4.2. Sensitivity Analysis
65
ticeable impact on model results-either qualitatively or quantitatively.
Knowing which parameters are crucial for what kind of outcome helps generate confidence in a model 's performance and it can help guide data collection . If under a wide range of assumptions one parameter value has no
significant impact on model results, then we can save time and effort in
tracking down specific information on that parameter. Actually, we may
even alter our model so as not to use that parameter at all. If, however, our
model is very sensitive to the choice of some parameter or initial condition,
then we should do our best to find reliable data and to report that sensitivity when we present or discuss the model.
A good model contains only the elements essential for the description of
a system, and a good presentation of a model includes a discussion of its
sensitivity to alternative assumptions about initial conditions and parameter
values . Model results are obviously also influenced by model structure. So,
in order to be able to say that our model is a good representation of the
system of interest, we need to explore how changes in model structure are
related to changes in model results. Take , for example, the epidemic model
discussed in Section 4.1. A key assumption of that model was that natura l
birth and death rates are equal to each other. This assumption enabled us
to concentrate on the effects of the disease on population dynamics . But by
so doing haven 't we limited ourselves to a small set of drivers behind the
spread of a disease? If the individuals infected with the disease are too sick
to reproduce, then surely we may expect that the population dynamics will
be affected by the outbreak of the disease .
The model of Figure 4.12 explicitly includes the natural birth and death
processes, and the effects that the disease may have on reproductive activity of sick individuals . In that model we have defined the net births as
NET BIRTHS = NETBIRTHRATE*(IMMUNE+SUSCEPTIBLE)
*O-(IMMUNE+INFECTED+SUSCEPTIBLE)/4000). (4)
If you set NET BIRTH RATE = 0, then the dynamics of this model are identical to that in Section 4.1. It is in this sense that an analysis of the sensitivity of model results with respect to the structure of the model may be
thought of as another case of sensitivity analysis with respect to the choice
of a parameter.
Set the net birth rate to .02. Before you run the model, make an educated
guess as to the results. Here we have a case in which the population increases towards a maximum of 4000 if there is no disease present. Confirm
this observation by setting the initial value of INFECTED to zero . However,
if the disease is present in the population, the number of births is lowered
at those times during which individuals are sick. During the outbreak of a
disease, the net birth rate is reduced, and following an outbreak it increases
again . Consequently, we would expect that fluctuations in population sizes
follow the spread of the disease. And vice versa, with a steady stream of
65
ticeable impact on model results-either qualitatively or quantitatively.
Knowing which parameters are crucial for what kind of outcome helps generate confidence in a model 's performance and it can help guide data collection . If under a wide range of assumptions one parameter value has no
significant impact on model results, then we can save time and effort in
tracking down specific information on that parameter. Actually, we may
even alter our model so as not to use that parameter at all. If, however, our
model is very sensitive to the choice of some parameter or initial condition,
then we should do our best to find reliable data and to report that sensitivity when we present or discuss the model.
A good model contains only the elements essential for the description of
a system, and a good presentation of a model includes a discussion of its
sensitivity to alternative assumptions about initial conditions and parameter
values . Model results are obviously also influenced by model structure. So,
in order to be able to say that our model is a good representation of the
system of interest, we need to explore how changes in model structure are
related to changes in model results. Take , for example, the epidemic model
discussed in Section 4.1. A key assumption of that model was that natura l
birth and death rates are equal to each other. This assumption enabled us
to concentrate on the effects of the disease on population dynamics . But by
so doing haven 't we limited ourselves to a small set of drivers behind the
spread of a disease? If the individuals infected with the disease are too sick
to reproduce, then surely we may expect that the population dynamics will
be affected by the outbreak of the disease .
The model of Figure 4.12 explicitly includes the natural birth and death
processes, and the effects that the disease may have on reproductive activity of sick individuals . In that model we have defined the net births as
NET BIRTHS = NETBIRTHRATE*(IMMUNE+SUSCEPTIBLE)
*O-(IMMUNE+INFECTED+SUSCEPTIBLE)/4000). (4)
If you set NET BIRTH RATE = 0, then the dynamics of this model are identical to that in Section 4.1. It is in this sense that an analysis of the sensitivity of model results with respect to the structure of the model may be
thought of as another case of sensitivity analysis with respect to the choice
of a parameter.
Set the net birth rate to .02. Before you run the model, make an educated
guess as to the results. Here we have a case in which the population increases towards a maximum of 4000 if there is no disease present. Confirm
this observation by setting the initial value of INFECTED to zero . However,
if the disease is present in the population, the number of births is lowered
at those times during which individuals are sick. During the outbreak of a
disease, the net birth rate is reduced, and following an outbreak it increases
again . Consequently, we would expect that fluctuations in population sizes
follow the spread of the disease. And vice versa, with a steady stream of