The Mathematics of Infectious Diseases
SIAM Review
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Infectious disease outbreaks, caused by nature or bioterrorism, are unfortunately very real threats to the general population. Planning an effective response to an infectious disease outbreak requires a coordinated effort in multiple locations to best allocate the limited resources. This decision problem is further complicated by the non-linear nature of disease propagation and the fact that outbreaks can jump urban, even national, boundaries. In this work we present a multi-city resource allocation model to distribute a limited amount of vaccine in order to minimize the total number of fatalities due to a smallpox outbreak. The model decides the amount of limited supplies to deliver and which infection control measure (isolation, ring, or mass vaccination) to use in each location in order to decrease the number of fatalities. The proposed model approximates the disease propagation dynamics in order to represent the problem as a mixed integer programming problem. Furthermore we develop an efficient heuristic to solve the resulting large scale mixed integer programming problem. Our results analyze the quality of the approximate disease propagation model and the efficiency of the heuristic algorithm. We also conduct a case study applying the multi-city model in planning an emergency response to a hypothetical national smallpox outbreak, which shows the possibility of saving a significant number of lives compared with a prorated allocation policy.