Biology Reference
In-Depth Information
a particular relevance as it explains why travel restrictions
appear to be highly ineffective in containing epidemics: the
complexity and heterogeneity of the current human
mobility network favor considerably the global spreading
of infectious diseases, and only unfeasible mobility
restrictions that reduce the global travel fluxes 90% or more
would be effective
[57,64,69]
.
Reaction
of a timescale separation between the network evolution
and the dynamical process unfolding on its structure. At
one extreme we can consider the network as quenched in its
connectivity pattern, thus evolving on a timescale that is
much longer that the dynamical process itself. At the other
extreme, the network is evolving at a much shorter time-
scale than the dynamical process, thus effectively dis-
appearing from the definition of the interaction among
individuals that is conveniently replaced by effective
random couplings. While the timescale separation is
extremely convenient for the numerical and analytical
tractability of the models, networks generally evolve on
a timescale that might be comparable to that of the
dynamical process. Furthermore, the network properties
that inform models generally represent a time-integrated
static snapshot of the system. However, in many systems
the timing and duration of interactions define processes on
a timescale very different from, and often conflicting with,
those of the time-integrated view. This makes clear the
importance of considering the concurrency of network
evolution and dynamical processes in realistic models in
order to avoid misleading conclusions
[76
diffusion models lend themselves to the
implementation of large-scale computer simulations
(Monte Carlo and individual-based simulations) that allow
microscopic tracking of the state of each node and the
evolution of the dynamical process. For instance, state of
the art data-driven meta-population models combine highly
detailed population and transportation databases. For
instance, the recently developed GLobal Epidemic and
Mobility (GLEaM) model
[70]
integrates census and
mobility data in a fully stochastic meta-population model
that allows for the detailed simulation of the spread
of influenza-like illnesses (ILI) around the globe. Meta-
population models are also amenable to the inclusion of an
age structure in the population by simply modifying the
compartmental structure to include the age group contact
matrix, M, taking them one step further in terms of realism
while still keeping all the advantages of the conceptual
clarity that are the hallmarks of this class of models.
Agent-based models, where each agent represents
a simplified human individual going through their daily
activities, push to the limits the realism of data-driven
models. Infection spreads from individual to individual
whenever they come into contact with each other, whether
within the household, at school or work, or at random in the
general population
[14]
. A key feature of models such as
CommunityFlu
[71]
, Flute
[72]
and Epifast
[73]
is the
characterization of the network of contacts among indi-
viduals based on realistic data-driven models of the soci-
odemographic structure of the population being considered
[74,75]
. All these highly structured models provide a novel
approach to evidence-based and quantitative scenario
analysis. Although even among modelers there are con-
trasting opinions, those models are assuming increasing
relevance in the public health domain, providing rationales
and quantitative analysis to support
e
79]
.
A second challenge is the co-evolution of networks with
the dynamical process. Access to the mathematical and
statistical laws that characterize the interplay and feedback
mechanisms between the network evolution and the
dynamical processes is extremely important, especially in
social systems where the adaptive nature of agents is of
paramount importance
[58,78,80]
. The spreading of an
opinion is affected by interactions between individuals, but
the presence and/or establishment of interactions between
individuals is affected by their opinion. This issue is more
and more relevant in the area of modern social networks
populating the information technology ecosystem, such as
those defined by the Facebook and Twitter applications. In
this case the network and the information spreading cannot
be defined in isolation, especially because of the rapidly
changing interactions and modes of communication that
depend upon the type of information exchanged and the
rapidly adaptive behavior of individuals (
Figure 27.7
).
The adaptive behavior of individuals to the dynamical
processes they are involved in represents another modeling
challenge, as it calls for the understanding of the feedback
among different and competing dynamical processes. For
instance, relatively little systematic work has been done to
provide coupled behavior
e
the decision- and
policy-making processes.
disease models able to close the
feedback loop between behavioral changes triggered in the
population by an individual's perception of the disease
spread and the actual disease spread
[59,81]
. Similar issues
arise in many areas where we find competing processes of
adaptation and awareness of information or knowledge
spreading in a population.
Finally, the eventual goal is not only to understand
complex systems, mathematically describe their structure
e
CONCLUSIONS AND FUTURE
CHALLENGES
Although in recent years our understanding of dynamical
processes in complex networks has progressed at an
exponential pace, there are still a number of major chal-
lenges that see the research community actively engaged.
The first challenge stems from the fact that the analysis of
dynamical processes is generally performed in the presence