250 S. Stijven et al.
The basic reproduction number R 0 is the most important indicator of how
dangerous the infectious disease is. R 0 is defined as the expected number of
secondary infections caused by a primary infection in a fully susceptible population.
In the presence of an actual pandemics threat, R0 can be estimated from a small
population of early infected cases quite accurately within a couple of days. For the
NHN1 influenza virus the R0 value observed was 1.8.
Robust evaluation of worst and best case scenarios, realistic predictions of
whether or not the pandemics will happen and robust forecasts of the damages, are of
critical importance to the governments and National Health institutes. This global
economic impact and the need to understand pandemics has made influenza the
subject of many simulation studies. The most recent state-of-the art dynamic models
for influenza are a lot more realistic than static compartmental deterministic models,
but realism comes at price of much higher complexity. Dynamic individual-based
models require a lot more simulation time, provide less transparency and are looked
at as a black-box simulators with many “knobs to turn” of unknown significance for
simulation results.
Many fundamental parameters in individual-based models are unknown a priori
and the computational complexity severely hinders experimental approaches with
different scenarios of distributions of these fundamental parameters.
Computational complexity and the presence of too many variables of unknown
significance as well as the need to understand relationships and dependencies in
input response data make symbolic regression the perfect tool for model-based
understanding of dynamic models.
In Willem et al. ( 2014 ) the authors proposed a hybrid approach for understanding
the complex black-box simulations through an iterative strategy of collecting the
simulation data, reducing dimensionality, identifying new optimal experiments
and repeating the process until ensembles of reliable and transparent symbolic
regression meta-models is found and can be used to sensitivity analysis and design
space exploration.
4.1 Flute Simulator
As a basis for a simulator we took an open-source individual-based model for
influenza epidemics called FluTE and developed by Chao et al. ( 2010 ). This state
of the art model is written in C++. All individuals are simulated as members of
different social mixing groups (Fig. 7 ). Within each group influenza transmission
is based on random mixing. The geographical distribution, employment rates and
commuting behavior of the population are based on the 2000 Census data for Seattle
(500,000 people) and the Los Angeles County (11 million people). The data is
distributed together with the source code of the model. The simulation runs for
180 days in 12-h time steps, representing daytime (work, school and community
contacts) and nighttime (home and community contacts). The contact probabilities
in the model were tuned such that the final age-specific clinical attack rates were