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<p>Hi,</p>
<p>My experience with the SIR model (not SEIR) is that the estimated
parameters are very sensitive to the initial condition of the
Infected pool. Hence, this initial condition should be also
considered as a parameter to be identified. However, the main
problem (at least with France data) is that fitting Infected and
Recovered (cured or dead people) together gives not satisfactory
results. <br>
</p>
<p>My two cents...</p>
<p>S.<br>
</p>
<div class="moz-cite-prefix">Le 30/04/2020 à 18:44, Chin Luh Tan a
écrit :<br>
</div>
<blockquote type="cite"
cite="mid:171cbfa1738.dd223406246274.6201721570385894168@bytecode-asia.com">
<meta content="text/html; charset=UTF-8" http-equiv="Content-Type">
<div style="font-family: Verdana, Arial, Helvetica, sans-serif;
font-size: 10pt;">
<div>Just notice that this email was stuck due to the image
attached was too large, and notice the new post by <span
style="color: rgb(0, 0, 0); font-family: Verdana, Geneva,
Helvetica, Arial, sans-serif; font-size: 13.44px;
font-style: normal; font-variant-ligatures: normal;
font-variant-caps: normal; font-weight: 400; letter-spacing:
normal; orphans: 2; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: 2;
word-spacing: 0px; -webkit-text-stroke-width: 0px;
background-color: rgb(255, 255, 255); text-decoration-style:
initial; text-decoration-color: initial; display: inline
!important; float: none;">Claus with the SEIR model from
Matlab, perhaps Scilabers could make the model more
realistic together.<br>
<br>
</span>CL<br>
<div data-zbluepencil-ignore="true" style=""
class="zmail_extra"><br>
<div id="1">============ Forwarded message ============<br>
From: Chin Luh Tan <<a target="_blank"
href="mailto:chinluh.tan@bytecode-asia.com"
moz-do-not-send="true">chinluh.tan@bytecode-asia.com</a>><br>
To: "Users mailing list for Scilab"<<a target="_blank"
href="mailto:users@lists.scilab.org"
moz-do-not-send="true">users@lists.scilab.org</a>><br>
Date: Thu, 30 Apr 2020 00:03:46 +0800<br>
Subject: Re: [Scilab-users] Corona modelling<br>
============ Forwarded message ============<br>
</div>
<br>
<blockquote style="border-left: 1px solid rgb(204, 204,
204); padding-left: 6px; margin: 0px 0px 0px 5px;">
<div>
<div style="font-family: Verdana, Arial, Helvetica,
sans-serif;font-size: 10.0pt;">
<div>Hi, <br>
<br>
I just modified Stephane's nice GUI to make it able
to load the real world data from internet so that we
could overlapped the data to the SIR model to study
the effect of locked-down, and the meaning of the
coefficients. <br>
<br>
From some reading from the internet, the
"Susceptible" population is kind of like difficult
to determined, and some suggested to use "current
cases" as "optimum model" assuming the condition is
recovering. As or the "optional model", the "total
population" is being used.<br>
<br>
While "beta" is the transmission coefficient,
"gamma" the recovery factor, can anyone explained
more details, perhaps in layman term, how to relate
these parameters to one country condition, such as
the relationship between gamma with the number of
days (what days is it referring to), beta "actual
meaning" in layman term, and perhaps link with some
"technical term" the newspaper always seen on
papers? <br>
<br>
I attached the GUI, which will load 3 sets of data
from Johns Hopkins Github, (<a
href="https://antispam.utc.fr/proxy/2/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data/csse_covid_19_time_series"
target="_blank" moz-do-not-send="true">https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data/csse_covid_19_time_series</a>)<br>
which could be download using following 3 lines
directly from the Scilab:<br>
<br>
<br>
--> fn = getURL('<a
href="https://antispam.utc.fr/proxy/2/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_deaths_global.csv"
target="_blank" moz-do-not-send="true">https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_deaths_global.csv</a>')</div>
<div>--> fn = getURL('<a
href="https://antispam.utc.fr/proxy/2/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv"
target="_blank" moz-do-not-send="true">https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv</a>')<br>
</div>
<div>--> fn = getURL('<a
href="https://antispam.utc.fr/proxy/2/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_recovered_global.csv"
target="_blank" moz-do-not-send="true">https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_recovered_global.csv</a>')<br>
<br>
and run the GUI as attached.<br>
<br>
<br>
<br>
<br>
<div class="x_1112360482zmail_extra">rgds,<br>
CL<br>
<br>
<br>
<div>---- On Mon, 30 Mar 2020 14:13:40 +0800 <b>Stéphane
Mottelet <<a
href="mailto:stephane.mottelet@utc.fr"
