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FitSimpleModelSerialIntVar.m
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function [resnorm]= FitSimpleModelSerialIntVar(T)
close all
warning off;
% stop/start figures from displaying in matlab, switch 'off' to 'on to display
set(0,'DefaultFigureVisible','off')
% import data
ChinaData = readtable('ChinaDataReshaped.csv');
ProvincePops = readtable('ChinaProvincePops.csv');
ProvincePops = table2array(ProvincePops);
% national total cases
CCt = table2array(ChinaData(:,end-2));
CData2 = table2array(ChinaData(:,15));
CData1 = CCt - CData2;
% national total quarintined
QCt = table2array(ChinaData(:,end));
T_e=2.71;
tau=3;
rho=1;
sqwt=0.01;
alphac=1/14;
p = .06;
N1 = sum(ProvincePops); % China pop
N1 = N1 - ProvincePops(14); % China pop les Hubei
N2 = ProvincePops(14);
CC1 = CData1;
CC1 = CC1(CC1 > 0);
td1=2:length(CC1);
CC2 = CData2;
CC2 = CC2(CC2 > 0)
td2 = 2:length(CC2);
if length(td1) > length(td2)
td = td1;
end
if length(td1) <= length(td2)
td = td2;
end
QC = QCt;
M=table2array(ChinaData(:,end-1));
Qd = M(2:end);
% provincial daily cases
Cd1 = diff(CC1);
% account for data irregularities
if Cd1(1) == 0
Cd1(1) = (Cd1(2))/2;
Cd1(2)= (Cd1(2))/2;
if Cd1(2) == 0
Cd1(1) = Cd1(3)/3;
Cd1(2) = Cd1(3)/3;
Cd1(3) = Cd1(3)/3;
end
end
if Cd1(end) == 0
Cd1(end) = (Cd1(end-1))/2;
Cd1(end-1)= (Cd1(end-1))/2;
if Cd1(end-1) == 0
Cd1(end) = Cd1(end-2)/3;
Cd1(end-1) = Cd1(end-2)/3;
Cd1(end-2) = Cd1(end-2)/3;
end
end
if Cd1(1) < 0
Cd1(1) = -Cd1(1);
end
ind0=find(Cd1==0);
if isempty(ind0)==0
Cd1(ind0)=1/3*Cd1(ind0-1)+1/3*Cd1(ind0+1);
Cd1(ind0-1)=2/3*Cd1(ind0-1);
Cd1(ind0+1)=2/3*Cd1(ind0+1);
end
Cd2 = diff(CC2);
if Cd2(1) == 0
Cd2(1) = (Cd2(2))/2;
Cd2(2)= (Cd2(2))/2;
if Cd2(2) == 0
Cd2(1) = Cd2(3)/3;
Cd2(2) = Cd2(3)/3;
Cd2(3) = Cd2(3)/3;
end
end
if Cd2(end) == 0
Cd2(end) = (Cd2(end-1))/2;
Cd2(end-1)= (Cd2(end-1))/2;
if Cd2(end-1) == 0
Cd2(end) = Cd2(end-2)/3;
Cd2(end-1) = Cd2(end-2)/3;
Cd2(end-2) = Cd2(end-2)/3;
end
end
if Cd2(1) < 0
Cd2(1) = -Cd2(1);
end
ind0=find(Cd2==0);
if isempty(ind0)==0
Cd2(ind0)=1/3*Cd2(ind0-1)+1/3*Cd2(ind0+1);
Cd2(ind0-1)=2/3*Cd2(ind0-1);
Cd2(ind0+1)=2/3*Cd2(ind0+1);
end
tq = find(QC > 0);
C1 = Cd1(1:end);
C2 = Cd2(1:end);
[mx,im]=max(Cd2);
ids=[1:im-2,im+2:length(Cd2)];
tds=td(ids);
C2 = C2(ids);
Cdd1 = C1;
Cdd1(1)=Cd1(1);
Td1=.1609*C1;
Cdd2 = Cd2;
Cdd2(1)=Cd2(1);
Td2=.1609*C2;
I01g = (C1(1)/rho)*T;
I02g = (C2(2)/rho)*T;
% fit values from entire country fit with exception of I0
paramguess = [632.864026481429,5.99999999986307,74367.0214604314,...
0.308064520308229,1018.50380516702,5.99999999999980,...
561.569333839141,0.0489799044337563,9923332.46179674]
lb = [632.864026481429*.5, 2/T , 79769*.5 , .01 , 1018.50380516702*.25, 2/T , 0 , .01];
ub = [632.864026481429*2,6/T, 79769*2 , 1 ,1018.50380516702*2, 6/T , inf , 1];
M = M';
C1 = C1';
C2 = C2';
function X0 = IC(param,QC,C1,C2,M,tq,Td,N,its)
I0 = param(1);
beta = param(2);
phi = param(4);
S0=N;
if its == 1
C = C1;
end
if its == 2
C = C2;
end
E0=beta*(1-phi*rho)*tau*I0;
Ec0=beta*(phi*rho)*tau*I0;
Ic0=phi*rho*I0;
X0=[S0 E0 I0 Ec0 Ic0 p*QC(1) C(1) phi*rho*C(1) M(tq(1))*(C(tq(1))/(C1(tq(1))+C2(tq(1))))];
end
function[z] = Solve_sys(param,td)
beta = param(2);
sigma = param(3);
phi = param(4);
N = N1;
param1 = param(1:4);
X01 = IC(param1,QC,C1,C2,M,tq,Td1,N,1);
psi = sigma + ((1-p)/p)*phi*rho;
Eode = @(t,X) [-(1+psi)*X(1)*((beta/N)*X(3)),...
