Dynamic resource allocation in disaster response: tradeoffs in wildfire suppression

Birth-death-suppression Markov process and wildfires

Birth and death Markov processes can model stochastic physical systems from percolation to disease spread and, in particular, wildfires. We introduce and analyze a birth-death-suppression Markov process as a model of controlled culling of an abstract, dynamic population. Using analytic techniques, we characterize the probabilities and timescales of outcomes like absorption at zero (extinguishment) and the probability of the cumulative population (burned area) reaching a given size. The latter requires control over the embedded Markov chain: this discrete process is solved using the Pollazcek orthogonal polynomials, a deformation of the Gegenbauer/ultraspherical polynomials. This allows analysis of processes with bounded cumulative population, corresponding to finite burnable substrate in the wildfire interpretation, with probabilities represented as spectral integrals. This technology is developed to lay the foundations for a dynamic decision support framework. We devise real-time risk metrics and suggest future directions for determining optimal suppression strategies, including multievent resource allocation problems and potential applications for reinforcement learning.

A data-driven analysis and optimization of the impact of prescribed fire programs on wildfire risk in different regions of the USA

In the current century, wildfires have shown an increasing trend, causing a huge amount of direct and indirect losses in society. Different methods and efforts have been employed to reduce the frequency and intensity of the damages, one of which is implementing prescribed fires. Previous works have established that prescribed fires are effective at reducing the damage caused by wildfires. However, the actual impact of prescribed fire programs is dependent on factors such as where and when prescribed fires are conducted. In this paper, we propose a novel data-driven model studying the impact of prescribed fire as a mitigation technique for wildfires to minimize the total costs and losses. This is applied to states in the USA to perform a comparative analysis of the impact of prescribed fires from 2003 to 2017 and to identify the optimal scale of the impactful prescribed fire programs using least-cost optimization. The fifty US states are classified into categories based on impact and risk levels. Measures that could be taken to improve different prescribed fire programs are discussed. Our results show that California and Oregon are the only severe-risk US states to conduct prescribed fire programs that are impactful at reducing wildfire risks, while other southeastern states such as Florida maintain fire-healthy ecosystems with very extensive prescribed fire programs. Our study suggests that states that have impactful prescribed fire programs (like California) should increase their scale of operation, while states that burn prescribed fires with no impact (like Nevada) should change the way prescribed burning is planned and conducted.

Modeling the Cost Effectiveness of Fire Protection Resource Allocation in the United States: Models and a 1980-2014 Case Study

The estimated cost of fire in the United States is about $329 billion a year, yet there are gaps in the literature to measure the effectiveness of investment and to allocate resources optimally in fire protection. This article fills these gaps by creating data-driven empirical and theoretical models to study the effectiveness of nationwide fire protection investment in reducing economic and human losses. The regression between investment and loss vulnerability shows high R² values (≈0.93). This article also contributes to the literature by modeling strategic (national-level or state-level) resource allocation (RA) for fire protection with equity-efficiency trade-off considerations, while existing literature focuses on operational-level RA. This model and its numerical analyses provide techniques and insights to aid the strategic decision-making process. The results from this model are used to calculate fire risk scores for various geographic regions, which can be used as an indicator of fire risk. A case study of federal fire grant allocation is used to validate and show the utility of the optimal RA model. The results also identify potential underinvestment and overinvestment in fire protection in certain regions. This article presents scenarios in which the model presented outperforms the existing RA scheme, when compared in terms of the correlation of resources allocated with actual number of fire incidents. This article provides some novel insights to policymakers and analysts in fire protection and safety that would help in mitigating economic costs and saving lives.

