isolation')
ylabel ('Total % infected')
set(gca,'FontSize',16,'LineWidth',1.5)
figure;
for i = 1:3
plot(R0vec, peakinf(i,:), 'color', colorsets3(i,:), 'LineWidth', 2)
hold on
end
hold on
%plot( R0vec, 20*ones(length(R0vec),1), 'k--', 'LineWidth', 2)
%plot([Rcrit Rcrit], [0 20], 'k--', 'LineWidth', 2)
%text(Rcrit, 23, ['Realistic R_{crit} =' num2str(round(Rcrit,1))], 'FontSize', 12)
%plot([Rcritperf Rcritperf], [0 20], 'k--', 'LineWidth',2)
%text(Rcritperf, 23, ['Perfect R_{crit} =' num2str(round(Rcritperf,1))], 'FontSize', 12)
%plot([beta0 beta0], [0 20], 'k--', 'LineWidth', 2)
%text(beta0, 23, ['COVID-19 R_0 =' num2str(round(beta0,1))], 'FontSize', 12)
legend ('perfect', 'realistic', 'no isolation', 'Location', 'NorthWest')
legend boxoff
xlabel ('R_0')
xlim([R0vec(1) R0vec(end)])
title('Peak % infected vs. R_0')
ylabel ('Peak % infected')
set(gca,'FontSize',16,'LineWidth',1.5)
figure;
for i = 1:3
plot(R0vec, Reffi(i,:), 'color', colorsets3(i,:), 'LineWidth', 2)
hold on
end
hold on
plot( R0vec, ones(length(R0vec),1), 'k--', 'LineWidth', 2)
plot([Rcrit3 Rcrit3], [0 1], 'k--', 'LineWidth', 2)
text(Rcrit3, 0.9, ['Realistic R_{crit} =' num2str(round(Rcrit3,1))], 'FontSize', 12)
plot([Rcrit4 Rcrit4], [0 1], 'k--', 'LineWidth',2)
text(Rcrit4 , 0.9, ['Perfect R_{crit} =' num2str(round(Rcrit4,1))], 'FontSize', 12)
plot([beta0 beta0], [0 1], 'k--', 'LineWidth', 2)
text(beta0, 0.9, ['COVID-19 R_0 =' num2str(round(beta0,1))], 'FontSize', 12)
legend ('perfect', 'realistic', 'no isolation', 'Location', 'NorthWest')
legend boxoff
xlabel ('R_0')
xlim([R0vec(1) R0vec(end)])
title('Critical R_0 vs R_{eff} for symptomatic isolation')
ylabel ('R_{eff}')
set(gca,'FontSize',16,'LineWidth',1.5)
%% Plot I0 curves
trem = 2+tsym;
alpha = 0.6;
params = [beta0, gamma, alpha, infend, trem];
% Time to remove
I0vec = [0.01 0.1 1 10];
y0i = y0;
paramsi = params;
colorsets2 = varycolor(length(I0vec));
for i = 1:length(I0vec)
y0i(3) = I0vec(i);
y0i(1) = 1000-y0i(3);
[y, B, new_inf, R_t, new_exp, Reff] = fwd_SEIRD_model(params,tau_params, tvec, y0i, dt, disease);
tot_inf = sum(y(:,3));
S_t(:,i) = y(:,1);
new_infi(:,i) = new_inf;
i20 = find(y(:,1)<0.8*N, 1, 'first');
t20(i) = tvec(i20);
pct_infected(i) = 100.*(1-(S_t(end,i)./N));
inf = y(:,3)+y(:,4);
peakinf(i) = 100*max(inf)/N;
inf_t(:,i) = y(:,3);
Reffj(i) = Reff;
end
figure;
subplot(1,2,1)
for i = 1:length(I0vec)
plot(tvec, 100*S_t(:,i)/N, '-', 'color', colorsets(i,:), 'LineWidth',2)
hold on
%text(tvec(20*i), S_t(20*i), ['t_{isolate post symptoms}=', num2str(tremvec(i)-3)], 'FontSize', 14)
end
legend( 'I_0 = 0.001%','I_0 = 0.01%', 'I_0 = 0.1%', 'I_0 = 1%' )
legend boxoff
xlabel('epidemic time (days)')
