The documents includes chapter 3 of the course ecology, epidemiology and control of infectious diseases taught by prof. Leirs. The document does not contain the exercises, as these were made in an excel document.
CHAPTER 3: MODELLING
TRANSMISSION
INTRODUCTION: A MODEL IS…
A model will try to give us an impression about the reality. So it can help us to get an impression about if we
change something what it will do with the reality.
“A model is a representation of an object or a system that maintains an accurate relationship between all
important aspects of the model, although the absolute values of the original properties need not to be
preserved.”
We don’t want to describe everything in detail or exactly what we see but we want to represent
the important aspects.
Why do we want to use such models?
o Crystallize important shared properties of unique systems:
we want to make a set of rules with what we know about the system
insights from one system used to understand the other system
o Extract essentials from complex systems
o “common language”
Common language used to describe different systems in such a way that
what we describe, can be applied to other systems as well
We should make sure that the way we talk about the system uses as much as
possible general terms
o Show properties of system that we did not know exist
What will happen under conditions we did not see before, properties we
were not aware of, …
o See consequences of assumptions
o Guide future work
If model doesn’t work out: some of the rules we made were wrong, indicates
on what future research we can focus
o Make predictions for the future (applied questions)
If reliable model: simulation of intervention strategies without really doing it
in the fields
If we make a model, we must make sure that the model is:
- Accurate: the most accurate model for a system is to say that for every place on the x-axis,
there is one particular value on the y-axis
exactly represents what is observed in reality
- Informative: shows a general characteristic of the system
, The most accurate model for these data (dots) are the dots itself. This model will represent exactly the same as
what is observed in reality but this model is not very much informative because it doesn’t tell me anything else
than I can see! The most informative model is the red linear line that is drawn because you can see that there
seems to be a relation between the dots (when x increases, y increases as well), but it’s not very accurate as
there are dots quite for away from that curve. BUT maybe these dots are one of the details we want to leave
out of our model.
CONCLUSION
We always need to find the balance between being accurate and being informative:
o Model must adequately describe or mimic the real world:
model should be as accurate as possible
BUT: a model that completely describes the reality is as complicated
as the reality itself
The model must be adequate for the questions that you’re raising
Depends on what your question is
How far must the level of detail need to go?
Example:
o If you want to know where Tanzania is: world map
o If you want where O building is: map of CDE
MATHEMATICAL AND PHENOMENOLOGICAL MODELS
MATHEMATICAL MODELS
Mathematical models are the best models you can use because they force us to use a common language for
the different system (symbols) and because the relations can be expressed in a mathematical way. Therefore,
we can also use mathematical techniques to investigate what is happening in the system if we change
something: we can make use of the properties of mathematics to investigate the dynamics of a model.
- Statistical models
o Recognise patterns in data
o Testing model fit: how well does the model fits to the data?
- Theoretical models: result of our thinking about the mechanisms that happen in the system
o Formalised hypothesis/rules
o Predictions/simulations
Most of the time, a combination of statistical and theoretical models are used: rules are made based on
theoretical models, this rules can lead to a mathematical model that can tell us whether the model fits or not. If
the model fits, we can make predictions or simulations under certain conditions. If the model does not fit, we
need to re-think about some parts of the theoretical model.
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