target="_blank" moz-do-not-send="true">stephane.mottelet@utc.fr</a>></b>
wrote ----<br>
</div>
<br>
<div><br>
</div>
</div>
</div>
<div><br>
</div>
</div>
<br>
</div>
<blockquote style="border-left: 1.0px solid
rgb(204,204,204);padding-left: 6.0px;margin: 0.0px 0.0px
0.0px 5.0px;">
<div>
<p>Hello Heinz,<br>
</p>
<p>Here is an interactive version (made for my
children last week...) :<br>
</p>
<pre style="font-family: Monospaced;font-style: normal;"><span class="colour" style="color:rgb(100, 174, 100)"><i>// Confinement COVID-19 !</i></span>
<span class="colour" style="color:rgb(100, 174, 100)"><i>// Stephane MOTTELET, UTC</i></span>
<span class="colour" style="color:rgb(100, 174, 100)"><i>// Tue Mar 24 08:55:03 CET 2020</i></span>
<span class="colour" style="color:rgb(100, 174, 100)"><i>// </i></span>
<span class="colour" style="color:rgb(176, 24, 19)">function</span> <span class="colour" style="color:rgb(131, 67, 16)"><b>dydt</b></span><span class="colour" style="color:rgb(92, 92, 92)">=</span><span class="colour" style="color:rgb(0, 0, 0)"><u>sir</u></span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(131, 67, 16)"><b>t</b></span><span class="colour" style="color:rgb(0, 0, 0)">, </span><span class="colour" style="color:rgb(131, 67, 16)"><b>y</b></span><span class="colour" style="color:rgb(0, 0, 0)">, </span><span class="colour" style="color:rgb(131, 67, 16)"><b>bet</b></span><span class="colour" style="color:rgb(0, 0, 0)">, </span><span class="colour" style="color:rgb(131, 67, 16)"><b>gam</b></span><span class="colour" style="color:rgb(0, 0, 0)">, </span><span class="colour" style="color:rgb(131, 67, 16)"><b>N</b></span><span class="colour" style="color:rgb(74, 85, 219)">)</span>
<span class="colour" style="color:rgb(131, 67, 16)"><b>dydt</b></span><span class="colour" style="color:rgb(92, 92, 92)">=</span><span class="colour" style="color:rgb(74, 85, 219)">[</span><span class="colour" style="color:rgb(92, 92, 92)">-</span><span class="colour" style="color:rgb(131, 67, 16)"><b>bet</b></span><span class="colour" style="color:rgb(92, 92, 92)">/</span><span class="colour" style="color:rgb(131, 67, 16)"><b>N</b></span><span class="colour" style="color:rgb(92, 92, 92)">*</span><span class="colour" style="color:rgb(131, 67, 16)"><b>y</b></span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(92, 92, 92)">*</span><span class="colour" style="color:rgb(131, 67, 16)"><b>y</b></span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">2</span><span class="colour" style="color:rgb(74, 85, 219)">)</span>
<span class="colour" style="color:rgb(131, 67, 16)"><b>bet</b></span><span class="colour" style="color:rgb(92, 92, 92)">/</span><span class="colour" style="color:rgb(131, 67, 16)"><b>N</b></span><span class="colour" style="color:rgb(92, 92, 92)">*</span><span class="colour" style="color:rgb(131, 67, 16)"><b>y</b></span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(92, 92, 92)">*</span><span class="colour" style="color:rgb(131, 67, 16)"><b>y</b></span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">2</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(92, 92, 92)">-</span><span class="colour" style="color:rgb(131, 67, 16)"><b>gam</b></span><span class="colour" style="color:rgb(92, 92, 92)">*</span><span class="colour" style="color:rgb(131, 67, 16)"><b>y</b></span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">2</span><span class="colour" style="color:rgb(74, 85, 219)">)</span>
<span class="colour" style="color:rgb(131, 67, 16)"><b>gam</b></span><span class="colour" style="color:rgb(92, 92, 92)">*</span><span class="colour" style="color:rgb(131, 67, 16)"><b>y</b></span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">2</span><span class="colour" style="color:rgb(74, 85, 219)">)]</span><span class="colour" style="color:rgb(0, 0, 0)">;</span>
<span class="colour" style="color:rgb(176, 24, 19)">endfunction</span>
<span class="colour" style="color:rgb(176, 24, 19)">function</span> <span class="colour" style="color:rgb(0, 0, 0)"><u>draw</u></span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(131, 67, 16)"><b>bet</b></span><span class="colour" style="color:rgb(0, 0, 0)">, </span><span class="colour" style="color:rgb(131, 67, 16)"><b>gam</b></span><span class="colour" style="color:rgb(74, 85, 219)">)</span>
<span class="colour" style="color:rgb(0, 0, 0)">t</span><span class="colour" style="color:rgb(92, 92, 92)">=</span><span class="colour" style="color:rgb(188, 143, 143)">0</span><span class="colour" style="color:rgb(255, 170, 0)">:</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(255, 170, 0)">:</span><span class="colour" style="color:rgb(188, 143, 143)">360</span><span class="colour" style="color:rgb(0, 0, 0)">;</span>
