dynamic networks, and methods from dynamic queuing theory and Markovian decision
process analysis, which can be used to develop optimal evacuation strategies.^2 In the
case of floods, we may want to identify which flooded roads to reopen in which order.
This could involve finding minimum spanning trees in order to achieve connectivity of a
road network. This is a well-studied problem, but there are new complications arising
from the need to take other priorities into account, and inaccurate reports about and
uncertainties concerning which roads are open.
Research Challenge for the Mathematical Sciences: Develop new methods for
classical operations research problems involving multiple criteria in the context of major
uncertainty as to requirements for and availability of resources, duration of events, and
stochastic effects of uncontrollable factors such as climate.
Example 3. Climate Change and Human Health: The Case of Heat Waves
Climate change is anticipated to influence public health through a wide range of
pathways, largely through exacerbating current day risks (NIEHS 2010). As an example,
air pollution levels may be affected, especially for pollutants with photochemical
formation (Chang et al. 2010, Bell et al. 2007, Barr 2010). The distribution of infectious
diseases, such as malaria and dengue fever, may shift into populations that have not
been previously affected (Parham and Michael 2010, Tanser et al. 2003).
Efforts to quantify the health impact from a changing climate face several
challenges. A key challenge is estimating future conditions, which is often achieved
through use of global circulation models (GCMs), often in conjunction with regional
modeling systems. Researchers have extensively evaluated GCMs and improved the
representation of the climate system and estimates of extreme conditions (IPCC 2007).
Still, limitations remain. New mathematical approaches are needed in the area of
uncertainty quantification and propagation and in the area of linking heterogeneous and
complex data sets. For example, uncertainty in the estimation of health impacts from
climate change involves uncertainties inherent in the GCMs, linking of multiple systems
and downscaling output from GCM models to a finer spatial resolution. To estimate
health consequences from climate change in the future, we must understand current day
impacts. Thus, the uncertainties associated with models to estimate modern effects also
play a role. Mathematical models need to be developed that can incorporate different
assumptions on baseline, changing demographics and other factors.
Perhaps the most direct link between climate change and human health is
through changes in weather patterns, with anticipated higher overall temperatures and
more frequent and severe extreme events (Meehl and Tebaldi 2004), as also discussed
in Example 2. Several studies have examined how heat and heat waves affect
temperature in the current day (Anderson and Bell 2009, Ostro et al. 2009) and some
have explored heat-related mortality impacts under a changing climate (Gosling et al.
2007). However, new approaches to generate quantitative estimates are needed (Xun et
al. 2010, Kinney et al. 2008). Specifically, mathematical models for estimating current
day effects and how to apply such models to future conditions are limited. Below, we
describe many of the challenges to quantitative estimation of the human health
consequences of higher temperatures under a changing climate, with a focus on the
(^2) Much of this paragraph is taken from the description of the DIMACS Climate and Health Research
Initiative.