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38 - Newsletter EnginSoft Year 6 n°4
Figure 6: The peak is plotted versus the peak position. The bubble color is used to represent the mortality.
The cloud of points summarizes the simulated scenarious. It can be easily seen that even the worst previsions
in terms of peak and mortality rate have nothing in common with a pandemia or a catastrophic outbreak.
To launch these simulations a new modeFRONTIER project has
been organized (see Figure 5): the Latin-Hypercube
algorithm has been set up to plan an appropriate DOE and a
batch call to the project described before has been applied
in order to solve the model tuning problem. A Scilab routine
finally extracts the results in correspondence with the best
solution found.
In Figure 6 a bubble chart is shown: the peak value is plotted
versus the peak position and the bubble color is used to
represent the expected mortality. It can be easily seen that
we obtain three ranges of existence; we can say that the
peak position ranges between 45.29 and 45.60 weeks and
that the peak ranges between 13.19 and 13.24 infected for
one thousand inhabitants. The mortality rate never passes
the 0.00347 over 1000 persons. It is interesting to observe
that the resulting cloud of points is not uniformly nor
homogeneously distributed, but it has important voids and
regions with high densities.
To understand how the probability of the couple peak and
peak position is distributed, we have built the diagram
plotted in Figure 7. The cloud of points has been divided in
a 20 x 20 cells regular array, and we have counted the
number of designs inside each cell. These counts have been
divided by the total number of computed designs obtaining
the relative frequency, which can be reasonably associated
with the probability. This plot allows to say
that peaks of around 13.35 infected falling
between the 45.43 and 45.44 week are the
most probable ones. We can conclude that,
even if considering uncertainties in the
target values, it is possible to estimate the
spread of the disease with a reasonable
accuracy: it is certainly possible to exclude
catastrophic scenarious even if few data are
available. During the next weeks we will see
if the model presented in this work has
been able to correctly predict the spread of
the swine flu or, on the contrary, if a
terrible outbreak will happen. Let's hope for
the best and be optimistic!
Conclusions
In this work we have shown how it is
possible to model the natural spread
of a disease, within a population,
with relatively simple equations. If
some observed or measured data are
available it is possible to tune the
model and predict the evolution of
the disease with sufficient accuracy
at macro scale.
The Scilab platform has been used to
numerically solve the ODEs system
and modeFRONTIER to tune the
model and manage the uncertainties
on available information. We would
like to emphasize that the
methodology adopted in this work can be used in the same
way, also in other contexts, when a prevision is needed and
experimental data are affected by errors.
References
[1] http://www.scilab.org/ to have more information on
Scilab.
[2] http://www.iss.it/iflu/ to have more information on the
italian sentinel surveillance. The data relative to the
infected have been downloaded here.
[3] http://www.ministerosalute.it to have a complete
description of the swine flu.
[4] http://www.wikipedia.com to have more information on
the SIR model.
[5] P. Blanchard, R. L. Devaney, G. R. Hall, Differential
Equations, (2006) Thomson Brooks/Cole, 3nd ed.
[6] K. S. Bhamra, O. R. Bala, Ordinary Differential Equations.
An Introductory Treatment with Applications, (2003)
Allied Publishers PVT. LTD.
For more information on this document please contact the
author: Massimiliano Margonari - EnginSoft S.p.A.
info@enginsoft.it
Figure 7: The frequency of the couples peak and peak position. The most probable scenarios are those
characterized by a peak of around 13.35 infected falling around the 45.44 week of the year.