Merci Stéphane, for the very interesting code and Heinz for the reference to
the math behind the epidemy “curve”, or one of its models.
From: users <users-boun...@lists.scilab.org> On Behalf Of Stéphane Mottelet
Sent: Monday, March 30, 2020 9:14 AM
To: users@lists.scilab.org
Subject: Re: [Scilab-users] Corona modelling
Hello Heinz,
Here is an interactive version (made for my children last week...) :
// Confinement COVID-19 !
// Stephane MOTTELET, UTC
// Tue Mar 24 08:55:03 CET 2020
//
function dydt=sir(t, y, bet, gam, N)
dydt=[-bet/N*y(1)*y(2)
bet/N*y(1)*y(2)-gam*y(2)
gam*y(2)];
endfunction
function draw(bet, gam)
t=0:1:360;
N=6e7;
if exists("gcbo") && is_handle_valid(gcbo)
sb = gcbo;
if sb.tag=="beta"
bet=sb.value;
gam=findobj("gamma").value
else
gam=sb.value;
bet=findobj("beta").value
end
y=ode('stiff',[N-1;1;0],0,t,list(sir,bet,gam,N));
curves = findobj("curves");
curves.children(1).data(:,2)=y(3,:);
curves.children(2).data(:,2)=y(2,:);
curves.children(3).data(:,2)=y(1,:);
else
y=ode('stiff',[N-1;1;0],0,t,list(sir,bet,gam,N));
scf(0)
clf
plot(t,y)
gce().tag="curves";
gce().children.thickness=2;
legend("Susceptible","Infected","Recovered",-1)
sb1 = uicontrol("style","slider",...
"units","normalized",...
"Position", [0.85,0.2,0.05,0.48],...
"BackgroundColor", [1,1,1],...
"Callback_Type",12,...
"sliderstep",[1/1000,1/10],...
"min",0.15,"max",0.3,"value",bet,...
"Callback","draw","tag","beta");
uicontrol("style","text",...
"string","$\beta$",...
"units","normalized",...
"Position", [0.85,0.125,0.05,0.08],...
"BackgroundColor", [1,1,1],...
"HorizontalAlignment","center");
sb1 = uicontrol("style","slider",...
"units","normalized",...
"Position", [0.90,0.2,0.05,0.48],...
"BackgroundColor", [1,1,1],...
"Callback_Type",12,...
"sliderstep",[1/1000,1/10],...
"min",0,"max",1/15,"value",gam,...
"Callback","draw","tag","gamma");
uicontrol("style","text",...
"string","$\gamma$",...
"units","normalized",...
"Position", [0.9,0.125,0.05,0.08],...
"BackgroundColor", [1,1,1],...
"HorizontalAlignment","center");
end
end
clf
draw(0.3,1/15)
Le 30/03/2020 à 02:14, Heinz Nabielek a écrit :
Colleagues:
is there an straightforward Scilab approach for solving the three coupled
nonlinear differential equations of first order given by the Standard Model of
Epidemics?
S= number Susceptible: S'=-aSI
I= number Infected: I'=aSI - bI
R= number Recovered: R'=bI
whereby 'a' is the transmission coefficient, 'b' the recovery factor (after
Reed-Frost 1928).
Initial values for S, I, R are available.
Thank you
Heinz
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--
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
http://www.utc.fr/~mottelet
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