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    Metadata details:
    filename: DEM_COVID_WID.m
    path of file: ./repos/spm/toolbox/DEM
    
    the code of the file until where you have to start completion: function DCM = DEM_COVID_WID
% FORMAT DCM = DEM_COVID_WID
%
% Demonstration of COVID-19 modelling using variational Laplace
%__________________________________________________________________________
%
% This routine addresses the global factors that underwrite mortality and
% morbidity (and economic cost) by comparing different countries in terms
% of the epidemiological and sociobehavioural parameters that best explain
% the trajectory of daily cases and deaths. a subset of countries with a
% large population and a low vaccination rate are modelled by optimising a
% subset of country specific (free) parameters that capture differences in
% exposure to the virus and subsequent responses; in terms of quarantine,
% containment, resistance to infection and so on. The remaining model
% parameters are assumed to be conserved over countries and are based on
% posterior estimates derived from comprehensive timeseries data from the
% United Kingdom. The between country analyses are based upon available
% timeseries from Our 
    
function
    M.FS   = @(Y)real(sqrt(Y));    % feature selection  (link function)
    M.pE   = pE;                   % prior expectations (parameters)
    M.pC   = PC;                   % prior covariances  (parameters)
    M.hE   = hE + 2;               % prior expectation  (log-precision)
    M.hC   = 1/512;                % prior covariances  (log-precision)
    M.T    = Y;                    % data structure
    
    U      = [Y.U];                % outputs to model
    
    % model inversion with Variational Laplace (Gauss Newton)
    %----------------------------------------------------------------------
    [Ep,Cp,Eh,F] = spm_nlsi_GN(M,U,xY);
    
    % save in DCM structure
    %----------------------------------------------------------------------
    DCM(k).country = D(r).country;
    
    DCM(k).M  = M;
    DCM(k).Ep = Ep;
    DCM(k).Eh = Eh;
    DCM(k).Cp = Cp;
    DCM(k).F  = F;
    DCM(k).S  = S;
    DCM(k).U  = U;
    DCM(k).D  = D(r);
    
    save('DCM_OWID.mat','DCM')
    
    % posterior predictions
    %======================================================================
    spm_figure('GetWin',DCM(k).country); clf;
    M.T     = datenum(date) + 512 - datenum('01-02-2020','dd-mm-yyyy');
    v       = [1 2 23];
    u       = [find(U == 1) find(U == 2) find(U == 23)];   
    [Z,X]   = spm_SARS_gen(DCM(k).Ep,M,v);
    spm_SARS_plot(Z,X,DCM(k).S(:,u),v)
    
    % data fits
    %----------------------------------------------------------------------
    spm_figure('GetWin',[DCM(k).country ' data fits']); clf;
    for i = 1:numel(U)
        subplot(4,2,i)
        spm_SARS_ci(Ep,Cp,S(:,i),U(i),M);
        title(Y(i).type,'FontSize',14), ylabel(Y(i).unit) 
    end