Modeling initial attack success of wildfire suppression in Catalonia, Spain

In southern European regions, the few fires that escape initial attack (IA) account for most of the burned area. Nonetheless, limited effort has been conducted to develop spatiotemporal models aiming at improving pre-positioning and deployment of fire-fighting brigades on the first dispatch. To this end, we calibrated a model to assess the probability of containment of fire by IA in Catalonia (northeastern Spain). The model was trained using machine learning algorithms from georeferenced historical fire ignition locations, fire response and weather conditions. Our results indicated that early detection, ground accessibility, and aerial support governed the broad spatial pattern of fire containment probability, with strong gradients that ranged from lowest chances of containment in northwestern mountains to highest in the coastal belt. In turn, weather conditions and fire simultaneity were crucial to explain the differences during wildfire season. We found that fires igniting above the 85th percentile of temperature and wind speed, during simultaneous fire episodes (n > 10), and 12.5 km away from the nearest fire station will probably escape IA, and grow into large events. These hazardous fire danger conditions were met 13 days per year on average during the period 1998-2015, with 5 fire simultaneous episodes escaping IA that burned 1546 ha in total. Results were provided as a set of high-resolution raster grids (100 m), which replicated the most typical weather and fire occurrence scenarios that first responders are likely to face during the wildfire season. This study reveals existing limitations in the dominant fire exclusion policy of Mediterranean areas and advocates for a comprehensive long-term wildfire management solution. Our model may help inform science-based decision-making on IA and general fire response planning in the study area.

Optimizing Real-Time Vaccine Allocation in a Stochastic SIR Model

Real-time vaccination following an outbreak can effectively mitigate the damage caused by an infectious disease. However, in many cases, available resources are insufficient to vaccinate the entire at-risk population, logistics result in delayed vaccine deployment, and the interaction between members of different cities facilitates a wide spatial spread of infection. Limited vaccine, time delays, and interaction (or coupling) of cities lead to tradeoffs that impact the overall magnitude of the epidemic. These tradeoffs mandate investigation of optimal strategies that minimize the severity of the epidemic by prioritizing allocation of vaccine to specific subpopulations. We use an SIR model to describe the disease dynamics of an epidemic which breaks out in one city and spreads to another. We solve a master equation to determine the resulting probability distribution of the final epidemic size. We then identify tradeoffs between vaccine, time delay, and coupling, and we determine the optimal vaccination protocols resulting from these tradeoffs.

Optimal vaccination in a stochastic epidemic model of two non-interacting populations

Developing robust, quantitative methods to optimize resource allocations in response to epidemics has the potential to save lives and minimize health care costs. In this paper, we develop and apply a computationally efficient algorithm that enables us to calculate the complete probability distribution for the final epidemic size in a stochastic Susceptible-Infected-Recovered (SIR) model. Based on these results, we determine the optimal allocations of a limited quantity of vaccine between two non-interacting populations. We compare the stochastic solution to results obtained for the traditional, deterministic SIR model. For intermediate quantities of vaccine, the deterministic model is a poor estimate of the optimal strategy for the more realistic, stochastic case.

Modeling wildfire incident complexity dynamics

Wildfire management in the United States and elsewhere is challenged by substantial uncertainty regarding the location and timing of fire events, the socioeconomic and ecological consequences of these events, and the costs of suppression. Escalating U.S. Forest Service suppression expenditures is of particular concern at a time of fiscal austerity as swelling fire management budgets lead to decreases for non-fire programs, and as the likelihood of disruptive within-season borrowing potentially increases. Thus there is a strong interest in better understanding factors influencing suppression decisions and in turn their influence on suppression costs. As a step in that direction, this paper presents a probabilistic analysis of geographic and temporal variation in incident management team response to wildfires. The specific focus is incident complexity dynamics through time for fires managed by the U.S. Forest Service. The modeling framework is based on the recognition that large wildfire management entails recurrent decisions across time in response to changing conditions, which can be represented as a stochastic dynamic system. Daily incident complexity dynamics are modeled according to a first-order Markov chain, with containment represented as an absorbing state. A statistically significant difference in complexity dynamics between Forest Service Regions is demonstrated. Incident complexity probability transition matrices and expected times until containment are presented at national and regional levels. Results of this analysis can help improve understanding of geographic variation in incident management and associated cost structures, and can be incorporated into future analyses examining the economic efficiency of wildfire management.