<span class="colour" style="color:rgb(0, 0, 0)">N</span><span class="colour" style="color:rgb(92, 92, 92)">=</span><span class="colour" style="color:rgb(188, 143, 143)">6e7</span><span class="colour" style="color:rgb(0, 0, 0)">;</span>
<span class="colour" style="color:rgb(160, 32, 240)">if</span> <span class="colour" style="color:rgb(50, 185, 185)">exists</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">"gcbo"</span><span class="colour" style="color:rgb(74, 85, 219)">)</span> <span class="colour" style="color:rgb(92, 92, 92)">&&</span> <span class="colour" style="color:rgb(50, 185, 185)">is_handle_valid</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(0, 0, 0)">gcbo</span><span class="colour" style="color:rgb(74, 85, 219)">)</span>
<span class="colour" style="color:rgb(0, 0, 0)">sb</span> <span class="colour" style="color:rgb(92, 92, 92)">=</span> <span class="colour" style="color:rgb(0, 0, 0)">gcbo;</span>
<span class="colour" style="color:rgb(160, 32, 240)">if</span> <span class="colour" style="color:rgb(0, 0, 0)">sb</span><span class="colour" style="color:rgb(92, 92, 92)">.</span><span class="colour" style="color:rgb(170, 170, 170)">tag</span><span class="colour" style="color:rgb(92, 92, 92)">==</span><span class="colour" style="color:rgb(188, 143, 143)">"beta"</span>
<span class="colour" style="color:rgb(131, 67, 16)"><b>bet</b></span><span class="colour" style="color:rgb(92, 92, 92)">=</span><span class="colour" style="color:rgb(0, 0, 0)">sb</span><span class="colour" style="color:rgb(92, 92, 92)">.</span><span class="colour" style="color:rgb(170, 170, 170)">value</span><span class="colour" style="color:rgb(0, 0, 0)">;</span>
<span class="colour" style="color:rgb(131, 67, 16)"><b>gam</b></span><span class="colour" style="color:rgb(92, 92, 92)">=</span><span class="colour" style="color:rgb(0, 0, 0)">findobj</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">"gamma"</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(92, 92, 92)">.</span><span class="colour" style="color:rgb(170, 170, 170)">value</span>
<span class="colour" style="color:rgb(160, 32, 240)">else</span>
<span class="colour" style="color:rgb(131, 67, 16)"><b>gam</b></span><span class="colour" style="color:rgb(92, 92, 92)">=</span><span class="colour" style="color:rgb(0, 0, 0)">sb</span><span class="colour" style="color:rgb(92, 92, 92)">.</span><span class="colour" style="color:rgb(170, 170, 170)">value</span><span class="colour" style="color:rgb(0, 0, 0)">;</span>
<span class="colour" style="color:rgb(131, 67, 16)"><b>bet</b></span><span class="colour" style="color:rgb(92, 92, 92)">=</span><span class="colour" style="color:rgb(0, 0, 0)">findobj</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">"beta"</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(92, 92, 92)">.</span><span class="colour" style="color:rgb(170, 170, 170)">value</span>
<span class="colour" style="color:rgb(160, 32, 240)">end</span>
<span class="colour" style="color:rgb(0, 0, 0)">y</span><span class="colour" style="color:rgb(92, 92, 92)">=</span><span class="colour" style="color:rgb(50, 185, 185)">ode</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">'stiff'</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(74, 85, 219)">[</span><span class="colour" style="color:rgb(0, 0, 0)">N</span><span class="colour" style="color:rgb(92, 92, 92)">-</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(0, 0, 0)">;</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(0, 0, 0)">;</span><span class="colour" style="color:rgb(188, 143, 143)">0</span><span class="colour" style="color:rgb(74, 85, 219)">]</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">0</span><span class="colour" style="color:rgb(0, 0, 0)">,t,</span><span class="colour" style="color:rgb(50, 185, 185)">list</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(0, 0, 0)"><u>sir</u>,</span><span class="colour" style="color:rgb(131, 67, 16)"><b>bet</b></span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(131, 67, 16)"><b>gam</b></span><span class="colour" style="color:rgb(0, 0, 0)">,N</span><span class="colour" style="color:rgb(74, 85, 219)">))</span><span class="colour" style="color:rgb(0, 0, 0)">;</span>
<span class="colour" style="color:rgb(0, 0, 0)">curves</span> <span class="colour" style="color:rgb(92, 92, 92)">=</span> <span class="colour" style="color:rgb(0, 0, 0)">findobj</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">"curves"</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(0, 0, 0)">;</span>