ylabel('% of population not infected')
set(gca,'FontSize',14,'LineWidth',1.5)
%title(' infections over time')
subplot(1,2,2)
for i = 1:length(I0vec)
plot(tvec, 100*inf_t(:,i)/N, '-', 'color', colorsets(i,:), 'LineWidth',2)
hold on
%text(tvec(20*i), S_t(20*i), ['t_{isolate post symptoms}=', num2str(tremvec(i)-3)], 'FontSize', 14)
end
legend( 'I_0 = 0.001%','I_0 = 0.01%', 'I_0 = 0.1%', 'I_0 = 1%' )
legend boxoff
xlabel('epidemic time (days)')
ylabel('% of population')
set(gca,'FontSize',14,'LineWidth',1.5)
%% Heatmap of % removed vs time of removal colored by total % infected
alphav = [0.1:.1:0.9]; % vary % that gets isolated
tremv = [0:1:8]; % vary the time of removal
[ALPHA,TREM] = meshgrid(alphav,tremv); % big ol grid of parameters
ALPHAflat = reshape(ALPHA,1,[]);
TREMflat = reshape(TREM,1, []);
paramsi = params;
y0i = y0;
I0vec =[0.1 1 10 100];
sdvec = [0.5 0.75 1 1.5];
%sdvec = [0.9 1 1.05 1.1];
beta0vec = beta0.*sdvec;
cell{1}.I0 = y0(3);
pct_infected = [];
peakinf = [];
%% Run a loop to save the total % infected and the Reff
% total number infected distribution
for i = 1:length(beta0vec)
for j = 1:length(ALPHAflat)
paramsi(1) = beta0vec(i);
paramsi(3) = ALPHAflat(j);
paramsi(5) = TREMflat(j);
[y, B, new_inf, R_t, new_exp, Reff] = fwd_SEIRD_model(paramsi,tau_params, tvec, y0i, dt,disease);
tot_inf(j) = sum(y(:,3));
new_infi(:,j) = new_inf;
% iquart = find(y(:,1)<0.8*N, 1, 'first');
% if isnan(iquart)
% tquart(j) = 0;
% end
% if ~isnan(iquart)
% tquart(j) = tvec(iquart);
% end
pct_infected(j) = 100.*(1-(y(end,1)./N));
inf = y(:,3)+y(:,4);
peakinf(j) = 100*max(inf)/N;
Reffvec(j) = Reff;
end
PCTINF = reshape(pct_infected, size(ALPHA));
PEAKINF = reshape(peakinf, size(ALPHA));
REFF = reshape(Reffvec, size(ALPHA));
cell{i}.I0 = y0(3);
cell{i}.R0 = beta0vec(i);
cell{i}.PCTINF = PCTINF;
cell{i}.PEAKINF = PEAKINF;
cell{i}.REFF = REFF;
end
%% Plot heatmaps for total infected, time to 20% infected, and peak infections
figure;
for i = 1:length(beta0vec)
subplot(2, 4, i)
minmax = @(x)([min(x) max(x)]);
imagesc(minmax(1*(alphav)),minmax(tremv-tsym),cell{i}.PCTINF);
%imagesc(minmax(1*(alphav)),minmax(tremv),PCTINF);
[C,h]=contourf(100*ALPHA,TREM-tsym,cell{i}.PCTINF); clabel(C,h);
if i == length(beta0vec)
colorbar;
end
%[C,h]=contourf(ALPHA,TREM,PCTINF); clabel(C,h); colorbar
hold on
% plot(100*alphav, 0*ones(length(alphav),1), 'w--', 'LineWidth', 1.5)
% plot([80 80], [-tsym 8-tsym], 'w--', 'LineWidth', 1.5)
plot([10 80], [0 0], 'g-', 'LineWidth', 3)
plot([80 80], [0 8-tsym], 'g-', 'LineWidth', 3)
plot([10 80], [8-tsym-.05 8-tsym-.05], 'g-', 'LineWidth', 3)
plot( [11 11], [0 8-tsym-.05], 'g-', 'LineWidth', 3)
caxis([0 100]);
