Fuel shortages during hurricanes: Epidemiological modeling and optimal control

Hurricanes are powerful agents of destruction with significant socioeconomic impacts. A persistent problem due to the large-scale evacuations during hurricanes in the southeastern United States is the fuel shortages during the evacuation. Computational models can aid in emergency preparedness and help mitigate the impacts of hurricanes. In this paper, we model the hurricane fuel shortages using the SIR epidemic model. We utilize the crowd-sourced data corresponding to Hurricane Irma and Florence to parametrize the model. An estimation technique based on Unscented Kalman filter (UKF) is employed to evaluate the SIR dynamic parameters. Finally, an optimal control approach for refueling based on a vaccination analogue is presented to effectively reduce the fuel shortages under a resource constraint. We find the basic reproduction number corresponding to fuel shortages in Miami during Hurricane Irma to be 3.98. Using the control model we estimated the level of intervention needed to mitigate the fuel-shortage epidemic. For example, our results indicate that for Naples- Fort Myers affected by Hurricane Irma, a per capita refueling rate of 0.1 for 2.2 days would have reduced the peak fuel shortage from 55% to 48% and a refueling rate of 0.75 for half a day before landfall would have reduced to 37%.