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    Metadata details:
    filename: DEM_COVID_LTLA.m
    path of file: ./repos/spm/toolbox/DEM
    
    the code of the file until where you have to start completion: function [DCM] = DEM_COVID_LTLA(LA)
% FORMAT [DCM] = DEM_COVID_LTLA(LA)
% LA - local authority
%
% Demonstration of COVID-19 modelling
%__________________________________________________________________________
%
% This demonstration routine fits multiple regional death by date and new
% cases data and compiles estimates of latent states for local
% authorities.
%
% Technical details about the dynamic causal model used here can be found
% at https://www.fil.ion.ucl.ac.uk/spm/covid-19/.
%__________________________________________________________________________
% Copyright (C) 2020 Wellcome Centre for Human Neuroimaging

% Karl Friston
% Copyright (C) 2008-2022 Wellcome Centre for Human Neuroimaging

% download from web options
%-------------------------------------------------------
    
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 prior and posterior estimates (and log evidence)
    %----------------------------------------------------------------------
    DCM(r).M  = M;
    DCM(r).Ep = Ep;
    DCM(r).Eh = Eh;
    DCM(r).Cp = Cp;
    DCM(r).Y  = Y;
    DCM(r).xY = xY;
    DCM(r).S  = S;
    DCM(r).F  = F;
    
    % now-casting for this region and date
    %======================================================================
    H      = spm_figure('GetWin',D(r).name{1}); clf;
    %----------------------------------------------------------------------
    M.T    = numel(dates) + 16;
    u      = [find(U == 1) find(U == 2) find(U == 23)];
    S      = DCM(r).S(:,u); S(isnan(S)) = 0;
    [Y,X]  = spm_SARS_gen(DCM(r).Ep,M,[1 2 23]);
    spm_SARS_plot(Y,X,S,[1 2 23]);
    
    % plot incidence
    %----------------------------------------------------------------------
    subplot(3,1,3)
    spm_SARS_ci(Ep,Cp,[],19,M); hold on
    spm_SARS_ci(Ep,Cp,[],20,M); hold on
    ylabel('cases per 100,000'), title('Incidence per 100,000','FontSize',14)
    plot(datenum(date)*[1,1],get(gca,'YLim'),':')
    plot(get(gca,'XLim'),[100,100],'-.r')
    plot(get(gca,'XLim'),[10,10],  '-.g')
    text(datenum('01/02/2020','dd/mm/yyyy'), 100,'Red Zone','Color','r','FontSize',8)
    text(datenum('01/02/2020','dd/mm/yyyy'), 10,'Greem Zone','Color','g','FontSize',8)
    
    legend