%redgreencmap
%cmap = [[zeros(32,1);[.2:.8/31:1]'] zeros(64,1) [1-[0:0.8/31:.8]';zeros(32,1)] ]; % green to red colormap
colormap(jet);
xlabel('% of population removed');
ylabel('days after symptom onset');
title([num2str(sdvec(i)*100), '% transmission, Total % Infected'])
%title(['R_{0}^{COVID}= ',num2str(beta0vec(i)), ', Total % Infected']);
set(gca,'Ydir','normal'); hold on;
set(gca,'FontSize',16,'LineWidth',1.5)
end
% Reff
for i =1:length(I0vec)
xvals = [];
yvals = [];
subplot(2,4,i+4)
minmax = @(x)([min(x) max(x)]);
imagesc(minmax(1*(alphav)),minmax(tremv-tsym),cell{i}.REFF);
[C,h]=contourf(100*ALPHA,TREM-tsym,cell{i}.REFF); clabel(C,h);
[x,y,z] = C2xyz(C);
j=find(z==1);
hold on
plot(x{j}, y{j}, 'w-', 'LineWidth', 3)
if i == length(beta0vec)
colorbar;
end
hold on
%plot(100*alphav, zeros(length(tremv),1), 'w--', 'LineWidth', 1.5)
%plot([80 80], [-tsym 8-tsym], 'w--', 'LineWidth', 1.5)
plot([10 80], [0 0], 'g-', 'LineWidth', 3)
plot([80 80], [0 8-tsym], 'g-', 'LineWidth', 3)
plot([10 80], [8-tsym-.05 8-tsym-.05], 'g-', 'LineWidth', 3)
plot( [11 11], [0 8-tsym-.05], 'g-', 'LineWidth', 3)
caxis([0 4]);
%redgreencmap
%cmap = [[zeros(32,1);[.2:.8/31:1]'] zeros(64,1) [1-[0:0.8/31:.8]';zeros(32,1)] ]; % green to red colormap
colormap(jet);
xlabel('% of population removed');
ylabel('days after symptom onset');
title([num2str(sdvec(i)*100), '% transmission, R_{eff}'])
%title(['R_{0}^{COVID}= ',num2str(beta0vec(i)), ', Peak % Infected']);
set(gca,'Ydir','normal'); hold on;
set(gca,'FontSize',16,'LineWidth',1.5)
end
%% Heatmap of days after sym onset vs lower transmission
tremv = linspace(0.5,tsym+4, 10);
R_0vec = linspace(1, 3.5,10);
R_0vec = fliplr(R_0vec);
[R0MAT,TREM] = meshgrid(R_0vec,tremv); % big ol grid of parameters
R0flat = reshape(R0MAT,1,[]);
TREMflat = reshape(TREM,1, []);
paramsi = params;
paramsi(3) = 0.6;
for j = 1:length(R0flat)
paramsi(1) = R0flat(j);
paramsi(5) = TREMflat(j);
[y, B, new_inf, R_t, new_exp, Reff] = fwd_SEIRD_model(paramsi,tau_params, tvec, y0, dt,disease);
tot_inf(j) = sum(y(:,3));
new_infi(:,j) = new_inf;
% iquart = find(y(:,1)<0.8*N, 1, 'first');
% if isnan(iquart)
% tquart(j) = 0;
% end
% if ~isnan(iquart)
% tquart(j) = tvec(iquart);
% end
pct_infected(j) = 100.*(1-(y(end,1)./N));
inf = y(:,3)+y(:,4);
peakinf(j) = 100*max(inf)/N;
Reffvec(j) = Reff;
end
PCTINF = reshape(pct_infected, size(R0MAT));
PEAKINF = reshape(peakinf, size(R0MAT));
REFF = reshape(Reffvec, size(R0MAT));
%%
figure;
minmax = @(x)([min(x) max(x)]);
imagesc(minmax(1*(R_0vec)),minmax(tremv-tsym),PCTINF);
%imagesc(minmax(1*(alphav)),minmax(tremv),PCTINF);
[C,h]=contourf(R0MAT,TREM-tsym,PCTINF); clabel(C,h);
caxis([0 100]);
