No part of the world is impervious to natural disaster. Epidemics, earthquakes, floods, hurricanes, drought, tornadoes, wildfires, tsunamis, and extreme temperatures routinely take their toll. Mathematical sciences can help in predicting, monitoring, and responding to such events, and mitigating their effects.
Responding to Natural Disasters: The workshop will study mathematical problems arising in disaster response, e.g., in measures like evacuation, stockpiling supplies, quarantine, vaccination, and emergency communication. Mathematical challenges in evacuation include dynamic routing under changing road conditions; locating, staffing, supplying, and managing movement to relief facilities. Research challenges in this area include choices about optimal location and routing, interconnected with predictions of duration, onset time, and severity of events, under uncertain spatial distribution of populations and events. While location theory, network routing, and resource allocation are classical subjects in operations research and discrete mathematics, they are complicated by uncertainty and multiple objectives and call for new methods in stochastic optimization. Emergency transportation and evacuation involve routing in real-time under dynamically changing network structure. Spatial analysis, analysis of dynamic networks, and methods from dynamic queuing theory and Markovian decision process analysis can all be used to develop optimal evacuation strategies.
Plans for swift, organized response to a public health emergency include use of quarantine or vaccination and provision for needed supplies. We will review recent examples of public health emergencies, e.g., the worldwide outbreak of H1N1 flu in 2009, cholera in Haiti after the 2010 earthquake, dengue in Puerto Rico in 2010, and avian influenza cases worldwide. We will revisit responses to such outbreaks, assess the effectiveness of the response, and identify where mathematical sciences can assist in the future. Relevant are spatio-temporal modeling and network modeling of disease, evolution of pathogens and emerging infections, criteria for vaccination or quarantine, complications from varying behavioral responses to disasters, and planning for "surge". Emergencies can also occur when food supplies are contaminated, as in outbreaks of. E. coli in beef (2009), salmonella in eggs (2010), and listeriosis in cantaloupes (2011). Building on these examples we will explore models of the food system from "farm to fork" to pinpoint vulnerabilities and design redundancies.
Responses to natural disasters are often initiated with limited information and considerable uncertainty about the post-event environment. Stochastic programming is often applied when there is uncertainty about the environment. Since every disaster is different, formalization of the uncertainty by probabilities of different states of the post-event environment is typically not possible. Robust optimization and online optimization are modeling approaches we will explore for decision making under uncertainty that focus on performing well for all potential environments.
Widespread use of social media can revolutionize emergency communication, spreading warning messages by authorities to large groups of people. Emergency managers currently study ways to word warning messages, to utilize social media, and to avoid overloading communication networks. We need models (as in of how emergency messages spread through social networks and how they will impact the population (targeted and non-targeted) and network resources. Such models would include stochastic parameters representing success of message design and branching probabilities for behavioral responses to messages. Models will enable us to explore limits on behavior and find values for model parameters that cause the network to overload and break down. Trust is a key consideration in emergency messaging, so theories of player trust in communication groups are required.
Mitigating the Effect of Natural Disasters: We can take steps to mitigate the damage from disasters. Flooding illustrates the challenges we will review. In the U.S., FEMA monitors potential for, responds to, and oversees recovery from floods; makes insurance payments for damage; and undertakes flood mitigation projects. Among potential flood mitigation strategies are improved flood forecasting and warning systems; retrofit of green infrastructure (e.g., cisterns and rain barrels, green roofs, pervious concrete) to reduce upstream runoff; flood-proofing and elevation of assets; cleanout of urban drainage systems; construction of dams, reservoirs, dikes, levees, and floodwalls; channel alterations; and high flow diversions and spillways. To compare these strategies, we need to be able to estimate their cost and benefit (in terms of reduced flood damage). This requires hydrological models to determine effect of a given mitigation strategy on water levels and risk assessments that include probabilities of different kinds of weather events and of damage from different water levels.
Hydrological models combine information on rainfall, soil moisture, seasonality, river levels prior to a rain event, elevation, watershed properties and land cover (natural and built environment) to produce flood inundation maps. Mathematical sciences can enhance hydrological models by providing better methods of calibration, improved models for land cover and soil types, analysis of the effect of channel geometry and flow speed, and more precise handling of uncertainty. Risk assessments include estimates of likelihood of weather events (amount and duration of rain, season, soil conditions, etc.) and prediction of related consequences. These may include loss of life, business, personal property, and the psychological impact of repeated flooding events. Different consequences must be "weighed" differently. We need to determine the extent to which we can rigorously combine consequences, which depends on the nature of the data. Methods used by EPA and the World Health Organization in their risk analyses are relevant, as is the theory of measurement.
Monitoring and Predicting Natural Disasters: Early warning can greatly reduce damage from an event. We will review the state of the art in prediction of flood levels, hurricanes and their landfall locations, tsunamis, heat waves, etc. We will consider the use of novel tools for surveillance, such as methods of information theory in disease surveillance; statistical methods of "syndromic surveillance" in public health events; sub-cluster statistics to give early warning of earthquakes; and spectral analysis of time series data to predict extreme events.