Natural disasters around the world claim tens of thousands of lives per year and cause billions of dollars in damage. Current technology enables some types of natural disasters to be predicted hours or even days before their occurrence. Yet, it remains challenging to disseminate this information to the public in a timely manner, particularly in developing countries, where people may have limited access to communication channels. To provide insight into this challenge, we develop a mathematical model to describe the spread of information within a population through direct interactions between informed individuals (“spreaders”) and uninformed individuals (“ignorants”). The model is adapted from the well-known Susceptible-Infected model from the domain of epidemiology. We assume that the government facilitates the spread of information by actively recruiting new spreaders from the population. We formulate an optimal control problem in which the goal is to inform a predefined proportion of the population regarding an upcoming natural disaster, while minimizing the amount of time required to spread the information and the costs associated with recruitment efforts. We characterize the optimal policies under different conditions. All optimal policies entail either recruiting the maximum possible number of spreaders per time period, recruiting no one, or some combination of the two. The model is applied to a case study of a dust storm that hit the city of Agra in India in May 2018.
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© 2019 Elsevier Ltd
- Disaster operations management
- Dynamic systems
- Natural disasters
- Optimal control
- Pontryagin maximum principle