colorbar;
colormap(jet);
xlabel('R_0');
ylabel('days after symptom onset');
title('Total % Infected')
%title(['R_{0}^{COVID}= ',num2str(beta0vec(i)), ', Peak % Infected']);
set(gca,'Ydir','normal'); hold on;
set(gca,'FontSize',16,'LineWidth',1.5)
figure;
minmax = @(x)([min(x) max(x)]);
imagesc(minmax(1*(R_0vec)),minmax(tremv-tsym),REFF);
%imagesc(minmax(1*(alphav)),minmax(tremv),PCTINF);
[C,h]=contourf(100*R0MAT/beta0,TREM-tsym,REFF); clabel(C,h);
colorbar;
[x,y,z] = C2xyz(C);
j=find(z==1);
hold on
plot(x{j}, y{j}, 'w--', 'LineWidth', 3)
caxis([0 3.5]);
colormap(jet);
xlabel('% transmission');
ylabel('days after symptom onset');
title('R_{eff}')
%title(['R_{0}^{COVID}= ',num2str(beta0vec(i)), ', Peak % Infected']);
set(gca,'Ydir','normal'); hold on;
set(gca,'FontSize',16,'LineWidth',1.5)
figure;
minmax = @(x)([min(x) max(x)]);
imagesc(minmax(1*(R_0vec)),minmax(tremv-tsym),REFF);
%imagesc(minmax(1*(alphav)),minmax(tremv),PCTINF);
[C,h]=contourf(R0MAT,TREM-tsym,REFF); clabel(C,h);
colorbar;
[x,y,z] = C2xyz(C);
j=find(z==1);
hold on
plot(x{j}, y{j}, 'w--', 'LineWidth', 3)
caxis([0 3.5]);
colormap(jet);
xlabel('R_0');
ylabel('days after symptom onset');
title('R_{eff}')
%title(['R_{0}^{COVID}= ',num2str(beta0vec(i)), ', Peak % Infected']);
set(gca,'Ydir','normal'); hold on;
set(gca,'FontSize',16,'LineWidth',1.5)
%%
% PEAK INF
% for i =1:length(I0vec)
% subplot(2,4,i+4)
% minmax = @(x)([min(x) max(x)]);
% imagesc(minmax(1*(alphav)),minmax(tremv-tsym),cell{i}.PEAKINF);
% [C,h]=contourf(100*ALPHA,TREM-tsym,cell{i}.PEAKINF); clabel(C,h);
% if i == length(beta0vec)
% colorbar;
% end
% hold on
% plot(100*alphav, zeros(length(tremv),1), 'w--', 'LineWidth', 1.5)
% plot([80 80], [-tsym 8-tsym], 'w--', 'LineWidth', 1.5)
% plot([10 80], [0 0], 'g-', 'LineWidth', 3)
% plot([80 80], [0 8-tsym], 'g-', 'LineWidth', 3)
% plot([10 80], [8-tsym-.05 8-tsym-.05], 'g-', 'LineWidth', 3)
% plot( [11 11], [0 8-tsym-.05], 'g-', 'LineWidth', 3)
% caxis([0 100]);
% %redgreencmap
% %cmap = [[zeros(32,1);[.2:.8/31:1]'] zeros(64,1) [1-[0:0.8/31:.8]';zeros(32,1)] ]; % green to red colormap
% colormap(jet);
% xlabel('% of population removed');
% ylabel('days after symptom onset');
% title(' Peak % infected');
% title(['R_{0}^{COVID}= ',num2str(beta0vec(i)), ', Peak % Infected']);
% set(gca,'Ydir','normal'); hold on;
% set(gca,'FontSize',16,'LineWidth',1.5)
% end
%% Vary I0
cell2{1}.I0 = I0vec(1);
for i = 1:length(I0vec)
for j = 1:length(ALPHAflat)
paramsi(1) = 2.3;
paramsi(3) = ALPHAflat(j);
paramsi(5) = TREMflat(j);
y0i(3) = I0vec(i);
y0i(1) = 1000-y0i(3);
[y, B, new_inf, R_t, new_exp, Reff] = fwd_SEIRD_model(paramsi,tau_params, tvec, y0i, dt, disease);
