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Updated the examples + the function to fit multiple waves

getMultipleWaves.m

@@ -1,33 +1,54 @@
-function [Q,R,D,T] = getMultipleWaves(guess,Npop,time,Confirmed,Recovered,Deaths,tStart1,tStart2,tEnd,Q0,E0,I0)
+function [Q,R,D,T] = getMultipleWaves(guess,Npop,time,Confirmed,Recovered,Deaths,tStart1,tStart2,tEnd,varargin)
 % [Q,R,D,T] =
 % getMultipleWaves(guess,Npop,time,Confirmed,Recovered,Deaths,tStart1,tStart2,tEnd)
 % simulate the number of recovered, deaths and active cases for the
 % situation were two epidemic waves occur
-% 
+%
 % Inputs:
 %   guess:  double [1x10]: Initial guess for the fitting algorithm
 %   Npop:  double [1x1]: Population
 %   time: datetime: [1xN]: time array
-%   Confirmed: double [1xN]: Time histories of the confirmed cases (Active+recovered+deaths) 
-%   Deaths: double [1xN]: Time histories of the deceased cases 
-%   Recovered: double [1xN]: Time histories of the recovered cases 
+%   Confirmed: double [1xN]: Time histories of the confirmed cases (Active+recovered+deaths)
+%   Deaths: double [1xN]: Time histories of the deceased cases
+%   Recovered: double [1xN]: Time histories of the recovered cases
 %   tStart1: datetime [1x1]: Initial time for the first wave
 %   tStart2: datetime [1x1]: Initial time for the second wave
 %   tEnd: datetime [1x1]: Final time for the simulation
 %   Q0: datetime [1x1]: Initial number of quarantined cases
 %   E0: datetime [1x1]: Initial number of exposed cases
 %   I0: datetime [1x1]: Initial number of infectious cases
-% 
+%
 % Outputs
-%   Q: double [1xN1]: Time histories of the quarantined/active cases 
-%   D: double [1xN1]: Time histories of the deceased cases 
-%   R: double [1xN1]: Time histories of the recovered cases 
+%   Q: double [1xN1]: Time histories of the quarantined/active cases
+%   D: double [1xN1]: Time histories of the deceased cases
+%   R: double [1xN1]: Time histories of the recovered cases
 %   T: datetime: [1xN1]: time array
-% 
+%
 % Author: E. Cheynet - UiB - last modified: 07-05-2020
-% 
+%
 % see also SEIQRDP.m fit_SEIQRDP.m
 
+%% varargin
+
+Active = Confirmed-Recovered-Deaths;
+Active(Active<0) = 0; % No negative number possible
+
+%% Inputparseer
+p = inputParser();
+p.CaseSensitive = false;
+p.addOptional('Q0',Active(1));
+p.addOptional('E0',0.3*Active(1));
+p.addOptional('I0',5*Active(1));
+p.parse(varargin{:});
+%%%%%%%%%%%%%%%%%%%%%%%%%%
+Q0 = p.Results.Q0 ; % initial number of active cases
+E0 = p.Results.E0 ; % Initial number of exposed cases. Unknown but unlikely to be zero.
+I0 = p.Results.I0 ; % Initial number of infectious cases. Unknown but unlikely to be zero.
+
+
+
+
+
 %% Remove unecessary data
 Confirmed(time<tStart1) = [];
 Recovered(time<tStart1) = [];
@@ -36,25 +57,24 @@
 Active = Confirmed-Recovered-Deaths;
 Active(Active<0) = 0; % No negative number possible
 
-
 %  Time for first wave
 indT1 = find(time>=tStart1 & time<tStart2);
 % Time for  second wave
 indT2 = find(time>=tStart2);
 
 %% Simulate first wave
 % Initial conditions
-R0 = Recovered(indT1(1)); 
-D0 = Deaths(indT1(1)); 
+R0 = Recovered(indT1(1));
+D0 = Deaths(indT1(1));
 [E1,I1,Q1,R1,D1,T1] = computeWave(Active(indT1),Recovered(indT1),...
     Deaths(indT1),E0,I0,Q0,R0,D0,time(indT1),tStart1,tStart2,guess);
 
 %% Simulate second wave
-E0 = E1(end); 
-I0 = I1(end); 
-Q0 = Q1(end); 
-R0 = R1(end); 
-D0 = D1(end); 
+E0 = E1(end);
+I0 = I1(end);
+Q0 = Q1(end);
+R0 = R1(end);
+D0 = D1(end);
 [~,~,Q2,R2,D2,T2] = computeWave(Active(indT2),Recovered(indT2),...
     Deaths(indT2),E0,I0,Q0,R0,D0,time(indT2),tStart2,tEnd,guess);
 
@@ -64,7 +84,66 @@
 D = [D1,D2];
 T= [T1,T2];
 
+%% Check RMSE and refit with different I0 if needed
+
+[~,ind] = unique(T);
+newQ = interp1(T(ind),Q(ind),time);
+[rmse] = RMSE(Active(~isnan(newQ)),newQ(~isnan(newQ)));
 
+
+if rmse <1e5,
+    fprintf('Fitting succeded. Check the initial value of E0 and I0 \n');
+    Q = [Q1,Q2];
+    R = [R1,R2];
+    D = [D1,D2];
+    T= [T1,T2];
+    return
+end
+
+
+newI0 = [1:2:10].*Active(1);
+count = 1;
+while rmse>1e5
+
+    R0 = Recovered(indT1(1));
+    D0 = Deaths(indT1(1));
+    [E1,I1,Q1,R1,D1,T1] = computeWave(Active(indT1),Recovered(indT1),...
+        Deaths(indT1),E0,newI0(count),Q0,R0,D0,time(indT1),tStart1,tStart2,guess);
+    % Simulate second wave
+    E0 = E1(end);    I0 = I1(end);    Q0 = Q1(end);    R0 = R1(end);
+    D0 = D1(end);
+    [~,~,Q2,R2,D2,T2] = computeWave(Active(indT2),Recovered(indT2),...
+        Deaths(indT2),E0,I0,Q0,R0,D0,time(indT2),tStart2,tEnd,guess);
+    % Concatenate outputs
+    Q = [Q1,Q2];
+    R = [R1,R2];
+    D = [D1,D2];
+    T= [T1,T2];
+    count = count+1;
+    [~,ind] = unique(T);
+    newQ = interp1(T(ind),Q(ind),time);
+    [rmse] = RMSE(Active(~isnan(newQ)),newQ(~isnan(newQ)));
+
+    if rmse <1e5,
+        fprintf('Fitting succeded. Check the initial value of E0 and I0 \n');
+        Q = [Q1,Q2];
+        R = [R1,R2];
+        D = [D1,D2];
+        T= [T1,T2];
+        return
+    end
+    if count >=numel(newI0)
+        warning('Fitting failed. Check the initial value of E0 and I0');
+        Q = [Q1,Q2];
+        R = [R1,R2];
+        D = [D1,D2];
+        T= [T1,T2];
+        return
+    end
+
+end
+
+plot(time,newQ,time,Active)
 %% Nested functions
 
     function [E,I,Q,R,D,newT] = computeWave(Active,Recovered,Deaths,E0,I0,Q0,R0,D0,time,tStart,tEnd,guess)
@@ -81,6 +160,11 @@
             Npop,E0,I0,Q0,R0,D0,t,lambdaFun,kappaFun);
     end
 
+    function [rmse] = RMSE(y1,y2)
+
+        rmse = sqrt(nanmean((y1(:)-y2(:)).^2));
+
+    end
 
 end