Toda a aula

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Collaborative Course on Infectious
Diseases January 2009
LECTURE 10 Why Bother with Modeling? Eduardo
Massad edmassad_at_usp.br
Harvard School of Public Health Centro de
Pesquisa Gonçalo Moniz, Fundação Oswaldo Cruz
(Fiocruz) Brazil Studies Program, DRCLAS,
Harvard University
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• How would you describe
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•     The flickering of a flame?
•     The texture of an oil painting?
•     Highway traffic during the rush hours?
•     Twinkling stars?
•     Breaking glass?
•     A bowling ball hitting pins?
•     Melting ice?
•     The sound of a violin?
• The spread of infections?

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  Find an effective description of how the
players motion are related to the sound made by
the instrument (Inductive) Numerical model
based on a first principle description
or analytical solution of the governing equations
(Deductive)  
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Inductive reasoning Looking for patterns
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The Hilleman Hypothesis
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Deductive reasoning Looking for the first
principles
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A Model can be defined as a convenient
representation of something important
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art is a lie that help us to discover the
truth
Pablo Picasso
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Definition of Modelling   A model can be defined
as a convenient representation of anything
considered important. This is an operational
definition and, when the representation consists
of quantitative components, the model is called a
mathematical model   The process of Modelling
consists of a set of complex activities
associated with the designing of models
representing a real-world system and their
solution. As we shall see later on the solution
may be analytical or numerical.
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A Model is composed by the following
items     Variables the quantities of interest
that varies with time or age, like the number (or
proportion) of susceptibles to a given
infection   Parameters quantities that
determine the dynamical behavior of the systems,
like the incidence rate   Initial and boundary
conditions the initial values of the variables
with time (initial conditions) or age (boundary
conditions).
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Models classification  Stochastic include
probability elements on its dynamicsDeterminist
ic once defined the value of the parameters and
initial conditions, all the course of its
dynamics is determined.
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The three qualities of models  1.   
Parsimony2.    Generality3.    Prediction.
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Purposes of Modelling   -        to help the
scientific understanding and precision in the
expression of current theories and concepts   -
identification of areas in which epidemiological
data is required   - prediction.
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Forecasting vs Projection Models   -   
Forecasting prediction before the happening   -
Projection what would have happened if
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• Three conflicting properties
• Accuracy
• Transparency
• Flexibility.

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The natural world is complex and a model must
reduce this complexity by focusing on the
essential components that are minimally necessary
and sufficient to understand the problem at
hand Taper and Lele, 2004
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All models are wrong some models are
useful... Albert Einstein
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THRESHOLD CONDITIONS
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The Reproductive Rate of Infections   The Basic
Reproductive Number, R0, is the number of
secondary infections produced by a single
infectee during his/hers entire infectiousness
period in an entirely susceptible population.
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Nothing in biology makes sense except in the
light of evolution. T. Dobzhansky, 1973.
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For microparasites, in a homogeneously mixing
population, the reproductive value, R, is a
function of the product of the number of
potentially infective contacts, b, the proportion
of susceptible hosts, x, and the time of
permanence in the infective condition,
T     R(t) bTx(t)
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R0 ma2bexp(-mn)/rm gt 1  
mth rm/a2bexp(-mn)
 
dY(t)/dt bX(t)Y(t) gY(t) gt 0 ? epidemics
  bX(t) g gt 1   t 0, X(0) 1  
b gt g ? dY(t)/dt gt
0 ? epidemics
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The critical proportion to vaccinate Let us
assume that a fraction p of the susceptible is
vaccinated against a certain disease, as soon in
life as possible. Then X(0) 1 p dY(t)/dt
b(1 p) gY(t) b(1 p)/ g 1 R0(1
p) 1 R0(1 p) lt 1 ? eradication Pcrit 1
1/R0
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