tot_inf(j) = sum(y(:,3));
new_infi(:,j) = new_inf;
Reffvec(j) = Reff;
pct_infected(j) = 100.*(1-(y(end,1)./N));
inf = y(:,3)+y(:,4);
peakinf(j) = 100*max(inf)/N;
Reffvec(j) = Reff;
end
PCTINF = reshape(pct_infected, size(ALPHA));
REFF = reshape(Reffvec, size(ALPHA));
PEAKINF = reshape(peakinf, size(ALPHA));
cell2{i}.I0 = I0vec(i);
cell2{i}.R0 = 2.5;
cell2{i}.PCTINF = PCTINF;
cell2{i}.PEAKINF = PEAKINF;
cell2{i}.REFF = REFF;
end
%% Plot heatmaps varying by I0
figure;
for i = 1:length(I0vec)
subplot(2, 4, i)
minmax = @(x)([min(x) max(x)]);
imagesc(minmax(1*(alphav)),minmax(tremv-tsym),cell2{i}.PCTINF);
%imagesc(minmax(1*(alphav)),minmax(tremv),PCTINF);
[C,h]=contourf(100*ALPHA,TREM-tsym,cell2{i}.PCTINF); clabel(C,h); colorbar
%[C,h]=contourf(ALPHA,TREM,PCTINF); clabel(C,h); colorbar
hold on
plot([10 80], [0 0], 'g-', 'LineWidth', 3)
plot([80 80], [0 8-tsym], 'g-', 'LineWidth', 3)
plot([10 80], [8-tsym-.05 8-tsym-.05], 'g-', 'LineWidth', 3)
plot( [11 11], [0 8-tsym-.05], 'g-', 'LineWidth', 3)
caxis([0 100]);
hold on
if i == length(beta0vec)
colorbar;
end
hold on
%redgreencmap
%cmap = [[zeros(32,1);[.2:.8/31:1]'] zeros(64,1) [1-[0:0.8/31:.8]';zeros(32,1)] ]; % green to red colormap
colormap(jet);
colorbar;
xlabel('% of population removed');
ylabel('days after symptom onset');
title(['I_0=', num2str(100*I0vec(i)/N), '%, Total % Infected']);
set(gca,'Ydir','normal'); hold on;
set(gca,'FontSize',16,'LineWidth',1.5)
end
% REFF
for i =1:length(I0vec)
subplot(2,4,i+4)
minmax = @(x)([min(x) max(x)]);
imagesc(minmax(1*(alphav)),minmax(tremv-tsym),cell2{i}.REFF);
[C,h]=contourf(100*ALPHA,TREM-tsym,cell2{i}.REFF); clabel(C,h); colorbar
hold on
[x,y,z] = C2xyz(C);
j=find(z==1);
hold on
plot(x{j}, y{j}, 'w--', 'LineWidth', 3)
caxis([0 3.5]);
if i == length(beta0vec)
colorbar;
end
hold on
plot([10 80], [0 0], 'g-', 'LineWidth', 3)
plot([80 80], [0 8-tsym], 'g-', 'LineWidth', 3)
plot([10 80], [8-tsym-.05 8-tsym-.05], 'g-', 'LineWidth', 3)
plot( [11 11], [0 8-tsym-.05], 'g-', 'LineWidth', 3)
caxis([0 3.5]);
%redgreencmap
%cmap = [[zeros(32,1);[.2:.8/31:1]'] zeros(64,1) [1-[0:0.8/31:.8]';zeros(32,1)] ]; % green to red colormap
colormap(jet);
colorbar;
xlabel('% of population removed');
ylabel('days after symptom onset');
title(['I_0=', num2str(100*I0vec(i)/N), '%, R_{eff}']);
set(gca,'Ydir','normal'); hold on;
set(gca,'FontSize',16,'LineWidth',1.5)
end
%% Plot weighted infectiousness at different times
figure;
plot(tvec, B(1,:),'-', 'LineWidth',2)
hold on
plot(tvec, B(2/dt+1,:),'-', 'LineWidth',2)
plot(tvec, B(4/dt+1,:),'-', 'LineWidth',2)
plot(tvec, B(6/dt+1,:),'-', 'LineWidth',2)
plot(tvec,B(20/dt+1,:), 'g-', 'LineWidth',2)