(beta/N)*(1-phi*rho)*X(1)*X(3)- 1/tau*X(2) - (sigma*beta)*(X(3)/N)*X(2),...
1/tau*X(2)-1/T*X(3) - (sigma*beta)*(X(3)/N)*X(3),...
(beta/N)*(phi*rho)*X(1)*X(3)- 1/tau*X(4),...
1/tau*X(4)-1/T_e*X(5),...
(beta/N)*(phi*rho)*X(1)*X(3),...
rho/T*X(3),...
1/T_e*X(5),...
(beta/N)*(phi*rho)/p*X(1)*X(3)-alphac*X(9)]';
[t,Sol1] = ode45(@(t,X)Eode(t,X),td1,X01);
beta = param(6);
sigma = param(7);
phi = param(8);
N = N2;
param2 = param(5:8);
X02 = IC(param2,QC,C1,C2,M,tq,Td2,N,2);
psi = sigma + ((1-p)/p)*phi*rho;
Eode = @(t,X) [-(1+psi)*X(1)*((beta/N)*X(3)),...
(beta/N)*(1-phi*rho)*X(1)*X(3)- 1/tau*X(2) - (sigma*beta)*(X(3)/N)*X(2),...
1/tau*X(2)-1/T*X(3) - (sigma*beta)*(X(3)/N)*X(3),...
(beta/N)*(phi*rho)*X(1)*X(3)- 1/tau*X(4),...
1/tau*X(4)-1/T_e*X(5),...
(beta/N)*(phi*rho)*X(1)*X(3),...
rho/T*X(3),...
1/T_e*X(5),...
(beta/N)*(phi*rho)/p*X(1)*X(3)-alphac*X(9)]';
[t,Sol2] = ode45(@(t,X)Eode(t,X),td2,X02);
Cdd1(2:end)=Sol1(2:end,7)+Sol1(2:end,8)-(Sol1(1:end-1,7)+Sol1(1:end-1,8));
Cdd2(2:end)=Sol2(2:end,7)+Sol2(2:end,8)-(Sol2(1:end-1,7)+Sol2(1:end-1,8));
CumSq=(Sol1(tq-(tq(1)-1),9))*sqwt + (Sol2(tq-3,9))*sqwt;
Cds1=Cdd1(1:end);
Cds2 = Cdd2(ids);
z=[Cds1',Cds2',CumSq'];
end
[paramfit,resnorm] = lsqcurvefit(@Solve_sys,paramguess,td,[C1,C2,M(tq)*sqwt],lb,ub);
[paramfitAggFixp,resnorm] = lsqcurvefit(@Solve_sys,paramfit,td,[C1,C2,M(tq)*sqwt],lb,ub);
% store fit parameters
%save('paramfitAgg.mat','paramfitAgg')
zfit = Solve_sys(paramfitAggFixp,td);
Cfit1 = zfit(1:length(td1));
Cfit2 = zfit(length(Cfit1)+1:length(tds)+length(Cfit1));
Qfit = zfit(length(Cfit1)+length(Cfit2)+1:end);
figure
plot(td1,Cfit1,'b-',td1,Cd1,'r*','linewidth',2)
title('China Less Hubei')
ylabel('New Daily Cases')
xlabel('Days Since First Reported Case')
% baseFileName = sprintf('CasesChinaLessHubeiFixp.png');
% fname = 'C:\Users\macdo\Dropbox\COVID-19_modelfitting_data\AggPlots';
% saveas(gca, fullfile(fname, baseFileName), 'png');
figure
plot(tds,Cfit2,'b-',td2,Cd2,'r*','linewidth',2)
title('Hubei')
ylabel('New Daily Cases')
xlabel('Days Since First Reported Case')
% baseFileName = sprintf('CasesHubeiFixp.png');
% fname = 'C:\Users\macdo\Dropbox\COVID-19_modelfitting_data\AggPlots';
% saveas(gca, fullfile(fname, baseFileName), 'png');
figure
plot(tq,Qfit/(sqwt),'b-',tq,M(tq),'r*','linewidth',2)
title('All China')
xlabel('Days Since First Reported Case')
ylabel('Quarintined Individuals')
% baseFileName = sprintf('AggQuarFixp.png');
% fname = 'C:\Users\macdo\Dropbox\COVID-19_modelfitting_data\AggPlots';
% saveas(gca, fullfile(fname, baseFileName), 'png');
% store fit parameters
paramfitAggFixp(2) = paramfitAggFixp(2)*T;
paramfitAggFixp(6) = paramfitAggFixp(6)*T;
paramfitAggFixp(9) = resnorm;
save('paramfitSerialIntVar.mat','paramfitAggFixp')
array2table(paramfitAggFixp)
end