<span class="colour" style="color:rgb(0, 0, 0)">curves</span><span class="colour" style="color:rgb(92, 92, 92)">.</span><span class="colour" style="color:rgb(170, 170, 170)">children</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(92, 92, 92)">.</span><span class="colour" style="color:rgb(170, 170, 170)">data</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(255, 170, 0)">:</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">2</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(92, 92, 92)">=</span><span class="colour" style="color:rgb(0, 0, 0)">y</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">3</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">:</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(0, 0, 0)">;</span>
<span class="colour" style="color:rgb(0, 0, 0)">curves</span><span class="colour" style="color:rgb(92, 92, 92)">.</span><span class="colour" style="color:rgb(170, 170, 170)">children</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">2</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(92, 92, 92)">.</span><span class="colour" style="color:rgb(170, 170, 170)">data</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(255, 170, 0)">:</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">2</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(92, 92, 92)">=</span><span class="colour" style="color:rgb(0, 0, 0)">y</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">2</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">:</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(0, 0, 0)">;</span>
<span class="colour" style="color:rgb(0, 0, 0)">curves</span><span class="colour" style="color:rgb(92, 92, 92)">.</span><span class="colour" style="color:rgb(170, 170, 170)">children</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">3</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(92, 92, 92)">.</span><span class="colour" style="color:rgb(170, 170, 170)">data</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(255, 170, 0)">:</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">2</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(92, 92, 92)">=</span><span class="colour" style="color:rgb(0, 0, 0)">y</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">:</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(0, 0, 0)">;</span>
<span class="colour" style="color:rgb(160, 32, 240)">else</span>
<span class="colour" style="color:rgb(0, 0, 0)">y</span><span class="colour" style="color:rgb(92, 92, 92)">=</span><span class="colour" style="color:rgb(50, 185, 185)">ode</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">'stiff'</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(74, 85, 219)">[</span><span class="colour" style="color:rgb(0, 0, 0)">N</span><span class="colour" style="color:rgb(92, 92, 92)">-</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(0, 0, 0)">;</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(0, 0, 0)">;</span><span class="colour" style="color:rgb(188, 143, 143)">0</span><span class="colour" style="color:rgb(74, 85, 219)">]</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">0</span><span class="colour" style="color:rgb(0, 0, 0)">,t,</span><span class="colour" style="color:rgb(50, 185, 185)">list</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(0, 0, 0)"><u>sir</u>,</span><span class="colour" style="color:rgb(131, 67, 16)"><b>bet</b></span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(131, 67, 16)"><b>gam</b></span><span class="colour" style="color:rgb(0, 0, 0)">,N</span><span class="colour" style="color:rgb(74, 85, 219)">))</span><span class="colour" style="color:rgb(0, 0, 0)">;</span>
<span class="colour" style="color:rgb(0, 0, 0)">scf</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">0</span><span class="colour" style="color:rgb(74, 85, 219)">)</span>
<span class="colour" style="color:rgb(0, 0, 0)">clf</span>
<span class="colour" style="color:rgb(0, 0, 0)">plot</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(0, 0, 0)">t,y</span><span class="colour" style="color:rgb(74, 85, 219)">)</span>
<span class="colour" style="color:rgb(0, 0, 0)">gce</span><span class="colour" style="color:rgb(74, 85, 219)">()</span><span class="colour" style="color:rgb(92, 92, 92)">.</span><span class="colour" style="color:rgb(170, 170, 170)">tag</span><span class="colour" style="color:rgb(92, 92, 92)">=</span><span class="colour" style="color:rgb(188, 143, 143)">"curves"</span><span class="colour" style="color:rgb(0, 0, 0)">;</span>
<span class="colour" style="color:rgb(0, 0, 0)">gce</span><span class="colour" style="color:rgb(74, 85, 219)">()</span><span class="colour" style="color:rgb(92, 92, 92)">.</span><span class="colour" style="color:rgb(170, 170, 170)">children</span><span class="colour" style="color:rgb(92, 92, 92)">.</span><span class="colour" style="color:rgb(170, 170, 170)">thickness</span><span class="colour" style="color:rgb(92, 92, 92)">=</span><span class="colour" style="color:rgb(188, 143, 143)">2</span><span class="colour" style="color:rgb(0, 0, 0)">;</span>
