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Finding a sensible balance for natural hazard mitigation with mathematical models
Date:4/30/2013

incidence and increases with time. Hence, the authors incorporate both these scenarios using the general probability model of drawing balls from an urn. If an urn contains balls that are labeled "E" for event and "N" for no event, each year is like drawing a ball. "If after drawing a ball, we replace it, the probability of an event stays constant. Thus an event is never 'overdue' because one has not happened recently, and the fact that one happened recently does not make another less likely," explains Stein. "In contrast, we can add E-balls after a draw when an event does not occur, and remove E-balls when an event occurs. This makes the probability of an event increase with time until one happens, after which it decreases and then grows again."

Since the likelihood of future earthquakes depends on strain accumulation at plate boundaries, the model incorporates parameters for how fast strain accumulates between quake incidences, and strain release that happens during earthquakes.

The authors select the optimal mitigation strategy by using a general stochastic model, which is a method used to estimate the probability of outcomes in different situations under constrained data. They minimize the expected present value of damage, the costs of mitigation, and the risk premium, which reflects the variance, or inconsistency, of the hazard. The optimal mitigation is the bottom of a U-shaped curve summing up the cost of mitigation and expected losses, a sensible balance.

To determine the advantages and pitfalls of rebuilding after such disasters, the authors present a deterministic model. Here, outcomes are precisely determined by taking into account relationships between states and events. The authors use this model to determine if Japan should invest in nuclear power plant construction given the Fukushima Daiichi nuclear reactor meltdown during the 2011 tsunami. Taking into account the financial and societal benefits of reactors, and balancing
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Contact: Karthika Muthukumaraswamy
karthika@siam.org
267-350-6383
Society for Industrial and Applied Mathematics
Source:Eurekalert

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