<span class="colour" style="color:rgb(0, 0, 0)">legend</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">"Susceptible"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"Infected"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"Recovered"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(92, 92, 92)">-</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(74, 85, 219)">)</span>
<span class="colour" style="color:rgb(0, 0, 0)">sb1</span> <span class="colour" style="color:rgb(92, 92, 92)">=</span> <span class="colour" style="color:rgb(50, 185, 185)">uicontrol</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">"style"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"slider"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"units"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"normalized"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"Position"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span> <span class="colour" style="color:rgb(74, 85, 219)">[</span><span class="colour" style="color:rgb(188, 143, 143)">0.85</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">0.2</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">0.05</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">0.48</span><span class="colour" style="color:rgb(74, 85, 219)">]</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"BackgroundColor"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span> <span class="colour" style="color:rgb(74, 85, 219)">[</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(74, 85, 219)">]</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"Callback_Type"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">12</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"sliderstep"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(74, 85, 219)">[</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(92, 92, 92)">/</span><span class="colour" style="color:rgb(188, 143, 143)">1000</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(92, 92, 92)">/</span><span class="colour" style="color:rgb(188, 143, 143)">10</span><span class="colour" style="color:rgb(74, 85, 219)">]</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"min"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">0.15</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"max"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">0.3</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"value"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(131, 67, 16)"><b>bet</b></span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"Callback"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"draw"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"tag"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"beta"</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(0, 0, 0)">;</span>
<span class="colour" style="color:rgb(50, 185, 185)">uicontrol</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">"style"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"text"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"string"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"$\beta$"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"units"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"normalized"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"Position"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span> <span class="colour" style="color:rgb(74, 85, 219)">[</span><span class="colour" style="color:rgb(188, 143, 143)">0.85</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">0.125</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">0.05</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">0.08</span><span class="colour" style="color:rgb(74, 85, 219)">]</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"BackgroundColor"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span> <span class="colour" style="color:rgb(74, 85, 219)">[</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(74, 85, 219)">]</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"HorizontalAlignment"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"center"</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(0, 0, 0)">;</span>
<span class="colour" style="color:rgb(0, 0, 0)">sb1</span> <span class="colour" style="color:rgb(92, 92, 92)">=</span> <span class="colour" style="color:rgb(50, 185, 185)">uicontrol</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">"style"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"slider"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"units"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"normalized"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"Position"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span> <span class="colour" style="color:rgb(74, 85, 219)">[</span><span class="colour" style="color:rgb(188, 143, 143)">0.90</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">0.2</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">0.05</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">0.48</span><span class="colour" style="color:rgb(74, 85, 219)">]</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"BackgroundColor"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span> <span class="colour" style="color:rgb(74, 85, 219)">[</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(74, 85, 219)">]</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"Callback_Type"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">12</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"sliderstep"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(74, 85, 219)">[</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(92, 92, 92)">/</span><span class="colour" style="color:rgb(188, 143, 143)">1000</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(92, 92, 92)">/</span><span class="colour" style="color:rgb(188, 143, 143)">10</span><span class="colour" style="color:rgb(74, 85, 219)">]</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"min"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">0</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"max"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(92, 92, 92)">/</span><span class="colour" style="color:rgb(188, 143, 143)">15</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"value"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(131, 67, 16)"><b>gam</b></span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"Callback"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"draw"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"tag"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"gamma"</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(0, 0, 0)">;</span>
<span class="colour" style="color:rgb(50, 185, 185)">uicontrol</span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">"style"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"text"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"string"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"$\gamma$"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"units"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"normalized"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"Position"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span> <span class="colour" style="color:rgb(74, 85, 219)">[</span><span class="colour" style="color:rgb(188, 143, 143)">0.9</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">0.125</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">0.05</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">0.08</span><span class="colour" style="color:rgb(74, 85, 219)">]</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"BackgroundColor"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span> <span class="colour" style="color:rgb(74, 85, 219)">[</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(74, 85, 219)">]</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(255, 170, 0)">...</span>
<span class="colour" style="color:rgb(188, 143, 143)">"HorizontalAlignment"</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">"center"</span><span class="colour" style="color:rgb(74, 85, 219)">)</span><span class="colour" style="color:rgb(0, 0, 0)">;</span>
<span class="colour" style="color:rgb(160, 32, 240)">end</span>
<span class="colour" style="color:rgb(160, 32, 240)">end</span>
<span class="colour" style="color:rgb(0, 0, 0)">clf</span>
<span class="colour" style="color:rgb(0, 0, 0)"><u>draw</u></span><span class="colour" style="color:rgb(74, 85, 219)">(</span><span class="colour" style="color:rgb(188, 143, 143)">0.3</span><span class="colour" style="color:rgb(0, 0, 0)">,</span><span class="colour" style="color:rgb(188, 143, 143)">1</span><span class="colour" style="color:rgb(92, 92, 92)">/</span><span class="colour" style="color:rgb(188, 143, 143)">15</span><span class="colour" style="color:rgb(74, 85, 219)">)
</span>
</pre>
<div class="x_-2117773561moz-cite-prefix">Le
30/03/2020 à 02:14, Heinz Nabielek a écrit :<br>
</div>
<blockquote>
<pre class="x_-2117773561moz-quote-pre">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
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<pre class="moz-signature" cols="72">--
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
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